Cambridge IGCSE® & 0 Level Complete Physics Fourth Edition Stephen Pople Anna Harris Naseemunissa Azam Elliot Sarkodie-Addo Helen Roff OXFORD OXFORD \.'NTVBRSITY PRESS (,ff;\l ( l.1JYJll1on ~ln: l O~onl OXl 601'. lJnltt'd Kingdom Oxlunl lh11\·1•"1 Pn", 1, .. tlr11.u111w•111 c>i lh\' l1'111-.,-n.1ry or O\lun1 II furth,•~ [ht' ll111\'t•l'\1I)..,. UlJJt'tll\'f' uf f').( >Jk'Otl' bi rl'".l".lh ll -.<ho t.mlup. ;md Nlui: ¥Ion by publblalng wurlctwklc. 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Pll~o library: p272l: 81}'.lll It C huty Alt'X,10C lt'r l'htAOf.l~phv/Arct c photo, p:Z72b. ~Wit~ \locli.:phot~ p:Z7.it L>orU nr. Kmd('r.lcy/l nc,/~ii.'ncc l'hoto lJbr.uy. p.l? Jb: Roo1.1n K1ucia11 ~h11UtT'\lo1 ._ p:Z74: ~ 1,•111; \' Pholo I al>rAI) , p275l Roy ..1 A<ill'01.--n11c ;\l ~ K IV/!.C' ac•aw i• PIMIIO I ihr.uy p:Z7"ih. ,A.\A. p277: P,•tN \ll'ULc\ Ol'UCl" Photo LihrM)-: p278 & p279: 1\-ler GoukV<XJP AltWo ct.: by: GrN'oG ll' l'Ublbhlug ~rvt f , . Q.B~ l.L'.mllog t.i IV I ISi~ l'l. l'N'n DlMlr en ('(1111 ¥"I, ori,Tf.111 ,•• •111-f', 41' lli~ l••IL. Au nal6,i•~ ~Ul l~ h' (llllNI lo thf' p1hlhl1"r. "dl1il't41J(1)l °' . OUI rnal n-pm.lllf'\"CI 1n rnuat~ U OICJn• l, rJ\rO 11\·ou an: tudying ph, ic~ forCJmbridge JGC E >, then lhi book i de\igned for\ ou. IC cxplai ns the concepts that you will meet, and should help \'OU \\ il h \'our practical work. It i mo!'lth \\Titten in double-page uni~ which we htl\e a lied !ipre ads. Th~c are group--d into sections. Sectio ns I to J 1 The main areas or ph) ic arc covered here. t the end of each ol thi..: e cction there i a 1-c,i ion un1n1at') g iving the main topic!-. covered in each spread. His tory o f key ideas ection 12 describe ' how scicnti t have devdoped 1heir unden,ttmding or phy~i.cs on:1· the \'ean,. Practical physics ection 13 te11 )OU how to p]an and ca1T)' out c,pcriments and interpret th,. 1-c uh . It include uggc lion for invc tigations, and guidance on taking prnctical te t~ . l\1athematic for physics ection 14 un1mmi:1~ the mnthcnialical kill you wilJ need \\hen stud\·ing ph)sics tor Cambridge IG E. Examinatio n questio ns The1-e are practice examination questions at the end ot each ection (1 to 11 ). Jn addition, ·ction 15 conlain a collection ol ome altetnatiYcto-practical que tion . Reference section ection 16 incJude e ential equation , unit of mea urement, ircuit )mhols, answers to questions, and an index. s Core s yllabus content Supplement syllabus content 11you ttrc following the Con..·~) llabu:,; contl·nt.) ou can ignun.- ..my matc1ial with a rc<l Ii nc hl·sidt· it. For thb, you n-..·cd all 1h-..· ma1crial on the while pages, indu<ling tht.• supplement matt·1ial markL-d ,, ith a red line. The..• Enhanced Online Book supports thb student book h • olTc..•ring hii!h-quality digital resources that help lo hui]d scientific an<l l'xamination skills in prl.'par~uion fur thl' high-slakes !GCSE assessml.'nl. H you purchasca1:ccss to the digital cou1~c.~c>U will find a \\l.'ahh ofac.Jdi1ional rl.'soun:c..•s 10 hdp)OU with )O\ff stu<.Hc., ;m<l n.:\·ision: • A \\ork...,fu:l.'t anc.l intcracti\t.' quiz frn·L'\L'I)' unil • On Your Mark:-, activitic to hdp )<>U ~chic,c )OUI" ~st • Glossary quizzes to consolid:ne ,·ow· und..:1 . landing of scientific 1tcrmino]ogy • Full prac tkc papc1'.S \\ it h mark schemes Each pe~on ha their own way of working, hul the lollo,, ing tip might help you to gel the most from 1his book: • U e the content · page - thi will pro\'ide infonnation on large topic • u~e lhe index - thi wiJI ollow you to u~e a single woa-d to dkect vou to page \\ here you can find out more. • Use the que~tions - thi · is the be t way of checking,, hether you ha\'e le~u-ned nnd understood Lhe n1aLe1ial on ~jch spread. Oucslions arc to be lound on mosl units and wiLhin or at the end of each seccion. Harder que ·lion are identified by the blue circle. tephen Pople iii • \Vatch for this~, mbol, bclo,, and throughout the book. It indical<.~ spreads or parts of spn:a<ls that ha\'c been included lo pro\'ide cxlen~ion material to set phy~ics in a broader context. For inionnation about the link bct\\'ccn ·cc page vii- x. Syllabus and spreads 0 1.1 1.2 1.3 1.4 1.5 1.6 0 2.1 2.2 2.3 2.4 2.5 2.,6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 0 3.1 3.2 3.3 3.4 3.5 1V 3.6 3.7 3.8 12 14 16 18 20 22 24 Forces and motion Speed, velocity, and acceleration Motion graphs Recording motion Free fall More motion graphs Forces in balance Force, mass, and acceleration Friction Force, weight, and gravity Action and reaction• Momentum (1) Momentum (2) More about vectors Moving in circles Check-up 28 30 32 34 36 38 40 42 44 46 48 so 52 54 56 Forces and pressure Forces and turning effects Centre of gravity More about moments Stretching and compressing Pressure and the \llnbu , VII Measurements and units Numbers and units A system of units Measuring Length and time Volume and density Measuring volume and density More about mass and density Check-up prcad 60 62 64 66 68 0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 Pressure in liquids Pressure from the air• Gas pressure and volume Check-up 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 74 76 Forces and energy Work and energy Energy transfers Calculating PE and KE Efficiency and power Energy for electricity (1) Energy for electricity (2) Energy resources How the world gets its energy Check-up C, 70 72 8o 82 84 86 88 go 92 94 96 Thermal effects Moving particles Temperature Expanding solids and liquids Heating gases Thermal conduction Convection Thermal radiation Liquids and vapours SpecUic heat capacity Latent heat 100 102 Check-up 120 104 106 108 110 112 114 116 118 G 6.1 6.2 6.3 6.4 6.5 6.6 0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 0 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.12 8.13 0 Waves and sounds Transverse and longitudinal waves Wave effects Sound waves Speed of sound and echoes Characteristics of sound waves Ultrasound 124 Check-up 136 126 128 130 132 134 Rays and waves Light rays and waves Reflection in plane mirrors (1) Reflection in plane mirrors (2) Refraction of light 140 Total internal reflection Refraction calculations 148 Lenses (1) Lenses (2) 152 More lenses in action Electromagnetic waves (1) 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 9.12 142 144 146 Eli) Magnets and currents Magnets Magnetic fields Magnetic effect of a current Electromagnets Magnetic force on a current Electrtc motors Electromagnetic induction More about induced currents Generators 198 200 202 204 206 208 210 212 214 Coils and transformers (1) Coils and transformers (2) 216 Power across the country Check-up 220 218 222 Atoms and radioactivity 150 154 Electromagnetic waves (2) Sending signals 156 158 160 162 Check-up 164 Electricity 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 10.10 Inside atoms Nuclear radiation (1) Nuclear radiation (2) Radioactive decay (1) Radioactive decay (2) Nuclear energy Fusion future Using radf oactivity Atoms and particles (1) Atoms and particles (2)• Check-up Electric charge (1) Electric charge (2) Electric fields Current in a simple circuit Potential difference Resistance (1) Resistance (2) 168 More about resistance factors Series and parallel circuits (1) Series and parallel circuits (2) More on components Electrical energy and power Living with electricity Check-up 182 170 172 174 176 178 180 184 186 188 190 e 11.1 11.2 11.3 11.4 11.5 11.6 11.7 226 228 230 232 234 236 238 240 242 244 246 The Earth in space Sun, Earth, and Moon The Solar System (1) The Solar System (2) Objects in orbit Sun, stars, and galaxies (1) Sun, stars, and galaxies (2) The expanding Universe Check•UP 250 252 254 256 258 260 262 264 192 194 V e 12.1 12.2 12.3 12.4 G) 13.1 13.2 13.3 13.4 13.5 13.6 13.7 0 History of key ideas Force, motion, and energy• Rays, waves, and particles• Magnetism and electricityThe Earth and beyond• Key developments in physics 268 '1:10 272 274 x,6 The essential mathematics El) 278 280 282 284 285 286 290 291 0 294 !GCSE practice questions Multichoice questions (Core) Multichoice questions (Extended) IGCSE theory questions IGCSE alternative-to-practical questions Practical physics Working safely Planning and preparing Measuring and recording Dealing with data Evaluating and improving Some experimental investigations Taking a practical test Check-up Mathematics for physics 298 300 302 312 Reference Useful equations Units and elements Electrical symbols and codes Answers Index 316 318 319 320 333 www.oxfordsecondary.com/complete-igcse-science Vl Below, is an outline ot the Cambridge lGC Es~ llabu~ as il tood at the time of puhJication, along ,,ith detail · of where each topic i~ covered in the hook. Before con tructing a teac hing or rcvi ion progran1mc, pica c c heck with the late t ver ion of the s, llabus/~pccificat ion fo1· any changes. IGCSE syllabus section 1 Motion, Forces and Energy 1. 1 Physical quantities and measurement techniques 1.2 Motion 1.3 Mass and Weight 1.4 Dens,ty - Spread 1.3 2.1 2.13 2.1 2.2 2.3 2.4 2.S 2.6 1.6 2.9 1.4 1.5 1.6 2.6 2.7 2.8 1.S Fofces 2.14 3.1 3.2 3.4 1.6 ~.'iomemum 1.7 Energy, Work and Power 1.8 Pressure 2 2.11 2.12 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 3.S 3.6 Thermal Physks 3.8 2.1 Kinetic particle model of matter S.1 S.2 5.4 The<rnal pcoperties and 1empera1ure S.2 5.3 5.4 2.2 S.8 S.9 S.10 Transfer of thermal energy 2.3 s.s 5.6 S.7 vii ~ IGCSE syllabus section 3 waves General propeuies of waves 3.1 3.2 Ught Spread = 6.1 6.2 7.1 7.2 7.3 7.4 7.5 7.7 Electromagnetic Spectrum 3.3 Souid 3.4 7.8 7.9 7.12 7.10 7.11 7.12 6.1 6.3 6.4 6.5 6.6 4 4.1 Electricity and Magnetism Simple phenomena of magnetism Electrical quantities 4.2 Electric circuits 43 4.4 4.S viii Electrical safety Elect1omagnetic effects 9.1 9.2 8.1 8.2 8.3 8.4 8.S 8.6 8.7 8.8 8.11 8.12 8.13 9.9 8.4 8.5 8.6 8.7 8.9 8.10 8.11 8.13 9.3 9.4 9.S 9.6 9.7 9.8 9.9 9.10 9.11 9.12 10.2 IGCSE syllabus section 5 Nudear physics The nuclear model of the atom s.1 Radioacli\licy 5.2 6 -- Space physics Eanh and the Soiar System 6.1 Spread 10.1 10.2 10.4 10.6 10.7 10.9 10.2 10.3 10.4 10.S 10.8 11. 1 11.2 11.3 11.4 11.5 Stars and the unive,se 6.2 11. 1 11.S 11.6 11. 7 Assessment for IGCSE The ICC E exam inatio n will induck questions that Lesl you in lh1~c diITcn:nt ,,·a, s. These arc called A scssmcnt Objec ti,cs (AO for short). Ho\\ these difkl'ent AOs are te ted in the c:..amination i · c,pl~,ined in the table below: Assessment Objective What the syllabus calls What this means in the examination these objectives ~--~~---------- A01 Knor.,'1edge wi tn understanding Questions which mainly test your recall (and unde.-standing) of what you ha\'e learned. About 50% of the marks in the examination are fOJ AOl. A02 Handling infOJmation and prob· lem solvmg A03 Experimental sblls and investi· gations Using what you have learned in unfamiliar situations. These questions often ask )'OU to exarrune data in graphs oc tables, or to carry out cakulations. About 30% of the ma s are for A02. These are tested on the Practical Paper or the Alternative to Practical (20% of the total marks). However. the skills you develop in practising for these papers may be valuable in handling questions on the theory papers. The cn<l-of-M~ction qucMions in this book include c'\'.amplcs of those testing AO I , A02 an<l A03. Your LL'achcr will help you lo attempt quC!,lion~ of all t~ pc . Yo u can cc from the abo\'c table that it will no t be enough to try onl) 'recall' QUL~tion . All candidate~ take lhrcc papers. The niakc-up o f eac h m, c m cnt progra mnic i hown below: Core assessment Quc ti on arc ba ed on Core content. Paper 1: Multiple Choice (Core), 45 mins Paper 3: Theory (Core), I hour 15 mins There are a total of 40 marts available, worth There are a total of 80 marh avaiable, worth 50% of your IGCSE. The paper consists of compu~ory short-answer and suuctured questions. 30% of yout iGCSE. The paper consists of multiple-choke questions. Extended assessment Questions arc based on the Core and upplemcnl s ubjec t content. Paper 2. Multiple Cno:ce (Ell.tended). 45 mIns Pape, 4. lheory (b:tended). I hour 1~ m,ns There are a total of 40 marls available, worth 30% of your IGCSE. The paper consists of multiple-choice questions. There are a total of 80 marls avaiable, worth 50% of your IGCSE. The paper consists of compu~ory shon-aM•Ner and structured questions. Practical assessment Lu dents take ei the,- Paper - or Paper 6. Paper 5: Practical Tests. 1 hour 15 mins Paper ,6: Ahemative to Practical, I hoUJ 15 mins There are a total of 40 marls available, worth 20% of your IGCSE. You will be required 10 do e:q:,eriments in a lab as part of the assessment. lhere are a total of 40 marks avaiable, worth 20% of your IGCSE. You v.;o NOT be required to do experments in a lab as part of the assessment. X An a~tronomical clock in Prague, in the C.1.ech Republic. A ,veil a · giving the tin1c, the clock al ·o sho\\ the position ~ of the Sun and Moon relat i\'e to the con tellation~ of the Lodiac. Until about fifty year ago. 'Cienti ·t had to reh on n1~chanical locks, ~uch a , the on above, to n1ea ur tit11e. Today, they have accc s to ato1nic clock ,vho ' c tin1ekeeping varie ~ by less than a s cond in a n1illion \Cal . chapt~r 1 11 - - - - - - - - - - - - - 10 m - - - - - - - - - - - -/ \ ourr ber unit (m 1s the ~yrnbol for metre) \Vhcn )OU make a 1ncasurcmcnt, you mighr gd a n..~ull like the one abo,c: a di~tancc of 10 m. The complete mca~urcmcnt is called a physical quantit . 1L i n1adc up o f two part ·: a number and a w1it. 0 Advanced units 5 m/s 1s a space-saving way of writing 5 ~ . m 1 But 5 sequals S ms. Also, { can be wntten as s- 1• So the speed can be written as S ms- 1• This method of showing units is mo,e common in advanced work. 10 m really mean · 10 x 111 (ten time · metre). just a in algebra, 1Q\· n1cans 10 x x (ten tim~x). You can treat them ju t like a , ,nbol in an algebraic equation. Thi is important when combining unit . Combining units In l he diagram abon?, the girl cycle!-. 10 met n!!-. in 2 s. So she l r..1.vcls 5 mctn.:s c,·c~ second. Her .\p.!ed L') S metres ~r second. To work out the spet.·d, you divide the <liMancc Lr'Jvclkd by Lhc time taken, like Lhis: spcl.'<-1 : 1O m ( · is the s~ rnbol (or econd) 2s A · m and · can be treated as algebraic ·ymbols: peed = .!Q , .m- Sm . ,o.,. save space,- -n,- . u ·ua IIy wnttcn . / as - ms. s 1s o m/s is Lhc unic of spcc<l. 0 Tables and graphs You mc1y see table headings or graph axes labelled hke this: cfiSt aoce or distance/m m That is because the values shown are just numbers, Vv'ithout units So If distance - 1O m Then distance _ 10 m 12 Rights and wrongs Thi equation i correct: Thi equation b incorn:ct: pced - 10 m _ 5 m/ 2s speed : 10 2 It h, incorr~ct because th e m and equals - , and noL - m/s. - m/ h,wl.! been left out. I 0 divided hy 2 t,;crly ~peaking, units should be indu<lcd at all stages of a calculation, nol just al the end. However, in thi~ book, the ·incorn..-ct' t~ pc of cquatjon "iU somL•Cimes be used so Lhat )OU can follow Lhe arithmetic without unit \\hich make the calculation look more complicated. MEASUREME TS AND U ITS Bigger and smaUler You can mak .. a unit bigger or mallcr bv putting an e-..:tra vmbol, caJlcd a prefh, in front. (Below, \ \' tand for watt, a unit of powc1: ) prefix meaning G (919a) 1000000000 M (mega) 1 000000 k (kao) d (dec1) (103) -1 (10 100 1 1000 1 p (rrucro) 1000000 1 n (nano) Powers of 10 GW (gigawatt) 1000 - 10 X 10 X 10 - 103 -1 0 X 10 0.1 -10 - 10 I 0.01 1 1 - 100 - 10 2 - 10 MW (megawatt) dm (decimetre) 1000000000 (10 2) cm (centimetre) (10 3) mm (rrnllimetre) (10 6> µW (micrO\vatt) (10 9 nm (nanometre) ) l 1 103 1 - 10-3 'm1lh' means 'thousandth', not ·m1lhonth' • You would not normally be tested on micro, nano or g1ga 1n d Cambridge IGCSE exarrunat,on (see also yellow pa, el at the start of the next spread. 1.2) Scientific notation An - 10 1 km (kilometre) 1 ) 2 100 0.001 - 1000 - 1 m (milli) (106) 1000 10 c (ceot1) (109) example ada~ says that the population of Jee land i~ this: 320000 There ill'\: two probh:ms "ith gi\ing the number in this form . \\'riling lots of LCl'O i n't \Cl"_\ con,enient. Al o, )OU don't knO\\ \\hich Lero arc accurate. Mo l arc onh there to ho\\ ,ou that it i a ix-figure number: Thc~c prob]cn1~ arc avoided if t lr" nu mbcr i \\Ti Hen u ing powc, of ten: 3.2x 10i; decimal fraction scientific notation (10~::; t 0x I0xl0x l 0x 10 = 100000) r 3.20 X rectangle: area - length x width. If a rectangle measures x m by 2 m, calculate its area, and include tt e units in your calculation. 5 100 5 0 .005 1000 X 102 5 X 10- 1 10 0 .05 l Or; 1 How many grams are there in 1 kilogram? 2 How many millimetres are there in l metre? 3 How many microseconds are there in 1 second? 4 This equation is used to work out the area of a 5 0 .5 Kun1be1 wriuen u ing powcl'~ of ten arc in cicntific notation or standard form . The cxamp1c!'I on the ,;ght arc to one ~ignificant figure. ® 5 500 '3.2 x I Or;, tells~ ou that the figurl.!S 3 an<l 2 are in1portanl. The number i being given to 1wo ~igni{icmll figure:... If the population \\Cl~ kno\\n rno1 ~ accuratch, to three ignificant figure , it might be \\rittc-n like d1i : 5 X 10 2 I 5 X 10 3 5 Write down the following in km: 2000 m 200 m 2 x 104 rn 6 Wnte dov\fn the following in s: S x 107µs 7 Using scientific notation. write down the following to two signifacant figures: 5000 ms 1500 m 1500000 m 0.15 m 0.015 m Related topics: SI units 1.2: speed 2 .1; sign•flcant figures 13.3 13 Mass Length oz lb A lme down the side of the kg 9 text means that the cwt material as only required for ~ Time cm s mile ft ton hour month da~ r(tn'\ km year ms Extended Level .. An asterisk 1nd cates extension material. proVlded to set physKs in a broader context. You v,ould not normally be tested oo this an a CA E !GCSE examination There are many different unils inducling those above. Bue in sc ientific work, life b much ca':)ic1· if C\'cryonc u c~ a common ') ·tcm ol units. SI units Mo ·t ' dcnti ts u ·c SI unit s (full name: u: y ·teme lnte1national d'Uniles). Thl" ba~ic l unib for inca ·udng mass, time, and length arc the kilogram, the econd, and the metre. Fro n1 th~c base unit come a whole range of unit for measuring \'Olumc, peed, fo1 e , ene1'S', and other quantitie . Other f base unit · include the amp~rc (for measuring electric current ) and the kch in ( for measuring tcmpcr~llure). Mass .& The mass of an object can be found using a bal ance hke this. The balance really detects the gravitational pull on the object on the pan, but the scale 1s marked to show the mass. Ma i a mclli>urc of the quantity of maucr in an object. ll h~ two cficc t • 11 object ar ~ attracted to the art h. The greater the n1a. of an object, the stronger i the a11h' gra\'itutional pull on it. • All obiects resisl being made to go lru,tcr, slower~ or in a different din: lion . The g rt!attc>r the mass, Lhc g l"\!aler the n.-si..,.lanc c lo changL' in motion. The I base unit of mas · is the k'ilogrnn1 ( ;ymbol kg). At one time, the !-.tanc.lard kilogram was a hloc k of platinum allo~ stored in Pad~. However. Lhcn: is now a more m.:curatc buL ,non: compli atcd dl:finition invoh ing an electromagnetic balance. Other unit baM:<l on the IJlogram arc ·ho\\ n below. mass com_pa rison ,with scientific base unit notation approximate size 1 tcrine lll - - - - - - - - - 1000 lg - - - 10, ►.g - - - - 1 kilov,•m (kg) - - - - - - - - 1 kg - - - - - - - - - l 9f~ ;g) - - - - i 9 - - - - 1 rtulgr.am (ffl9) - I i<oo 9 - - - 1 I ;o 9 - - 10, ~ ~ kg - - 10 bag of ~ugar ►-9 - - - - ~-0 - - - - ----~~--human hair 14 MEASUREME Time The second was originally The Iba c unit of time i the ccond ( \ n1bol ). Here at~ on1c shorter unit ba~cd on the ccond: l l milli~ccond ( m~) = l microsL-cond (µs) = I 000000 s - 10 6 ITS 0 defined as 60 x 6~ x 24 of a day, one dill being the - 10 's 1000 s TS AND U s l nanosecond (ns) - 1 000 000 000 s To keep Liml!, clocks and watches need somcLhing that beats at a stead~ rate. Some old dock.-.. used Lhe s\\ ing · of a pendulum. Modern digital \\~1tchc count the \'ibration · made b) a Liny quartz Cl') tal. Length The l ba.-;c unit of length is the metre ( ·ymbol m ). At one time, the ·tandard met,~ was the di tance bctwcc:n t\\o mark on a metal bar kept at the Office of \\'eight and Mca tu ... in Pari~. A mo1 .. accurate tandard i now u ed, ba c.'Ci on the pced of light, a c"plaincd on the right. time it takes the Earth to rotate once. But the Earth4s rotation is not quite constant. So, for accuracy, the second is now defined in terms of something that never changes: the frequency of an osdlatt00 which can occur in the nucleus of a caesium atom. 0 By definition. one metre is the distance travelled by light in a vacuum in 1 299 792 458 of a secood. There are la rger and smaller uniL~ of length based cm the metre: distance 1 lomtttt comparison w ith base unit 1 m) - - - - - I 0)() m - - - - - 10 1 metre (m) - - - - - - - , 1 milrr.ctre (lffll) - - - - - approximate si2e scientific notation m- - - m- - - - - - - - - - ----....,, .... _ '"r--~~--------~ ----------♦ 1O foo•ball o.tches ----- '!> EJ. . :. L.:. .'.:. .:. .; m- - - - - m- - - m - - - - - 10 m--- ....... mtW&J m - - - - - to-4m - - - 1 naromttre (Ml)- - - 1 ® 1 What is the SI unit of length? 2 What is the SI unit of mass? 3 What is the SI unit of time? 4 What do the following symbols stand for? g mg t µm ms 5 Write down the value of a 1564 mm in m b 1750 g in kg c 26 t in kg d 62 ~ in s e 3.65 x 104 gin ·g f 6 .16 x 10 7 mm in m 6 The 500 pages of a book have a mass of 2.50 kg. What is the ma~ of each page a in kg b in mg? 7 km pg µm t nm kg rn ms s mg ns µs g mrn Arrange the above units in three columns as below. The units in each column should be in order, with the largest at the top. mass time Related topics: numbers and units 1 .1~mass 2.7 15 Measuring length 0 20 30 40 50 60 70 80 90 100 110 120 no 140 mm Lc-ngth from a few mill metre up to a metre can be mea ured u ing a rule, n~ ~hown abo\'e. \ hen t1 ing the rule, the , cale :-.hould be placed right next to the ohje t bci ng mca~un:d. If thi~ i~ not po ~ihlc, calipers can he u:-,ed, a:-, sho\\n on lhc left. he calipcrs arc ~et so that their point:-, c:\m::tl) matc h 1he enc.ls of the ohjc<.:l. Then the~ arc moved across to a rule to make the measurement. E Lt!nglhs of sc\·crc1l mctn.""i can he nlcasun."<.I u~ing a tape with a :i,,calc on it. Acc:uratd, nw.._, · uring 1nall objl·Cts is mo1\..' difficult, but thct'-! arc wa)S around the problem. a,, for example, \OU wanted 10 find the thicknt: ~ ol a heet of A4 paper. l"sc a ruh:1- to mca~urc the 1hickncs~ of a -oo sheet pack: 49 mm Di, iding 49 n1m by 500 gi\ l.~ the thic:kne~~ of one sheet: 0.09 mm • If the rule cannot be placed next to the object being measured, calipers can be used. 0 Measuring Length with light Surveyors don't need a tape to mea5ure the dimensions of a room. They can ~e a laser tape measure instead. Despite its name, no tape is involved. The surveyor places the instrument against one wall, points it at the opposate wall, presses a button, and reads the distance on the display. There are various systems, but in one type, the instrument frres a pulse of laser light at the opposite wall, picks up the reflection, measures the time delay between the outgoing and returning pulses and uses this to calculate the distance. light travels at a speed dose to 300 000 000 metres p~r second. So. for example. if the pulse had to travel 30 metres out and back, it would take 100 nanoseconds. If this were the time measured, the display would show a distance of 15 metres. (In this example, the numbers have been simplified. Typically, the instrument is accurate to within 3 mm.) 16 MEASUREME TS AND U 0 Measuring time Tin1c interval o f man) ccond or minute ca n be n1ea ~ured u ing a topclock o r a stopwatch. Son1e in tn1mcnt ha\'C a n analogue displa~. wilh a needl e (' ha nd') m o\ ·ing ro und a ci1·cular ~calc. Other~ ha\'C a digital dis pla~. which s hows a numbe r. There an.: butto n~ fo r s ta r ling the timing, s to pping it, a nc..l n:~elling the im,trume nt to zero. \ ith a hand-opera ted topdo k or topwatch, making accurate ~econds or le- ) can be mca~uremcnt of hon tin1c intc1,al!- (a difficult. Thi i!-. bt.'Cau~ of the time it ta ke · vou to 1 "act whe n , ·ou have to pn,;.~._. the hulto n. Fortuna ld~. in some experiment""', then: is a ~imple wa~ o f overcoming the problem. Here i~ a n example: re,\ ngio support _ _ _ __ ITS Zero error You have to allow for this on many measuring instruments. For example, bathroom scales might give a reading of 46.2 kg when someone stands on them. but 0.1 g Vi/hen they step off and the expected reading is zero. In this case, the zero error is 0.1 . g and the cOC'rected measurement is 46.1 kg. A pendulum can be set up to investigate the time taken for a single swing. electromagnet ·o release ball !>tnng--------1 one complete swing simple pendulum bob--(sma!I m~~s) 0 ► Measuring the time t it takes for a steel ball to fall a distance h. The pcndulun1 above take about two econd to n1a ke o ne complete J,.wing. Pr odded the ~wings an: J,. m alJ, eve~ swing ta ke~ the sam e tim e. Thi~ time i ~ called its period. You can find it ac uratcl~ by m ca,uring the tinlc for 2- ~wing~. and th en di,·ic..ling the res ult b} 25. Fo1· example: Time rO J' 25 '\\ ing · h timer • ssecond l) o: time for 1 wing - · 5125 e ondi,. - 2.2 ccond~ Ano ther method o f impn>\·ing accurac, i~ to u.,c a utom a tic t iming, a, s ho wn in the ~xamplc o n the right. He~. the time La ken for a ~mall o bjecl to fall a short <lb La.nce i · being n1e~t..') Ut~d. The limer j~ staitcd a utom atically ,, hen the ball cut o ne Jight beam and ·topp..-d when it cut a nothet: ® 1 On the opposite page, there is a diagram of a rule. a What is the ,eading on its scale? b The rule has not be drawn to ,ts true s,ze. What is the length of the red line as printed? 2 A student measures the time taken for 20 swings of a pendulum. He finds that the tune taken in 46 seconds. a What trme does the pendulum take for one swmg? b How could t e student have found the time for one swing more accurately? hght ~ -~ I ba I ...J• sensor to stop timer 3 A student wants to find the thickness of one page of this book. a Explain how she might do this accurately. b Measure this book and then hod your own value for the thickness of one page. 4 a What ,s meant by zero ,error? b Grve an example of when you would have lo allow Related top1cs: units of tenglh and time 1.2 : timing a falling object 2.4 '°' it. 17 Volume The qunntity of space an object take · up i · called it volume. The l unit of ,·o]umc is the cubic me tre (m 3 ). Howe\'cr, thi~ i~ rather large tor evcr)da. work, ~o other units an~ often used for con,l:nicnce, a ho,, n in the diagram below: Cubk metre (m 3) Litre (1 or L) Cubic centimetre (cm 1) or millilitre (ml or ml) Note: the symbol I for Mre can be confused a ,...,th 1 (one). - 1000 cubic centimetres (c.m3> 1000 m1lhl1tres (ml) H>OO litres <I) 1 ~tie 1s the same vo ume as t <ub c 1 rubic ll'lClt(I (m ) ts 1e volume of a cube measur119 1 m 1 m x I m deometre (d m3) 1 cubic cent11T1etre (cm3) 1s the v01\Jme of a cube measur ng 1 cm . 1 cm It ~ the same vol 1me as 1 mBlihtre (ml) Density 1 lead heavier than ,,atcr? l\ot ncces ·aaily. It dcpcn~ on rhc voluml: oJ lead and water being compa1\.=-d. I loweYe1; lead i n1ore dense than water: it ha!-, more kilograms packed into e,·ery cubic metre. The dens ity of a material is cakulated like thi . ma-..-.. <.ll•ll~ll\' - - - - n>)umt.: In the case of ,,ater: a ma~s of I 000 kg of water has a \'Olumc ot I m 3 a ma~~ of 2000 kg of water has a volume of 2 n1' a mlli> ol 3000 kg of water htU> a \'olumc oi 3 n1', an<l o on. A The glowmg gas in the tail of sing any of Lhc c set~ of figu1·c in the above equation, the den ·ity o water\\ ork out to ~ I 000 kg/m 3• a comet stretches for millions of kilometres behind the comet's core. The density of the gas is less than a ilogram per cubic H m~~ are n1easured in gran,~ (g) and volume in cubic centimetre. (cm3 ), it i simple1· Lo calcula1c den iti~ in g/cm'. Con\·~rti ng to kg/m ~ is ea!-.): kilometre. The dtmsily of water is l g/cm ' . This simple \aluc is no accident. The kilogram ( l 000 g) was originaU) supposed to be the ma ·s of J 000 cn1 1 of 18 1 g/ m 3 = I 000 kgtin 3 MEASUREMENTS AND U walcr (pure, and at 4 °C). H O\\ t.:\'CC a \'Cl''\' lig ht ctTo r ,, a n1adc in lhc carh mca~ure mcnt, o thi i no lo nger ttM!d a~ a denni1io n o f lhc kilogram. density substance density substance air density granite expanded polystyrene 14 0.01 4 aluminium 1,vood (beech) 750 0.75 steel (stainless) 7800 7.8 petrol 800 0.80 copper 8900 8 .9 ice (0 °C) 920 0.92 lead 11400 n .4 polythene 950 0.95 mercury 13600 13.6 water (4 °C) 1000 1.0 gold 19300 19.3 concrete 2400 2.4 platinum 21 500 21 .S glass (varies) 2500 2.5 osmium 22600 22.6 2.7 ITS The densities of solids and liquids vary slightly with temperature. Most substances get a httle bigger when heated. lhe increase 1n volume reduces the density. lhe densities of gases can vary enormously depending on how compressed they are. The rare metal osmium is the densest substance found on Earth. If this book were made of osmium, it would weigh as much as a heavy suitcase. Density calculations T he cqualion linking density, mas~. and volume can be wrillcn in ~)mbols: Ill I' dcn_sity, 111 \I = mas.s. and V = \'olunlc Thi equation can be rcan~1gl-d lo give: Ill I' and Ill The:,c an: u ·dul if the den il~ b kno\\n , but the , olumc or rna · · i c alculated. On the 1igh t i a n1etho d o l finding all three equatio n . 10 be Emmpll.' u~ing dcn~itv da t~• from the t~,blc a bo,·c. cakukttc the nmss ol ~t.:"-•I having the s.unc , olumc as~400 kg of aluminium. Fin-it , calculate the \·olumc of - 400 kg o f alun1inium . l n this ca se, A Cover V in the triangle and p i s 2700 kglm ', m i s 5400 kg, a nd Vi ~ to be found. o: you can see what Vis equal to. It works form and /I as well. V = !E. P 5400 kg , ~ 2700 kg/m ' · - m · Thi i al o the vo lume o f th e tcel. Therefo re, fo r the tccl, p i 7800 kg/n11, \/ i~ 2 111 '. and 111 i to b ' found . So: m = Vp 7800 kg/m ' x 2 m' ~ I - 600 kg In the density equation, the symbol p is the Greek letter 'rho'. 0 So the mass of ~led is 15 600 kg. ® 1 How many cm3 are there in l m3 ? 2 How many cm 3 are there in 1 litre? 3 How many ml are there in l m3 ? 4 A tankful of liquid has a volume of 0.2 m3• What is the volume in a litres b cm3 c ml? 5 Aluminium has a density of 2700 kgtm 3. a What is the density in g/cm 3? b What is the mass of 20 cm 3 of aluminium? c What is the volume of 27 g of aluminium? Use the information in the table of densities at t~e top of the page to answer t e following: 6 What material, of mass 39 g. has a volume of 5 cm3? 7 What is the mass of air in a room measuring 5 m x 2 m x 3 m? 8 What is the volume of a stOJage tank which will hold 3200 kg of petrol? 9 What mass of lead has the same volume as 1600 kg of petrol? Related topics: pressure 1n liquids 3.6 19 <; 1000 cm>- - measuring cyt1nde, - - 1-- levEI Of'I sca1e g,...es volume . of hqutd .& tvteasuring the volume of a liquid c:; 1000 cml IOOOcnr . asuring volumP Liquid A \'olume of about a litre or ·o can be mca ·urcd u i ng a measuring cylinder. \ \'hen the liquid i._, poured into the cylinder, the le\ don the scale g ives the volume. 1o t mca::,uring cylinch:-1"' have 'Cale- · rnarkcd in millilitres (ml), or cubi centimctr~ (cm '). Regular solid Han object ha!> a simple hapc, it · volume can be calculated. For example: volume of a rectangular block length x width x height volume of a c~ tinder n X radius 2 X heig ht Irreg ular solid lf the s hape is 100 awkward for the \·olume to be calculated, the olid can bl" lowered into a parll~ filled mca udng cylinder a ho\\ n on the lclt. The ri e in level on the ,olume calc gh ·c the volume o f the ~olid. If the ~olid noaL,, it can be weig hl.!d down with a lump of metal. Thi.! total volume is found . The volun1c of the metal is n1casured in a separate experiment and then ·ubtrac ted lrom this total. .& Measurmg the volume of a small solid Using a displacement can lf the sol id is too big for a measuring cylinder, its \'Olun1c can be lound using a di~pla cmcnt can, shO\\ n below left. First. the can i~ filled up to the lc\'cl of 1hc spout (thi · is done b · o,·criilling it, and then waiting for the urplu water to run out) . Then the olid i lowl) lowered into the wate1: The olid i n ow taking up pace once occupied by the water - in other word~. it has di~placed it · own volume of water. The dis placed water i collected in a be~1ker and emptied into a mca~uring c..-ylin<lcr·. The displaccmcnl method, so the story goc , was disco\C1\:d by accident, b, A1 himcdc . You can find out how on the oppo itc page. Measuring dens ·ty The density of a material can be found by calculation, once thl.! volume and mass han! been measured. The ma~s of a ~mall solid or of a liquid can be mca-;urcd using a balance. Howcve1: in the case of a liquid, you must remember to allow for the ma of it~ co1uainl·1: -- .... .& Using a dispfacement can. Provided the can is filled to the spout at the start. the volume of water collected in the beaker 1s equal to the voJume of the object lowered into the can. 20 Here arc some r~adings from an experiment to find the density of a liquid: vol«Y".,...! of Liqt-tid t.'I. .~as1,o L,~ Ct:jlt~~r = ~ 00 c:,1.. ( A) == .~•Q.SS of '"""-a.;v.ri~ er;li ,-..der 0 ( B) w.nss of .~o.~.ot.v..g c~ti ,W.!r Vitt 1 LUli.tt.0. tv.. = r;w !3 (C) The refore: mas. of liquid - 560 g 2 ,,;o 240 g - 320 g 320 Therefore density of liquid = ma g - 0 g/cm 3 volume · 400 cn1 ' - · (C - B ) MEASUREME TS AND U ITS Checking the density of a t·quid* A q uick method of finding the den it\ ot a liquid it lo me a mall float called a hydrometer. There b an e'-an1plc on the right. It i~ bn~ on the idea tha t a Routing object floats higher up in a chmscr liquid. You can •·cad more abouL flo aling, ~inking, a nc.l thl' link \\ilh dcnsil\ in the n l!xt sprt!ad, 1.6 . The c.:alc on a h~ dromdel' non,1all) indicate the relmit-11 density (or ' ·pcci[k gra, it\ ') of the liquid: thar i th e den H, compar e<l \\1th wat er ( I 000 kg/m '). A reading of l.05 mean. tha l the d ~1i.s it, of the liquid i 10·0 kg/m 3• hydrometer De n ·ity check like this a re im port a nt in soml! production proces ·e~. For c xa mplt!, crt!am~ milk is !--.lightl, l~s dense Lhan skimmed milk, and s lrong beer is slighth le~~ d c nst.· tha n ,, eak beer. Archimedes and the crown Archimedes, a Greek mathemat.cian. lived in Syracuse (now 1n Sicily) around 250 BCE. He made important d1scovenes aboul levers and liquids. but 1s probabty best remembered for his clever solution to a problem set him by the King of Syracuse. The K1"9 had given his goldsmith some gold to make a crown. But when the aown was delivered, the King was suspicious. Perhaps the goldsmith had stolen some of the gold and mixed in cheaper silver instead. The King asked Archimedes to test the crown. Archimedes knew that the crown was the correct mass. He also knew that silver ""as less dense than gold. So a cro..,,m with silver in it \l\'Ould have a greater volume than it should have. But hO\v could he measure the volume? Stepping into his bath one day. so the story goes, Archimedes noticed the rise 1n water level. Here was the answer! He was so excited that he lept from his bath and ran naked through the streets, shouting "Eureka!", which means "I have found rt!". Later. Archimedes put the crown in a container of water and measured the rise in level. Then he did the same with an equal mass of pure gold. The rise m level was different. So the crown could not have been pure gold. ®- - - - - - - empty hquxi added stone added 148 I crown A aownB crown( mas~g 3750 3750 3750 volume/cm 3 357 194 31S 100 cm 3 cm _J density: gold 19 3 glcm3; sctver l 0 S glcm3 1 Use the information above to decide which crO"Nn 1s gold, which as salver, and which 1s a mixture. 2 Use the mformatton above to calculate: a the mass, volume, and density of the liquid b the mass, volume, and density of the stone. Related topics: \IOlume and density 1--4 21 Comparing masses Density essentials . mass density = volume 0 beam ► A simple beam balance The device above i~ called a beam balance. It is the si mplcst, and probably Lhl! okkst, wa) of l inding the mass of so,nething. You put the objec t in one pan, then add ~tandartl ma ·e · to the oLhcr pan until the beam balances in a level po ·ition. If , ou ha\'c to add 1.2 kg of tandard ma ·c , ~ in the diagran1, then , o u know that the object also ha a ma o f 1.2 kg. The balance i • reall\' compa,;ng weight · rather than ma~::.e ·. \r\'eig ht i::, the do\\nwarcl pull of gr.nily. The beam balances when the downward pull on one pan is equal lo the <lown\,ard pull on rhe other. However, ma."isc~ an be compared bccau c of the wa~ gr-j\ ity a CL"i on them. If the obj"-'Cl · in the two pan have the a mc weight , the) mu t also have the amc ma ~. .& A more modern type of balance. It detects the gravitational pull on the object on the pan, but gives its reading in units of mass. \r\'he n u ing a ha )ance like the one abo\'e, yo u might a \ ' that you we re 'weig hing' ·ome1hing. However, 1.2 kg is the mu · of the object, not its wei ghl. \ \'eight is a force, measured in fon:c units called newtons. Fo r m o ~ on this, and the differl!nce between mass an<l weighL , sec spn~a<ls 2.7 and 2.9. A more m odern t~ pc o f balance is sho\, non the left. 1 On the Moon, the force of gravity on an obJect 1s ontt about one sixth of its value on t:arth. Decide whether each of the following ,, 'Ould give an accurate measurement of mass 1f used on the Moon. a A beam balance like the ooe an the d agram at the top of the page. b A balance Me the one in the photograph above. 22 2 A balloon like the ooe on the opposite page contains 2000 m3 of air. When the air 1s cO,d, its density 1s 1.3 kgtm 3• When heated, the air expands so that some 1s pushed out of the hole at the bottom, and the density falls to 1.1 k!;;'m 3• Calculate the following. a The mass of air in the balloon when cold. b The mass of air in the balloon when hot. c The mass of air lost from the balloon during heating. MEASUR © TS AND U lTS Float or sink? You can tell whetl er a mateoal will float or sin by com.paring its density with that of the surrounding hquid (or gas). If it is less dense, at will float: if 1t is more dense, 1t will sink. For example. wood is less dense than water, so it floats; steel is more dense, so it sinks. 011 as less dense than water. so 1t floats on water. Density differences aren't the cause of floatmg or Sil ·mg, Just a way of predicting which wil occur. Floating is made possible by an up·ward force produced whe ever an object is immersed in a liquid (or gas}. To feel this force, try pushing an empty bottle down into water. .& Hot air is less dense than cold air, so a hot•a1r balloon wdl rise upwards - provided the fabnc, gas cylinders, bas et, and passengers do not increase the average density by too much. A Ice is le~ dense than water 1n its liquid form, so icebergs float. Related topics: mass 1.2; volume and denstty 1-4 planets 11.2 1..5; force 2.6, mass and weight 2.9. convection 5.6 ; densities of 23 F 1 ~ t1r a ,:. ions 6 \ Vhich of thl' [ollowing statements islal-C con·cct? A One milligran1 equal one million gram . B On~ lhou-.and milligrruns cqualli one gram. C One million milligrams ~quals one g111m. D One million milligrams equals one [2] kilogram. op~ and comp le Le Lhc table sho,, ll below: measurement unit length ? kilograrn 7 7 7 symbol ? ? s [6] 2 Write down the nu mbcr of A mg in I g 7 m g,'cm3 m3 km kg ms ml kg/m 3 cm 3 s \ Vhich ot the abo,•.c arc a unit ol ma ? b unit..'> ol length c unit~ of \'olumc? d units of time? e units of den ity? B gin I kg C 111g in 1 kg D n1m in 4 km E cm in 5 km 3 Write down the values of a 300 cm, in m I I01 8 \ Vhich block i n1ndc of lhc dense t matc1ial? b SOO g, in kg c 1500 m, in km d 250 n1 , in s e O. - ~, in n1~ blodc masslg breadthJcm height/cm A 4 4 B 10 4 3 f 0.75 km, in m C 10 5 7. g 2.5 kg, in g h 0.8 m, in m1n D ~ 4 3 600 [81 fll 4 The ,·olun1l: of a rcclangula1 block can be calculated u ing thi equation: volume length x ,, idth x h "1ghl sing lhi:-. inf01·mation, copy and complete 9 The m~1ss of a mcasur-ing cylinder and its contents at-e measured before and afLcr· pulling a slonc in it. r41 Lhc Lablc bclO\\. measuring ()finder length/cm width/cm height/cm volume of rectangular ------ blodclcmJ 2 3 4 ? 5 5 ? H>Cl 6 ? 5 300 ? 10 10 so same volume of water - - -- . balance \Vhich ot th "' Iollo" ing could vou calculate 5 l n each ol the follo\\ ing pairs, which quantity i ~ the larger? a 2 km or 2500 m? b 2 m or I -oo n1 m? c 2 tonnes or 3000 kg? d 2 li L1-e~ or 300 cm'? 24 using n1casur "ments taken from the apparatus abo\'c? A the density of Lhc liquid onh· B the dcnsitv . of Lhe stone onl\'. C the dcnsitic of the liquid and the tone ~ OUP: this may be reproduced for class use solely for the purchaser·s lnst1lule l2 I s 10 A plastic bag ril]ed wiLh air has a \'olume of 0.008 1n1. \ \'hen air in the bag i~ -..qucC/t.'<l into a rigid containe1, thL' nla ~ ot the containe1 (with air) incr~ase from 0.02 kg to 0.03 kg. ~, th, fon11ula density/ glcm1 copper 8.9 iron "/,9 kerosene mercury water 11 II I S 13 The table ~how~ the density of \'arious Mtl>!,,tance~. substance . ma-..-.. densll v - vo1ume to calcu1atc the dcnsit\ of the air in the hag. [21 s 0.87 13.6 1.0 Consider thl' tolJo,\ ing statements: A I c.:m l of men:un has a greater mass than I cm ' of ~lll\ other -,ubscance in thi-.. table tl'ue or lalse? B I cm' or \\atcr has a sn1allcr ma~s than I m' of an, other sub~tanc~ in thb tahl ' - 0.4 m tn.H~ or· I alsc? C I g of i,·on has n smaller \·olumc than I g of copper - tn1L" or la)se? hqu d X mass80kg D I g oi mercun ha~ a greater mas than I g o[ copper - true 01 fol-..c? [2) 14 A stud "n t decides to mcasur • the ()\:riod of n pendulum (the period is the time taken for om.· complC'tc s\\ ing). ~i ng a stop,\ atch, he [ incJ.~ that eight complete M\ ings lakt• 102m 7.4 ~ec.:ond~. \\' ith hi-, c.:aku]ator, h~ then u e thi data to work out the tirnc fo1 one ~wing. The numb 'r sho\\ n on his calculator b 0.925. a h it acceptable for the student to claim that the period of the pendulum i~ 0.925 liqutd Y mass SO kg In chc diagrnm above, the tank~ contain t\\O different liquid-... X and Y. a \ Vhat b thc \olumc ol each liquid in m ' ? [21 b 11 , ou had I m oi the liquid X, \\ hat \\ ottld it.-, ma-..~ be? c \Vhat b the dcn~it, ol liquid X? d \ Vhat i~ the densit, of liquid Y? 12 [2] [21 [21 seconds? Explain ,ouranM\l'r: [21 b Ho\\ could the student measure tht• period more accuratch? [ 2] c Later: another student find that I 00 complete \\ ings take 92. second . From thcs • n1 "a~ur "m "nt~. what is th' p •riod of thcp •ndulum? [21 ~c th' table ot data on pl9 ( pr "ad 1.4) to ans\\cr the follO\\ ing: a \ Vhi h of the ~olids in the table wi11 noat in water? E.\'.plain ho\\ ,ou 1nadc ,our ded~ion. f S] b \\'hich -,oli<l in the t~,ble will Hoat in pell ol? [2] P ·trol and \\~\lcr don't mix. 11 ,on,c water b t ippcd in to p 'l rol, wh~\l \\OU Id , ou e,pc l to happen? E,plain ~ouranS\\l.!l. r21 25 AS S N l S Use the list below when you revise for your IGCSE examination. The spread number, in brackets, tells you wh(!re to find more information. Revi ion checklist Core Level □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ D D □ Ho,, lo use units. ( l. I) Malcing bigger or smaller uniL, using prcfixl!s. ( 1.1) \\'riling numbl!rs in scientific (standard) notation. ( 1. I) ignificant figures. (I. I ) I unit • including the metre, kilogram, and ccond. ( 1.2) Ho,, to n1ca urc J ,ngth . (1.3) Ho,, to mea ure hort intervals of time. ( J .3) How to find the period of a simple pendulum. ( 1.3) nits for measuring volume. ( l .4) Ho,, dcm~it, is defined. ( 1.4) U ing the equation linking den itv, mass, and \Olumc. (I .4) Finding the \olun1e of a regular olid. (1 .5) U ing a n1casuring cvlind 'r to find the, olumc ol a liquid. ( 1.5) 1caswing th ~ den it\ of liquid. ( 1.5) Measuring the dcnsil\ of a r~1ar solid. ( 1.5) How lo use a displacement can. ( 1.5) Measuring the clcnsit, of an irrl!gular solid. ( 1.5) HO\\ to compare massl!s with a beam balance. ( J .6) Extended Level Core Lc\'el. plu the lollo\\ ing: D U c d 'n it\ data to pr~dict ,, hcthcr a n1atcrial will ink or float. ( 1.6) k, for 26 Abu ngce jumper leaps rnore than 180 n1ct rcs ti·on1 the top of thl: Sk, To,vcr in Auckland, c,v Zealand. \Vith nothing to oppose his fall, he \\ould hit the ground at ~ speed of 60 n1ctrcs pcr~cond. l Io,\·cvea~ his fall is slo\\ cd b} the re~i lane · of tht;; nir rushing past hiin, and eventually slopped b~ the pull of the bu ngec rope. ide ropes are also being used to ~top him crashing into the lO\\'er. chapter 2 27 ..... . ~ . ... . . ---· ~ - - . --- .. -•. ,. - . -~ ,_ ..... .. ..__ - ....,....., ---~ . .& Thrust su person c car travelling faster than sound. For speed records, cars are timed If a car lr-avds bct,,ccn two point o n a road , its a \'cragc speed can be over a measured distance (either cal ulatcd like thi ·: Speed one kdometre or one m1fe}. The speed lS worked out from the average of two runs - down the course and then back again - so that the effects of wind are cancelled out. di -.ta llC..'l' mo\ L'd timl.' takL·n tune ta en to travel ~ kilometre (1000 m) ~ Runner m t!asurcd in metres per second ( m l ·). For example: if a car move~ 90 m in 3 s , its avc n1ge spt!~d is 30 m /s. On most journC) S, the speed o f a c ar ,·a iies, so the ac tual speL-d at a ny m o ment i ' u~uall~ difte r~nt r om the a\'crage s pe ed. To find an actual peed, vo u n eed co di co\'er how tar the car mo\'e in the ho rte t time you can measurCll. Fo r e'(a mp)e, if a car move 0.20 m etre in 0.0 I ~: pced ISO s ~B Grand Pr Cclf 0 .20 m 0.01 20 m/ . Velocity 1Os Velocit) means the ·pccd of ·omething and il dirccLion o f travel. Fo r example, a C}dis t mig ht have a velocit) of 10 111/ due ea~l. On paper~ thi , elocit, can be ~ho\\ nu ing an an'O\\ : 45 l]m>})))))))))))}J)} I If di. tance i n1eas ured in n1e tre (m ) nnd time in seconds ( ), peed is 0 Trov• I times Jn ymbols: ,. = -·' lOm/~ 3, > Fo r mo tion in a traig ht Jine \ o u can u e a Fo r cxa mple: Sound o r - to indicate dh et io n. I O nl./~ (\'clucity o f I O m/s to rhe right ) - 10 nl/s (vclodt\' o f LO m/s tu the l e-fi) ote: l O m l~ mav be writte n without the :-, j u t a~ 10 ml~. (E) Qua ntilic , ~uch a ~ vclocit,, which have a di rec tion a well as a 28 I magnitude ( ize) arc called vectors. FORCES A D MOTIO Acceleration omething i accelerating if it \'elocit, i dza11gi11g. Acceleratio n i calculated like thi : ~l\·c..•ragc..• acc..dc..•ration change..· in ,clol:il\' time..• takl.'n (I The , n1bol time tand for 'change in'. or example, if a car inc rca c it \'docity a, ·rage acccl "'ration - 12/4 (i-0111 zero to 12 1n/ in 4 : ml 2 (omitting ·om , unit · for implicity) otc that a ccdcral ion is mcas un:d in mcLn!s per scco nd 2 ( m/s 2). Accdcration i · a \'Cc tor. lt can be ·hown u ·ing an anow (u ·ually c.Joublehcadcd). Alternatively, a or ign can be u ed to indicate whether thl: \'cloci tv i incrca~i ng or dccrca i ng. For c'\an1plc: + 3 rn/ 2 (velocity increa.sb1g by 3 m/ ' e,·e•~ econd) ml 2 (\'cl ocity decrea~-,ing b) 3 111/ ~ velocity Os O m/s 1s 3 m/s 2s 6 m/s 3s 9 m/s 4s 12 m/s The velocity of this car is increasing by 3 m/s f!Very second. The car has a steady acceleration of 3 m/s2• cvef) econd ) A m!gari,·e accclcnllion is called a deceleration or a re tarda tion. A 1mifon11 acceleration means a cons tant (ste-ady) acceleration. Solving a problem E.wu11ple The ,ar on the r ig h t pm,~!'i po!-.l A ,\ith a ,drn,;iL\ of 12 m/s. If it ha!-i a ~lead~ accdcrntion of 3 m /s2 • what is its \ t.•locil) - ~ later, at B? The car is gaining 3 1n/ · of \'clocity e, er~ second. o in Ss , it gain~ an extra 15 m/ on top o[ it o riginal 12 nt/ , Thea --l ore it final vdociC\' i 27 fft/ •• ote that the r~ uh i worked out like Lhi : final ,elocity o: orig inal velocity linal \'elo city - o liginnl velocily extra ,·clocil) (accclcrntion . time) The ;.1bo, ·c cquaLion also \\orks for rc1ardation. 1ra car ha... a retardation or 3 m /s 2, you tn:aL this a~ an at:cclerc1Lion or - 3 m /s 2. ® 1 A car travels 600 m in 30 s. What 1s its average speed? Wl y is its actual speed usualty different from its average speed? How 1s velocity different from speed? 3 A car has a steady speed of 8 m/s. a How far does the car travel m 8 s? b How long does the car take to travel 160 m? 4 Calculate the average speed of each thing in the chart of travel times on the opposite page. A car has an acceleration of 2 m/s2• What does this tell you about the velocity of the car? What 1s meant by an acceleration of 2 mls2 ? C, A car takes 8 s to increase its velocity from 10 m/s to 0 0 0 0 0 30 m/s. Wha t is ,ts average accerat,on? A motor cycle, travelhng at 20 m/s, ta ~es S s to stop. What 1s its average retardation? An aircraft on its take-off run has a steady acceleration of 3m/si. a What velocity does the aircraft gain in 4 s? b If the aircraft passes one post on the runway at a velocity of 20 mls, what 1s its velocity 8 s later? A truck travelling at 25 m/s puts its brakes on for 4 s. This produces a retardauon of 2 mls2 • \l\lhat does the truck's veloci ty drop to? 29 Distance-time graphs G1 aph C-J n be u clul whl'n tucl\ ing n1otion . Below, a C-Jr i tr~wclJing along a ~traight road, away from a marker po l. The car' di tance fron1 the post i. nicas ured e\'er) econd. The c hart and graph ho w four diflcrent c~ample · of what the car• , motion might he. I lr I ______ J On a graph. the Ii nc's rise on l he vertical scale di\ ide<l by its ,isc on the ho1iLontal ·cale is called the gradient , as sho,, non the ll"fL \Vich a <li ~1ancc--t imc g raph. the gradient tell you ho,, muc h e~tra di ·tan cc i · tl'a,·clled e\'en ~ccond. o: X A On a straight line graph hke this, the gradient has the same value wherever you measure y andx. On a di~ta ncc - tin1c g raph, the g rn<licnt of the line is nun1c1ically equal l o the speed. tme ("t>\ M-_ _ _ _ _ _ _ _ _ _ _ _ d1s1i:m,e ta en~ _ _ _ _ _ _ _ _ _ _ _ __ travelled A Car trawl ng at steady speed t,mets d~t.mc.e/ m 0 0 I IO 2 20 8 3 d s 30 40 50 Car travelrng at higher steady speed tlffif:"ls dtStaocelm 80 E E "r; 60 ~ I,; \ -"' 40 ~ ~ ~ "0 20 2 0 3 4 The line nses 10 m on the d tance sc 80 60 40 20 5 tml'/s 2 0 3 sca•e or f!Very 1 s on the trme sea' C D Car a«elerating E O O I 2 3 4 5 10 I 2S I 45 'iO 100 :ar stopped ~ 100 100 80 80 ~ 2 3 4 5 SO SO I~ SO _________ ..,_ 60 40 40 ~ 20 0 1 M'le'/ 5 dlstaoce/m "r; 60 •=------= ~ "0 5 t mels l 1e hne ,s steeper ari b fore tt uses '-0 m on the distance for every 1s on 1he tr.me scale time( s dist,mc.e/ m 2 3 4 20 S t mc/s The speed rises So the car tra Is further each second the one before. and ne curves upwards 30 1 2 3 4 s 20 40 60 80 100 100 100 "0 0 0 0 n 2 3 5 tmcls l 1e car ,s parked SO m from t 1e post. so ttus d1Star the sarne e stays FORCES A D MOTIO Speed-time graphs Each pc-cd- tin1' gra ph belo w j tor a car travc1ling along a tra ig ht road . The grad i,,mt tdl~ you how much c"tra ~pced i gain ,d C\'cn · econd. So: Velocity-time graphs 0 Velocity Is speed in a particular direction. Where there is no change in the direction of motion, a velocity-time graph looks the same as a speed-time graph . On a ~pct..•d- timc g raph, the g r,idicnt of the line is numcricnlly <..-qtml to the accderat ion. In gra ph E , the car tra\'c l · a t a tead~ 15 nl/~ tor 5 , o the- di ·tancc tra\'elled i 7- 111. The are a o l the hadcd rec tangle, calcula ted u ing the calc number , i~ a l o 75. Thi ptinci plc work~ fo r m ore complicated gra ph lines ,1s \\ell. In graph F, the a rea of the s ha d<.id tria ngle, 1 / 2 ,· base hei g ht, equa ls 50. o th e d ista nce trc1 vc llcd is -o metre~. On a ~pec<l- timt..• g l'aph, the area under the line i, numericalh l.'4ual to the dbtancc travelled. F Car with steady acceleration E Car Havellmg at s1eady speed I~ I1°s I ~~ I,2s I 1 I:5 , .~ I I ~~ nvs I~ I! I~ I,2 I,~ I2~ I 3 3 ~ m/S 20 20 ~ 15 } to 5 2 0 3 S timels 4 60 1 E E 40 "'c:) V C s "" "'b 20 5 -- 10 15 20 2 ~ 20 I 10 ~ 25 llmels lhe distance-time graph above is for a motor cy{"}le travelling along a straight road. a What is the motor cycle doing between points D and Eon the graph? b Between which points is it accelerating? c Between which points 1s its speed steady? d What is this steady speed? e What is the distance travelled between A and D? f What is the average speed bemeen A and 07 4 3 S t me/s As the car gains speed. the line rises 4 rm on l espeed sea! for eve('J 1s on the time sca'e. The speed stays tt e same. so the line stays at the same level ® 2 0 0 ------ 5 10 15 20 25 time/ s The speed- time graph above is for another motor cycle travelling along the same road. a What is the motor cycfe's maximum speed? 0 What is the acceleration during U1e first 10s? (t \AJhat is its deceleration during the last Ss? d What distance Is travelled during the first 10s? e What is the total distance travelled? f What Is the time taken for the wtiole Journey? g What is the average speed for the whole journey? Related topics: speed, vetoctty, and acceleratlon 2.1 31 Using ticker-tape ( SO dots punc ed on tape (!llf":ry second 0 Speed, velocity, and acceleration essentials speed*- distance mQ\led lime taken velooty 1s speed In a particular diJection acceleration· change in velocity In the laborator,•, motion can h' in,·cstigatcd using a trollc) like the on .. aboh!. A~ the lmJlcv tr~l\cl~ along lhc bench, ii pull~ u lengt h of paper capc (ticker-tape) behind it. The lapc passc~ through a tickcr-tapl! Lime,'' hic h punches ctu·bon <lou-. on the tape al regular intervals. At~ pical Limcr pro<lm:c -o dot~ en:I') second. Togctht.·1~ Lhc dot~ on the tapl' form a complcll: nx:ord of Lhc n1otion Lhc trolll.:\. The £u11hcr apan the dots. the taster the trolley i~ mo\ing. Hcrc arl.: omc cxampJc : time taken sta , •average I . ............... hi.g 1er steaay s?(!eo Motion can also be recorded photographically. These images of the Sun were taken at regular intervals, at midsummer, in Alaska. Even at midnight. the Sun is still above lhe horizon. ) -· ..... • • • • • • • • • ·• • ♦ o t-,nce betw en dots ~By:, the me :, •ady~eed 'If/ff or • distance bet\\'eefl dots greater tn n be•ore • acce crauon d tance between dois mcrr:ascs t -·. . . . . . . ccecratJOn - - - - - - - - - nen - - - - - - - - - retaroa· on FORCES A D MOTIO Calculations from tape I l-. () . l i Oi s • -- . 0 1s d c. . 0 1s l e • I 0 1s 1 _.._ • 0 1s I I I I I I ' When the sections above are arranged s1de-by-s1de as below. the d,art has the shape of a speed-time graph. start The ticke r-ta pe record a bo, ~ i · for a trolley \\ ith ·ready acceleratio n. The tape ha been marked off in cction • dot- pace long. One d ot- pace h:.. the cliMa nce tra\'e llc.~ by the trolley in tr o !-tccond (0.02 ). So 5 doH,pace · is the dista nce tra\'cllc.~ in 1/ 10 second (0 . 1 s). Tf the tape i ch opped up into it .. d ot- ·pace ection , a nd the t.'"Clio n put s idc-b~ -sidc in o rder, the re:-.ult is a c hart like the one on the rig ht. The chart is the s ha pe of a Sfl'!<..--<l time grjph. The lengths or the sectio ns represent speeds because the tro lley l ra\'cls rurthcr in eac h 0. 1 s as its speed increases. ide-by·idc, the ·cction · pro\ i<lc a rime -c.:alc bccau ·c each sectio n ·ta r ts 0. 1 sa lte r the one before. (E\ The acceleration of th e trolley can be fo und fro n1 n1ca urcn1 nt on the tape. Y Do q ueMions 2 a nd 3 below to disco, ·er how. ®. ~. . . . . . . Describe the motion of the trolley that produced the t,d::er-tape record above. 2 The dots on the tape below v.iere made by a tickertape timer producing 50 dots per second. a Count the number of dot-spaces bet1A-een A and B. Then calculate the time it took the tape to move from A to 8. b Using a ruler, measure the distance from A to B in mm. Then calculate the average speed of the trolley between A and 8, in mm/s. • • • • • 04s Is J • • 3 Look at the chart above. a Using a ruler, measure the distance travelled by the trolley in the first 0. 1 s recorded on the tape. b Calculate the trolley's average speed during this first 0. 1 s. c Measure the distance travelled by the trolley in the last 0 .1 s recorded on the tape. d Calculate the average speed during this last 0 .1 s. e Calculate the gain m speed during the 0.4 s. 0 Calculate the acceletation of the trolley in mrn/s2. B A • 01 L . c Measure the distance from C to D, then calculate the average speed of the trolley between C and D. ~ Section CD was completed exactly one second after section AB. Calculate the acceleration of the trolley m mm/s2. 1 .. . • . • • ♦ • Related top1cs: speed, veloctty, and acceteratfon 2. 1; mot ton graphs 2.2 and 2.5 33 The acceleration of free fall, g H yo u drop a k·ad weight and a feather, bolh tall downward bccau c of gr ~nitv. Ho wever, the leather b lowed n1uch more by the air. The diag ram on the lch sho\\~\\hat wo uld happen H lhcrc were no air re Ltance . Both object ,,ould full\\ ith the amc do\\nwa rd acceleratio n: 9. mJ-l ·. Thi i called the acceleration of free fall. It L the san1e for a/I obje t falljng near the Earth's urtace, lig ht and hea,: alike. The accderation of free falt is represented b~ the S)mhol g. IL~ \'alue \'arie · ·liglHly fro m o ne place on the Earth's surface to ano lhcr, because the Earth·~ gravi Lat io n al pull ,·aric . Ho\\ eve 1: the \'ariation is le ~ than 1c,. Mo \ing awa) lro m the Earth and o ut into pace, g dccrca e. fea·her thar the value of g m~ar the Earth's urfoce is clo e to 10 m/s 2. This ~implt' figurt' i~ uccun1tc enough for many calc ulation~. and will ht' the one used in thi~ book. oh! • in the experiment above, all the air has been removed from the tube. Without air resistance, a light obJect falls with the same acceleration as a heavy one. electromagnet to re ease ball ......_......., I ght sensor to start timer .6. On the Moon, the acceleration of free fall 1s only 1.6 rn/s1 . And as there 1s no atmospt ere, a feather would fall with the same acceleration aS a lead weight. ttmc l h An ex~dment to find g is hown on the left. The principle i to n1easure the timl.! taken for a ~led ball to drop throu gh a known heigh 1, and 10 calculate Lhc a ccdcratjon from thi~. Air resi~tance ha~ liulc cffo-ct on a small, hcav) ball faUing only a sho11 distance, ·o the balls ac dcration is eff~ti\'d) g. light _.__.sensor to stop t1met • Experiment to measure g 34 Measuring g* The ball i dropped by c utting the power to the elec tro mag net. The e lectt ni tin1er i automatica)h witched on whe n the ball pa~ e throug h the upper light b eam. and witc hed o fl when it pru ses thro ug h the lo\\'er beam. If the height of the fatl is I, and the time taken is 1, then g can be calcu latcd using thi~ equation (dcri\'cd from other equations): 2'1 ,.. g - -. FORCES A E Up and down In the (ollowing exa mple, a a ir rc ·i ta nce. Om/s un1c tha t g b 10 m/ 2, a nd that the re i no (3 s) I \ The ball o n the r ight is thrown upw.ir<ls \\ ith a veloc ity o r 30 m/s. The diagra m s ho \\ s Lhc Ydociry of the ball en ~ry second a s it d ses to iL~ highest point and then falls bac k to whe re it s tarted . 10 nv., (2 s) t the the the the the the I he down,\ a r<l, doc ii~ downward , ·clocit~ d o,\nwa n..1 ,clocit~ do\\ nward , ·clocit~ d o,\ nward \'clocit~ downwa rd \'docity d ownward \'docity is is i m /s 20 m/s -10 m/ Om/ 10 n1/s b being added to lhe down\\anl \ 'clod l~ C\'CI')' ccond i· i 10 m/~ i 20 m l~ is 30 m/s - ..__ 10 rr •, 4s t I f I I J A a n upward \'clocil\' o f 30 m/ i the a mc a~ a down u·ard \'clocity o f 30 ml , the n1o tio n of l he ba 11 can be described Ii kc l hi At O s .... Aftcr I s .... After 2 s .... A(tcr 3 .... Alte r 4 .... After S ·.... Afler 6 s .... D MOTION l f I ' ;::.. 20tM (l s) ' 1 20m/s ,r) s) ..,._ ....., I I I \Vhether the ball i · tra\'elling up or down, it i gaining downwa rd \'clocity a l the ra te of IO m/s per second. So it a lway~ has a d O\\ nwa rd accd e ratio n o l 10 m/s 2, whic h isg . Even when 1he ba ll i~ mo, ing up,\ a rds, or is s la Li o nm') at its highes t point, it still h ..L~ clo wn,\ a r<l accdcr,llio n . Belo,,, \ OU can sec a ,·clocitv- time gr•.-'ph for the motion. { l 30- - - - - - - 30 JM 20 t======::=======: (0 s) I '' I -- r nv, ~ ,t:, s) .A A ball in flight. As g is 10 m/s2• the ball's velocity changes by 1O m/s every second. ◄ The velocity- time graph for the ball's motion is shown on the left. ® Assume that g - 10 m/s2and that there is no air resistance. A stone is dropped from rest. Wt at is its speed a after 1 s b after 2 s c after 5 s? A stone is thrown downwards at 20 m/s. Vvhat is its 0 0 speed 0 a after 1 s b after 2 s c after 5 s? A stone ,s thre1Nn upwards at 20 m/s. \'\'hat 1s its speed b after 2 s c after 5 s? a after 1 s 0 1his question ,s about the three p01nts, A. 8, and C, on the graph above left. a In which direction is the ball moving at point C? b At which point 1s the ball stationary? c At which point 1s the ball at its maximum height? d What is the ball's acceleration at point C? e \"Jhat 1s the ball's acceleration at p01nt A? f What is the ball's acceleration at po·nt B? g At which point does the ball have the same speed as when 1t was thrown? Related top1cs: acceleraUon 2.1; motion graphs 2.2 and 2.5; gravitational rorce 2.9 35 0 Motion graph essentials Here are four exampfes of velocity-time graphs for a car travelling along a straight line: 20 20 ~ 20 ~ i ~c;., i 0 i 10 c;., c;., St St 0 t c/s Steady acceleration of 2 m/sl The speed of the car Increases by 2m/s ~ery second. The ,nmal ~Peed 1s :ero, so the car iS starting from rest. i i 10· c;., St 0 s 20 St 0 s tJme/s me/s Steady acceleration of 4 rnJsl The speed of the car tncrea5eS 10 Zero acceleration TI .e c.ar hdS a steady speed of 2onvs. by 4 m/s 'Nery second. The an,ual speed is zero. so the car 1s startmg from rest. . s 0 s mc/s Steady retardation (deceleration) of 4 ml~ The s ~ of the car decreases by 4mlS2• In other \YOf'ds: the acceleration rs -4mlS·. The f nal speed rs zero, so the car comes 10 rest. Uniform and non-uniform acceleration A car is lnl\·dling along a ~lraig ht road . If it has uniform accdcralion, this means that it~ accdcr&1tiot1 i::, slt:ad) (constant). In other wore.ls, it is g:.-'jning ,clocity at a tc-a<ly rate. In practice, a Cal'' accdc-r..1tion is ra1·dy teadv. For example, a::, a car approacht: it::, ma7\in1um vdocit\, the acceleratio n beconlc~ le ::, and k~~ until it b 7el'O , a h o wn in the e xample heJ o w. Als o lhc ca r d<.>cclerntc~ lig htlv durin g gear c han ge~. f If ac<.: dcraticm is not stead, lhen it i'i non-uniform. On a, clocity- timc graph , as bdow, th.: maximun1 accderacion i~ when: the gr'1ph line ha::, its highest gradient (::,tecpnc ). gear change gear zero acce:eration dlarlge at ma mum speed gear cl\ange h gt est gradient greatest acceleratK>n t1rne FORCES A Hen: an: mo n: cxampk·~ D MOTIO or uniform and no n-unifo1·n1 a cc:dcraLion: A stone h, d ropped from a gn~at height. \Vith no a ir resis tance, the \'clocityrimc gra ph for rhc ~Lo ne would be: a., shown below left. The accclcralio n woulcl be unjfo1m. It would be JO nl/s2, Lhc acceleration or frc~ tall,g. E In practice, there i air 1 • btance o n the to ne. Thi aHcct~ it n1otion , producing non-uni foa~m accckratio n, a hown b · IO\\ d ght. At 1he ins ta nt the st o ne is dropp<.>cl, ii has n o velocit). This mean · tha t it s initia l a cceleration is g bccam,c there b. no t yet an~ air resis ta nce on it. Howe\·cr, as Lhe ,clocit, increases , air rcs i~tancc also inc n:ases. E\'enluall~. the air re ·is tancc is so great tha t the \·clocit, n:ac: hes a maxin1t1m and the accelera tio n fa lls to zero. - - 0 A Uniform acceleration of a falling stone with no air A Non-uniform acceleration of a falling stone with air resistance acting. resistance acting. On a speed- rime g ra ph, the a rea under the ]inc is numcrica11~ equal to th e dislancc travcllecl . This applies whether the motion is unifo r m o r no n-uniform - in other words, \\ hct lu: r the g raph line i~ tra ight or c urvecl. \Vith a ·traighc-linc graph , the area can be ca lcula ted. \\'ith a cua,cd-linc graph, thi ma, no t be po iblc, althoug h a n c timatc can be n1adc b) counting ·quare ·. \ Vhcn doing thi , rcmen1bcr tha l the ar ·a mu t be worked o ut using the scale numb ~rs on the a '\is. ft isn't 1he 'real' a rea on the pape r. 1 A boat moves off from its mooring in a straight fine. A speedtime graph for its motion 1s shown on the right. The graph has been divided into sections. AB, BC, CD, and OE. OvN which sect10n (or sections) of the graph does the boat a have its greatest speed? b have its greatest acceleration? c have retardation? (> have uniform acceleration or retardation? Q have non-uniform acceleration or retardation? 0 travel the greatest distance? Sketch a speed-time graph for a beach-ball falling from a great height. How will this graph differ from that for a falling stone, shown above right? C 0 D E A Related topics: speed, vetoc;ty, and acceteraUon 2.1; motion graphs 2.2; g and free fall 2-4 37 Typical forces in newtons rorce lo switch on a bathroom light....... 0 10 N A force b a pw,h or a pull, c,crL1:d b, one ohjc I on :mc>thcr: le ha.s direct ion a~ wdl a~ n1agnitudc (~ize), :-.o it i!', a n!ctor·. 'l"hc 1 unit ol f orl'.'c i~ the ne,"\-10n ( 1) . rnal1 ron.:c!', cart be n,ea~unxl u~ing a pring balanc.e like the one bclo\\. The grcatc1 the lorcc, the n1orc Lhc pling i u 'lchcd and l he higher the reading on the scale: force lo pull open a drinks ca1 ...... 20N force to lift a heavy suitcase..... 2OON · .- . --- . :¥//I/Ill/Ii rorce from a large Ietengine.... 10 9 8 250000N 1 6 S :4 3 1 1 0N J e read ng• newtons Common forces Here arc ·omc e~a mplc ol lo1 1..: Upthrust The upward force frc m d l,qu1d (or ga!,) that mak~ ::.ome things flodt Tension The force 1n d we c.l ed n)ateraal. I e gr.wita,IOflal , ,, c , an ob;ect Weight hat oppc~ the mo:10n o! one ma•enal slid n Thrust The forword force from dn a1tcraft engine Air resistance 0,,e ype of fr .et 'J'1 Motion without force On Ea11h, unpo,\\..·t-cc.l ,chicle ·oon come to re t bl'CaUM~ ol friction. But wilh no l1iction, gravit,, or other external for con il, a 1noving objc twill keep moving for ·n:r - at a tcad, ~pc."'Cd in a ~trnight line. It doc n't need a forcl! Lo kct.!p it modng. T hi~ idt: a i~ su inmed up in a law fln-t put lorwartl by ir lsaac.: , l:\\ ton If no ~'\h!t-na1 for ' (..' b, a ,ling on it. nn objc ·t wi II A Deep in space with no forces to slow a moving obJect wdl keep moving for ever. ,t. - if !',[ationary, tl!main stationary - if moving, kL'L'p mrwing at a stL•a<ly spL•c.:d in a straight Iinl.'. Thi~ i:-. known as • ewton's first law of mo1ion. in 16 7: FORCES A D MOTIO Balanced forces An ob ject may ha\'c C\ Cra l forces o n it. But if the force arc in b ala n c, they caned each other out. The n, the object he ha\·e~ a~ if there i no fo1·ce o n it a l all. Here a re o m l.! e xample : upv,a,d orce from ben t beam Stationary gymnast Skater w ith steady veloci ty Skydiver w ith steady velocity \ ith bala nced fm c on it , an o bj~ t i eitlzer at ,~ t, or mo\'ing at a tcad, \clocit) ( tcady pced in a traight line). That follo\\ fron1 . C\\1on' fit t law. E Terminal velocity \\'hen a k\·di\'er fall fron1 a hovc1i ng h --licopt"t~ as her pecd incrca~ , the a ir 1 ~~i ta nce on her a l o increa c~. Eventually, it i enough to bala nce he r· we ight , a nd he gain · no more ·p~ d . he i a t her· terminal velocity. Typically, thi~ is a bo ut 60 m/s , though th l! actua l , a luc d epend ~ on a ir condition , as well m~the s ize, s ha pe, and ,, ~ight o f the s k\'cli, er. \ hen the k,dhc1 ope n · he r pa rachute, the c,rra area ol 1natc1ia l inc rca~e the a ir re i tancc. he lo~~ pccd ra pidly until the force arc aga in in ba la nce, at a greatl y re duced te rmina l \'d o ity. If air re.\ i "ilmrce bala11cec; lrer \\'eight, why doe.\ 11i a skydi,:er .,lay s till? If ~he wasn't mo, ing , there wo uldn't be any air r c!,is la ncc. AncJ \\ ith o nl) her wdght acting, he wo uld gain ,clodtv. ure('v, if he i trm•ellinf, downu·arcls, her weigl,111u1,r be ~rcau·r than the air re ·i taHce? Only if i ~he i gaining \'elocity. At a tcady velocity, th e fo rce · mus t be in bala nce. Tha t fo ll O\\S fm m \fowton's fit- ·t law. A If a skydiver is falling at a steady velocity, the forces on her are balanced: her weight downwards is exactly matched by the air resistance upwards. 1 Wl at is the SI uo,t of force? 2 What does Newton's first law of motion teU you about U e forces on an object that 1s a statiooary b rnoviny at a steady velocity? I he parachutist on the right is descending at a steady velocity. a What name h given to this velocity? b Copy the diagram. Mark in and label anot er force acting. c low does this force compare W1th the weight? d If the parachutist used a larger parachute, how \iVOuld this affect the steady velocity reacted? Explain \\thy. 0 Related topics: frlctlon and mov1rig vetucles 2 .8 ; weight al'Mt mass 2.9 39 Inertia and mass ► Once a ma.ssrve ship like this is moving, 1t is extremely difficult to stop. Velocity is speed in a particular direction. If an ohjL-cl bat n:~t. il takes a fore'-! lo maki! it m o\ ·c. If it i~ moving, it takes a force lo make it go faster, slower, or in a different direction. o all objects 1~ ·i ' ta change in ,·elodt) - l!\'Cn if the \'clocil) is lCl'o. Thi · re i tancc to change in vclocit,· i called inertia. The more mas ~on1ething ha , the n1ore inertia it ha . 0 Any change in \'docily is an acceleration. o the mon~ ma ·s something has, the more difficult ic is to make ic accelerate. Resultant force Jn 1hc diagram on the left, the L\\O forces are unbalanced. Togl! thcr, they are equi\aknt to a single force. This is called the resultant force . These two forces ... torcc ,H'C balanced , the rc:,uhant (orcc i~ zero and there b no acceleration. Anv other re ulcant force cau ~ an acceleration - in the . an1e direction ( the resultant for e. I( are equTValent to a single force of (S-3) N.. , E -•lll• 2N Linking force, mass, and acceleration There is a link between the n:suhant force acting, the mas~. and lhc acceleration produced. for example: This ,s the- resultant forc.e If Lhis resuhant force... I t\ 2 0 Symbols and units F force, in newtons (N) acts on this ma:s... I kg 2 kg then Lhis •~ lhc accderc.1Lion ... ") l n1/ .. 2 ml .. ., 3 m l· ") 2 kg 2 kg ln all cases, the following equation applies: m - mass, in kilograms (kg) a - acceleration.in metres/second2 (mts2) 40 In s\'mbols: F 11w Thi relation hip between force, ma , and acceleration i called cw1on' econd law of motion. omctin1e FORCES A ma~s 2 kg Example \ \'hat is the accde1~1lion of th(' modd car on the r,ight? Fil l , \\ ork o ut the re u ltan t force on th e car. A force of J8 ~ to the ,-;gl,J con1bined with a force of 10 to the le{r is eq ui\'a]ent to a for ce of (I I 0) " to the riglzl . o the f\! suha nl force i 8 J. Next, wo rk o u t th e accele ra tio n whe n F o: F- 111a 8 2a 8 i\ a n<l 111 = 2 kg: D MOTIO JO N - - - - ~ l8 N 1- -1 total f0<ce fr,ctional force from mo•or (o mjtting units tor si mp licity) Rcan-anged, thi gin~ a - 4. o the car'- accelera tion i 4 n1/ 2 . Finding the link paper ape > troteys 2 units of mas! flat bench E The ]ink between force, mas~. and accd er.llion can be found e;\pc1i mcntally using the equi pment a bon ~. Oifforenl fo rces arc applied to the Lr-ulle~ by p ulling it alo ng ,,i th o ne, t\\ o, or thrc(' ela tic cords, ll~ tchcd to the same length each time. Owing each run , the tickea~ta pc lin1cr m arks a ea·i~ of d ot~ o n the p:iper tape. The acceleratio n c:in be calculated from th e ~paci ng o f the do t . To v~U) the ma~~. o ne, two, o r thn:e trolle). a~ used in a tack. unstretched .__ ___,,,,,- cord ti-t=:_ ........-_-_-_-_-_-~-• 1 1,n,~ of force Defining the newton A I \l n.~u ha nl force act ing o n 1 kg p rodu ces a n ::iccelera tio n o f I m/· 2• Thi~ simple 1'! ·ult b. no accident. It arise~ from the wa) th e nl!'wto n i!-. d l.!fined : I newton is the lorn.~ n:quin .·tl to giH: a mass of J kilogram an accck·ration of l ,n/~2 • Further effects of forces Fo rce <lo no t onl) aflcct motion. If two or more lorcl: · act o n M>mcthing, the) change it hapc or , olun1e (or bo th ). The e ffect i light" ith hard objc l~. but can be vet" no ticeable with flc,iblc o ne , as hown o n the tight. ®0 a What equation hnlcs resultant force, mass, and acce eration? b Use this equation to calculate the resultant force on ,each of the stones shown betow. Forces causing a shape change 2 a What as t e resultant force on the car below? 0 What is the car's acceleration? G If the total frictional force rises to 1500 N, \-"mat happens to the car? m~s 800 ·g ~ o rrvs' SOON ◄4--• I total fr1C.t1onal force I --111111111111-►1 .I SOO N I force from eng ne Relat ed top1cs: mass 1.2; acceteratlon 2.1: ustng tlcke<-tape 2.3; balanced rorces 2.6; stretching and compressing 3-4 41 reduong fncuon ' roller beat•~ • grease 1 rtictio n i the lo t c that tric to ~top material sliding acr , eac h other. Then: i lliction between , ottr hand~ when , ou rub them tog ·thcr, and fri ction hct\\(.•cn ,our ~hoe and the gr ound \\h •n ,·ou ,, ,1lk alo ng. Fric tio n pr·c\·ent~ machinen From mo\ in r rrccl~ and hculs up it, m o \'ing pan~. To reduce rrict io n. ,, heds are mou ,ued o n ball or rollc, be..uings , "ith oil or g c'\:a.-;c lo m a ke the mo, ing w ftu.:L's slippt.•I). Ftiction i n o l alwav~ a nui a nee. Il give~ ·hoi.: and l\ 1 c~ giip on thl· ground, and it i u cd in m o l braking \ t ·n1,. On a bic, clc. for c~anip]e, rubber blo k~ arc prc~~c.."<..I ngaim,L the\\ he "I. to ~low th em do,, n. Two kinds of friction brake pad tyre gnpp,ng road using fnction A This wheel is mounted on rolle< bearings to reduce friction. ..- Air resistance is a form of dynamic (net.ton. When a car 1s travelling fast. it is the largest of all the frictional forces opposing motion. Air resistance wastes energy, so less air resistance means better fuel consumption. Car bodies are spec,alty shaped to smooth the air flow past them and reduce air resistance. A low frontal area also helps. \Vhcn the block b IO\\ b pull~d gcnth, fli ction Mop~ it moving. A, the fo rce i~ increased, the fri c ti o n lisc~ un1il the block is aboul to ~lip. Thi~ i, lhe ,tailing m sta tic fri cti o n. \ Vi th a g reater- d o \\ nwanI fo rce o n Lhe bloc"-, th~ sl..Hic tric Li o n i~ high~r. Once 1he block Marts lo ~lidc , the hiction <l, o ps: moving or d rnamic h ictio n i · le ~ than tatic la iction . stat,c fric ,on 1s greater an • • . dynam>e nctJor D~ 11ainic fric ti o n heat · mah~11als up. \\'hen , o mcthing i-., moved again..,l the tor ce o frictio n, iL ener~ of mocjon (ca1k-<l ldneLic cncrg~) b convened into thcrn1al cncrg\' (heat). Brake · and other n1a hincn mu l b de,igncd ~o th at the, gel dc.l ofthi. thcrn1al cncrg, . Othcn,i. · their n10,·ing ptu-l~ ma) become. o ho t tha t the\ sci1:e up. FORCES A D MOTJO Drag ·Ii .. nee fric tion\\ h , n the, 111 0 , ... through a liquid or a ga~. hb fore · is called drng. Drag (ah,o kno\\ a:-. ai1· resbtancc ) ac ts on ~m air n1ft a" it n10, c.s throu g h the afr. Drag ac t!-. on a boat a~ it mo\c.S acro~s wat e r: nd if ,ou d1np a pebble into dl.!1..'p water. dr-dg slo w:-i it. dcsc t?nl. Obj "'Cl C"\P Friction highs and lows As the Eanh moH~s 1lu-ough space, it rum, inlo ~mall bit · or m.ucrial, also orbiting the Sun. ThC""iC mo.sth· range in ~il'l! from g rain~ ol sand to sn1ull pebbles , anc.l the, can hit lh4..• atmosphl!re al .spt:c<l of up to 70 km/s ( 1-0 000 mph ). rric tional heating makc.s them btu-n up. cau-.ing a trcak or lig ht t:a lll!d a meteor (or· hoo ting tar'), a on the right. ometimc~. 1hc bun1ing pr ducc il fireball. Belo\\ arc n101 • C"\amplc~ ol fri lion in u tion. & A curling stone slides across the ice towards a target. To ma e the stone travel further, the sweepers brush vigorously in front of it with brooms. Friction from the brooms has a heating effect which melts some of the ice. The melting layer reduces fraction under the stone. 1 In a car, fnct,on 1s essential in some parts, but needs 10 be reduced in others GNe MO examples of where friction ,s a essential b needs to be reduced 2 Why are car bod es des191 ed so that air res,stance is reduced as much as possible? 3 Comparrig the top and bottom of a surfboard: a On which surface does the frtctJon need to be high? Explain why. A The top of a surfboard 1s often given a wax coating. Tiny bumps of wax increase friction by sticking to the surfer's feet. However, the underside of a surfboard has a smooth, glassy surf ace so that ,t can slide across the water W1th as little friction as possible. b On which surface does the fnct10n need to be IOIN? Explain why. 4 Write down whether, in each of t e following examples. the friction has a I eating effect: a The soles of your shoes gripping the ground when you are standmg on a slope. b A crate being dragged ac,os.5 the ground. Relat ed topics: speed 2.01, thermal energy 4-1; ene rgy transfers 4.2 43 Gravitational force TI you hang an object rom a pling balance, vou mea urea downward pull from I h~ Earth. Thi · pull i called a gravi tational force . I ' , ,, N o one i ure what cau e~ gra\'itational torcc, but here arc ome of it ma in feature : • All ma~ses allract each other. • The gn!ater the ma-.ses, Lhc stronger the force. • The closer the n,asscs, the sLronger the force. ;' The pull between mall rnaM>C i e,trcmcl\, weak. It i l than 10- 7 bet,,een you and thi book! But the Eru1h j o ma ive that it~ gravitational pull i strong enough to hold most thing firmly on the ground. Weight A Near the Earth'.s surface, a 1 kg mass has a grav,tat,onal force on 1t of about 10 nC?\AJtons. This is its weight. \Veight i • another na,nc for the E.a11h's gra\'itational force on an object. Like othc.:r forces, it i n1ea ·urc<l in newtons (N). . car the Earths surface, an object of mass I kg has a weight of 9.8 J • though 10 ' i · accurate enough (or man) cakulation and will be used in chi book. Grca tcr rna ~ have greater weight ~. Hea-c are on1c cxa,nple ~: 1 weight (gravitational ro,ce) ·g ·o N 2 kg 20N 50 kg SOON m mg 9 • QfclVltAlOOnaJ f teld strength • lO N/kg Gravitational field strength, g A gravitational field is a region in which a ma~ cxpcticncc a force clue to Symbols and units w 8 gt1l\itational attraction. The Earth ha a gra, ilalional Ueld around it. · car the tuface, thi exerts a force of l O newton on each kilogram of n1a. : the Ea11h~ gravitational field strength i 10 newtons per kilogram (N/kg). Gra\'iLational (ield sLn~ngLh i~ n.:prcscntcd by the ~ynlbol g. o: in newtons (N) m = ma~. in kilograms (kg) weeght, g - gra~tatiooal field strength, 10 N/kg near the Earth\ surface 44 (g - JO '/kg) In ~vmhols: ln c,·ery<la) language, we often u ·c the word 'weight' when iL s hould be ·m~ '. E,cn baJancc-. which detect \\eight, ar~ nonnall~ marked in mas unit . But the pet on in the diagram above d~n•t \\.cigh' SO kiloga'" m~. Ilc ha~ a ma*,-, ol 50 kilogram and a wcig/11 of ·oo ne\\ ton~. FORCES A D MOTIO £\·ample \\'h at is lh~ :.tccd~1~1lion of thl.' rock~t on lhc..• right? 3000 N fOfce from rocket To find the a ccle1 .. cion, \ou need to "now the re uhanr orce on the rocket. nd to find that,) ou need to know the ro kct' weight: weight o: re ultanl lorl:e (upwards) But: o: mg 200 kg x I O /kg 3000 1\ • 2000 l 000 engine 2000 l"\ weight ~ r ·.,_sultant force - n1a x acceleration I 000 ~ 200 kg x ucceleration Rean"nnged, thi~ gives: accderc.1lion Changing weight, fixed mass On the Moon, Your \\'eight ( in nc\\'lon~) would bi;! less 1han on Ear1h, mass weight 100 kg 1.ero because the :..1oon's gra\ ·itational fidd is weaker. ,·en on a11h, ,our weight can var , lightly froln place to place, bccam,c the Eat1h' gra\itational ncld 11 ~ngth ,-alic . Moving. J\\a, fron1 the Earth, ,our weight decre'1 e . Tf vott could go deep into :-,puce, and be fre\! of an) gnl\ itational pull, Your weight would be zero. \\'hclher on the arth , on the Moon, or deep in ·pace, _)our bod~ alway ha the same re i Lance to ::l change in motion. o , our ma~ On kg) doc n't change - at lea t. not under norn1al ci1'CLm1 tancc . But. .. Accor-ding to Ein ·tcin' · theory of ndativit), mas~ can c hange. For example, it incrca~es when an object gain~ speed. Howc\er, the change is far Loo smal l to detect al spcL-<ls much below 1he pced o[ light. For all practical purpo es. ou can assume that 1nass i · con · tant. ·g 160 N 100 kg 1000 N 100 Two meanings for g In the diagran1 oppo itc, the acceleration ot each object can be \\orkcd out u ing the equation lorce - ma " x acceleration. For example, the 2 kg ma~s ha~ a 20 1': force on it, so it acceleration i 10 m /s 2 . You get Lhc same n.:sulc tor all the other object ·. In each case, the acceleration work out at l O m/ 2, or g (" here g is the Earth'~ g1~1vitational field trcngth, 10 , "/kg). og ha~ two mt;!anings. In bolh case ·, g b a \'ector: • g is Lhe gravilalional field stn:ngth ( I O ne\\ tons pe1· kilogr'..im). 2 • g is the acceleration of free foll ( I O n1ctres per sccond ). ® Assume that g - 1 ON/kg and there Is no air resistance. 5 '9 10 kg 1 The roe ·s above are falling near the Earth's surface. a What Is the weight of each rock? b What ,s the gravttat1onal field strength? G What Is the acceleration of each rock? 2 A spacecraft travels from Earth to Mars, where the gravitational field strength near the surface 1s 3.7 Nlkg. The spaceCfah Is car;rymg a probe which has a mass of 100 kg when measured on Earth. a What 1s the probe's weight on Earth? b What 1s the probe's mass in space? c What 1s the probe's mass on Mars? d What 1s the probe's weight on Mars? O When the probe 1s falling, near the surface of Mars, what as its acceleration? Rela ted topics: kg 1.1; vectors 2.1 and 2.1.3; ,esultant force and acceleraUon 2.7. energy and mass 10.6 45 Action-reaction pairs A ~ingle force cannot exi t by it elf. Fore~ are always pu he or pull betwet!n two objects. o they alw"1ys occur in pairs. The cxpcrimcn t below shows the cffcct of a pair of ror C!-,. 'lb begin ,, ii h. the L,,o trollc) arc staliona1'). One of them contain · a spring-loaded pi ton which ~hoot ~ out ,, hen a rclca c pin j hit. Before spring tS released Sl)n n9-k>aded Aher sprrng ,s ,~se<J piston shoots out < I V - 01-- .___ - ~ ~ - -.---, ) ... V \Vhen the pi ton i relea -ed, the trolley ~hoot off in oppo ite direction . Althoug h the pi ·ton corn from one trolley only, two equal but oppo ite forces are produced, one acting on each trollc~. The paired forces are known as the: action and th<: reaction, but it doesn't matter which ,ou call whic h. One canno, e,ist wi1hout the other. Here are some more examples of action- reaction pairs: forward force on bullet: bullet shoots out backwclrd force on gun: gun tee()( s Earth pulls d0',V11Wards on Sk'.fd1ver runner pu5hes backwards on ground runner /on:e.s alwtl)'~ occur in p<lirs, why do11'r they cancel each orher 0 111 ? The force in each pair acr on diflerenr object , no t the ·amc o bject. I{ l{a kydit·er i pulled downwards, win· i-">ll'r t'1e Eanl, pulled 11pu·ard~? It is! But the Earth is o mas ·ive that the upward force on it has far too small an effoct for any mo\'ement to be dl!tecccd . FORCES A D MOTIO Newton's third law of motion I aac Kewlon wa the fi, l pc, o n lo point out that c, en lo t c ha!) an equal but oppo ite panner ac ting on a difierent o bject. Thi idea i s ummed up b~ e\\rton's third law of motion: fuel. 1ouxf hydrogen ll object A cxl.·rts =., force on objc..~ I B, thl.·n objt:c l B \\ ill exert an equal but oppo~itc force on o~jec t A. 1quxf oxygen Here is ano ther way of stating the same law: Toe, 1.•rv action then~ b. an l.•qual but oppo,itc reac tion. Rockets and jets Rocket u c the action- reac tion principle. A rocket L'nginc get thn1 ·t in o ne directio n hy pu ·hing out a huge ma -~ of ga vet)' quickl\' in the o pposite direc ti o n . The gas b produced h~ burning fuel and o:xygcn . These arc e ither s ton:d as cold liquids, or t he fuel ma~ be ~ton~d in c hem ical compound~ \\ h ich have been comprcssccl into so]icl pellets. How cau <l rocker accelerate through pace if ,here i 11orhing fo r it to push agaiH (? It does ha\'c omcthing to pu h again t - the huge ma o f ga fro n1 it bm·ning fuel and O\)'gcn. Fuel and oxygen n1akc up o,·cr 90<'c o f the m ass o f a fulJ~ loaded m ckct. Jct engine al~o get thn1 ·t bv pu hing out a huge ma.-....-.. o f gn . But the ga~ i~ nio!-.tl) air that hash ~"n dt1l\\n in at the front: cornbustron chamber turbine compress0t 1 combustion chamber nmle ~A rocket engine. In the combustion chamber, a huge mass of hot gas expands and rushes out of the nozzle. The gas is produced by burning fuel and oxygen. ◄ A jet engine. The big fan at the front pushes out a huge mass of air. However, some of the air doesn't come straigh t out. It is compressed and used to burn fuel in a combustion chamber. As the hot exhaust gas expands, 1t rushes out of the engine, pushing round a turbine as it goes. The spinning turbine drives the fan and the compressor. n e person on the right weighs 500 N. The diagram shows the force of his feet pr~sing on the ground. a Copy the diagram. label the size of the force (1n newtons). b Draw m the force that the ground exerts on the person's feet. Label the size of this force. 2 When a gun is fired. ,t exerts a forward force on the bullet. Why does the gun recoi backwards? 3 In the diagram on the opposite page, the forces on the runner and on the ground are equal. Why does the runner move forwards, yet the ground apparently does not move backwards? Related top1cs: fotce 2. 6: gravttaUonal force 2.9 47 ► Momentun1 - ma~ x \·elocitv, and l hi truck ha~ lot · of it. E People say lhat a hea\'\' vehicle travelling fa t hru. lot of momentum. Howe\'e•~ momentum ha · an exact cientific definition: mom~ntum Two versions of the same law - -- momentum of car moving to the ,i~/11 n1omentu1n ot car mo\ ing lo the le/; A resultant force Facts on an object of mass m for a ti~ t. As a result. its velocity increases from u to v, its acceleration over this time being a. from Newton's second law of mot,on: resultant force change io momentum time So: F- mv - mu t =m(•;u) Bot: For e'<an1ple, ii a n1odel car ha a ma ~ of 2 kg and a \'Clocitv of 3 m/ , its n1omentum - ma . x v locitv - 2 kg x 3 m /. - 6 kg m/ Like vdoc ily, momentum i~ a vcclor, so a + or a - is ofLen ust:!d to indicate it~ dircccion. For example: .~ ,, I ... .,,.- mass , n .· lm:i1,· ins\ mhol'.-,: p=nn· a=( v; u) 6 kg m / 6 kg m/ Linking force and momentum: Newton's second law of motion \'\firh a resultant torcc on it, an object will accck·ratc. Therefore, its \elocit\ will c hange, and o will it ,nomcntum. The Force and tht> momentum change are linked by thb equation: change in mom~ntum timL' or: re ultanl force - rate of change of momentum The link between a r~ ultJnt force and the rnte of change of momentum iL produces is kno\,·n as ewton's second law of motion. The above equation i really anolher way of sa'.·ing that 'for c - mas · x accdcral ion'. The p~1nel on the left explains why. Impulse From 1hc previous equation, it follows that: So. F = ma In 'vVOrds: resultant force = mass acceleration rl.·,uhant lorn: .,. tim~ clmngl' in mmlll.'lllum The quantity ·rorce . · time' is called an in1pulse. rewton noted that, when the ame lorce acted lor the same time on cliltercnt ma s.es, a large ma ·s would gain 1e ~ velocity than a ·mallcrone. but the c hange in 'mass x \·docily' was the same in every case. II wa~ chi obscna1ion thal led lo Lhc conct:!pl of moment um and the second la\\. FORCES A E Solving problems D MOTIO mass 2 kg I £xa,11ple I A modd c~u- of mass 2 lq.?. is ll~lh.· lling in a ~t1--..dght lilll', If its ,clocity incn:asc~, fron1 Jm,!'- to 91111~ in 4s, what is then: ultant force on it? velocity increases To begin with: m omentum = m a.-,~ -< , ·elochy 2 kg x 3 m/., from 3 m/s to 9 m/s 6 kg m/s m4 s .J seconds later: momentum - m ass x \'clocity = 2 kg So: 9 m/s 18 kg rn/ · c hange in mo n1 cntum - 12 kg n1/s change inmo1nentum 12kg ,n/s , . B ut: rcsu Itant ,o rce 1 tame "'t So: resultant fort:e 3:--.! The problem can al~o be oh·cd b, wo rking out the c ar' acceleration and the n u ing the equa tion : re ·uh ant fo r ce = m as x accd eratio n. E.m mp/e 2 * A small I ockct pushes out 2 kl! of l.'Xh..,u .. t gas I..'\ l.'I"\' sL-con<l :._1t a ,docity of 100m s. \\1hat th1ust ( force) is procluccd by tlk· cnginl.'? B~ l\ewto n' · chil'd law o f motion, the forward fore<: o n the cnginl.' i equal to the bac kward fo rce pu hing o ut the e~haus t gas. That fo rc e can be calculated bv J inding the ra te of change or mo n1cntum o l th ~ ga l n I ~e ond , 2 kg o f ga .s inc rea~es it \'elocily from Oto IOOm/s. o: c hange in mass n10111cntum Y ,·d ocity changl.' 2 kg x l 00ml fo rce o n gas change in mon1cntum tinl<: o: ®0 8 0 thn_1~t 200kg m/ 200 kg m/-.. ] !) / ..........._ 2 •:gof gas '-.... o -~ed out t ,cry second 200 K What equation is used to calculate momentum? W'hat quat1on lin s the resultant force with the change m momentum it produces? W'hen a resultant force acts for 3 seconds on the trolley belO'N, its velocity increases to 6 m/s. a What 1s the momentum of the trolley before t e force acts? b VVhat 1s the momentum after the force has acted? 4 m/s 100 nv·. c What 1s the change 1n momentum? d What 1s the change in momentum every second? e What 1s the resultant force on the trolley? Now you v-J1II calculate the resultant force on the trolley using different steps: f What 1s the trolley's change m velocity? g What is the trolley's acceleration? h What equation links force, mass, and acceleration? What 1s the resultant force on the trolley? 4* A Jet engine pushes out 50 kg of gas (mainly air) f!Very second, at a velocity of 1SO m/s. a What thrust (force) does the engine produce? b If the engine pushed out twice the mass of gas at half the velocity, what would the thrust be? Related topics: velocity, acceleration as vectors 2.1: force, mass, acceleration, Newton's 2nd law 2.8, Newton"s 3rd law 2.10; momentum and molecules 5,4 49 &!fore sprJng is released ~ ..-w.~•/ -mass 2 kg mas~ 4 kg • Aher spnng is rel~ased veloc ty 0.5 mls v~looty l Om/s ~ A Velocity and momentumV essentials Veloc,ty 1s speed in a particular direction. momentum - mass velocity (kg m's) (kg) (m/s) Velocity and momentum are vectors. They have direction as well as magnitude (size). Their direction can be shown using an arrow, or a + or - . ) momentum= 4 ·g x 0.5 ITV$ 2 ·g m/s (to the left) rnomentum = 2 kg x LO ml$ ~ 2 ·g mt5 (to the nghl) - E To begin \\ith, the trollc\ · above arc ~taLionary. But when a springloaded piston i re lea ·cd bl!L\\ L'Crl thcrn, the) ·hoot off in oppo~ilc direction~. Theil' \'Clociti~ can be mca urcd u ing tickc-t":.lapc cimet . \ Vhen the trolleys . hoot apart, the trolley with least mass ha. mo~t velocity. The diagram shows typical mass and velocity \'alue . These il1ustr..lle a rule which applit>s in al l such e~pc1imcnt~: ma x velocity to the left = ma!'ts x (trolley A) velocity to the tight (trolley B) Thb re ull i to be c:\pcctc<l. From Newton' · third law or motion, the lorce on the two trolley are equal but oppo i te. Al ,o, the force , act tor the ame time. o thev hould cau e equal but oppo ile changes in momentum (as force x time hange jn momentum). Conservation of momentum \ \1ith the mo. ·· and velocity nilu~ above, the total momentum of the trolleys hefort> and after separatjon can be found. As momenlum is a n~ctor, its direction n1usl bc allowed for. Jn the follo\\ ing calculations, a momentum gain to the rig/a is counted a · posith·e ( + ): &,fore the priug i, rele,Hetl: total n1omentum of trolley - 0 A/ier tire spring fa re/ea ·ed: momentum of trollc~ A - mass x \'doci1y momentum of Lrolk~ B :; ma~s o: 4 kg -< - 0.5 m /s n~locity = 2 kg J( 1.0 m/s tolal mon1cnIum of trollc\s - 2 kg m /s + 2 "-.g m/s 0 So the total momentum (L.Cl'o) i unchanged b, the .-clca~c ol the ·pling. Thb b an cxa mple ot the law of conservation of momcntllm: \ Vhcn two or 1110 n : obj1:cts ~1c t on eac h ot her~ their lotal m o1ncntum so remains cons tant, pn)\ idcd no c,tc1·nal fon.·c~ ,,u-c ac ting. FORCES A D MOTIO Collision problem Before the colltSion veloc ty 2 nvs Vl loc1ty ) 3 rn/~ ( Airer the collis,on velooty '? ) _L-- com bined mass Skg Pt!"",---0-1-.-l.0..l •__.__Q __ Exa,np/e \ \'hen the two trollc,, ..,bo,·~ collidt~. the, stick together. \\' hat i thcit· ,·doc ity after th • c;olli,icm ? Accordi,,g to the law o f co n cr\"ation ol mo mentum, the to tal mo mentum o ( the trolle) i the amc alter the colli ion as befo1 · : Bt!fort! the co/li~iu11: momentum o ( trollc~ A - ma&> x \'clocity - I kg x 2 nv -, 2 kg nl/ · momentum ol trolle, B - ma~ x velocity - 4 kg x - 3 nll - - 12 kg nl/ o: tota l mo me ntum of lt llcv A a nd B - - IO kg m/~ A/icr 1/11: ,·olli.\ ;0 11: to tal n1omcntum of Lro lle\'~ A and B - 10 kg m/~ o: combi ncd ma -~ x \'elocit\' . - 10 kg rn/ o: - kg x \'elocity o: , ·clo it,· of trollc, 10 kg m l - 2 m/ Therefore the tro lle):-. han! a ,·eloci l~ of 2 m/s to the I "ft. ®0 trolley of mass 2 kg rests next to a trolley of mass 3 kg on a flat bench. \'\then a sprmg is released betv.eeo the trolleys, and they are pushed apart, the 2 kg trolley travels to the left at 6 m/s. Bofore sepctration: a What ,s the total momentum of the trolleys? After separation: b What is the total momentum of the trolleys? c What 1s the momentum of the 2 kg trolley? d What is the momentum of the 3 kg trolley? e What 1s the velocity of the 3 kg trolley? A 0 0 Momentum and energy Mov ng objects have kinetic energy (see SPfead 4. 1). In a collision, some of that energy may be changed into ott er forms. If a collision is elastic. the total kinetic energy of the moving objects is the same after l e collision as before. In other wcxds. there is 'perfect bounce'. However. most col~sions are not hke this. The total ki etic energy is less after the col~sion than before. In such cases. the 'missing' energy is converted into thermal energy (heat). 16 kg mass travelling to the right at 5 m/s collides with a 4 kg ma~ travelling to tl e left, also at 5 m/s When the masses collide, they stick together and move along the same line as before. Before the collision: a What 1s the momentum of the l 6 kg mass? b What 1s the momentum of the 4 kg mass? c What 1s the total momentum of the masses? After the collision: d What 1s the total momentum of the masses? e What 1s the velocity of the masses? A Relat ed to p1cs: velocity and vectors 2 .1; using Ucker-tape 2 .3 ; Newton's 3rd law 2 .10; kinetic energy 4-1-4-3 51 Wh-en lhese are added .. 30 N 40N Vectors and scalars Ouantitie~ ~uch a~ lo~e. which hn\'e a direction as well a~ a magnitude (size), are called vectors. >~ the resultant IS •• -- Quantitic~ such as ma~ and , ·olume, which have magnitude but no direction, an.: called scalars. Adding scalar.,, is easy. A mas~ of 30 kg added to a mas · or 40 ah\a)S gi\'~S a mas~ or 70 kg. When these are ~dded 30 N 1\\'o \'e<.:tors acting at a poinr can be replaced by a singk ve<.:lor with Lhe ·ame cJkct. Thi~ i~ their resultant. On the lcl1, )OU Gln ·cc how to find it in t,,o ~iinpk ea e . Finding the re- ultant of two 01 more ,·cctot i ~ called addi11g the \'Cctors. 4ON "'g Adding vectors: the parallelogram rule the ,esultant ss .. 0 Why the rule works To see why the parallelogram rule works. consider this simple example using displacement vectors: N fin st), w-$-e /,,/ s / stan / / / 30m 0 "'------" 40 rn Ab<:Ne. someone starts at O. walks 40 m east then 30 m north. From Pythagoras' theorem, the person must end up 50 m from 0 . -----;,, ~~/ I ,C,7 ~.._1,:~Y 30m ~~~ / ~ I I 40m Above, the ;ourney has been shown as the sum of two displacement vectors. When the parallelogram is drawn, its diagonal gives the correct displacement. E The parallelogram rule is a method of finding the rc~ullanl in situations like Lhe one abo\'e, ,,here the vectors arc not in line. lL work~ like this: To lind the 1c ultant of two \crtor (for e:-,.amplc, lorc1..: of 30 40 and acling at a point 0, a in the diagram belo,\): On paper, draw two lines from O lo repn!~ent the \'CCtors. Th~ directions must bi.! accunlle, an<l the length of each lim: mu~t be in proponion lo the n1agnitude of each ,·eclor. 2 Draw in t\\o rnon: line~ to complete a parallclog.-am. 3 Draw in the diagonal from O and measure it length. The diagonal repre ent the re uhant in both 111agnitudc and direction. (Belo\\, for example, the re-'ultant i a tor e of 60 ~ at 26 to the hod1ontal.) -------------- 'Jlf # ~ # # ~'°°# i.,._ # # # I ,' II 1f'. # ,,_,,V~ # I I ,' # o..#_______ ...,,' force: 40 N 52 1 mm represents I N ·,·cl. \ At xtcnd ·d L ou will only be rcquin:d to use thi rule,, hen two fore~ are at tight angle~. FORCES A D MOTIO Components of a vector* _______ .., I I I componen : 40 N ... (0rn,, ... ... Orr<'f>t • .,... ~ <S tv , , ,, , , , ,' , ,, I , I ,, ,, . ---- ------ ------ ------z .~. ~ ,... I N ..; 1 C 81 -· --------- componen : 54 N The p arc.1 lldograrn n tl c also w orks in r L'n ~r !>C: a si ng lc , L'Cl o r can be r·cplaccd b) two \'Cclor · ha \'ing chc same cfJc cL. Scientificall~ ·peaking, a ingle , cctor can be resolved into l\\ O components . \Vhen u ing the parallelogram 1·ulc in thi way, the ingle \'Cctor forn1 the diagonal. Calculating componentsO The honzontal and vertical components of a force F can be calculated using trigonometry: f ------------- Abo\'e, vou can ec ·O1n e of the \\':"l\ S in which a 60 to t c can be re ol\'cd into two compo nent . There are endle other po ibilitie . som etimes helps Lo ~solve th e force into compo nent'-; a t rig ht a ngles. Fo r example, when a helicopter tills iL~ main r o tor, the rorcc ha s vertical and horizonta l com ponent · which lifL the hclicopccr and m o ve it fon,L rt.I: I I Fr I I Components at right angles Tn \\ Orking ou t the l;! fl ects or a force, it I : Fy ____ ...., F,. In t e tinted triangle above: F,. -1 vertical lift from comp<>nent main rotor I I I I I supports 1 weight I I honzonta compoc:l('nt : moves h ,copter fOfward ~ I F cos ll - - and sin {) - -1 F F So· FA - FcosO and F,,.- Fs'n 0 lhe horizontal and vertical components of Fare therefore as shoi.\lll below: f ------------- I I _____ ...,• I 8 I fcos 8 ®0 How 1s a vector different from a scalar? Give an example of each. Forces of 12 N and S N both act at the same p0tnt, but their directions can be varied. a What ,s their greatest possible resultant? b Y.lhat 1s their least possible resultant? c f the two forces are at right angles, find by scale drawing or otherw,se the size and direction of their resultant. 3* On the right, someone 1s pushing a lawnmO\ver. a By scale drav~1ng or otherwise, fmd the vertical and 0 b If the lawnmower weighs 300 N, \'"Jhat 1s the total downward force on the ground? c If the lawnmower 1s pulled rather than pushed, how does this affect the total dO\\'nward force? horizontal components of the 100 N force. Related top1cs: vectors 2 .1; force 2. 7 53 E Centripetal force On the lefl, omeone is whirling a ball around in a hori7,ontal c ircle at a steady ·pc~. An inward force is needed to make th~ h~lll follow a t:ircular path. The tcn~ion in the string prc>\·idt.->s this forc e . \Vitho ut it , the ball \\ ould tt-a\·d in a straig ht line, as predicted b) cw ton's first law of motion . Thi~ i~ cxaclly what happ~n H the string breaks. centnpetal f0tce (tens10n 1n stnng) Thi inward lorce needed to make an object mo\'e in a circle i called the centripetal force . Alo,.e centripetal to, e i needed if: • the 111ass of the object i • i11crca ed • the speed of the object is increa.-.ed • the rtuliu · of the cin:h: is rt!duc·ed . ► Wheo a m otorcyde goes round a corner hke this, the sideways friction between the tyres and the road prOVldeS the necessary centripetal force. 0 Centripetal force... Cen tripetal force isn't produced by circular motion. It is the f0<ce that must be suppHed to make something move in a circle rathe< than in a straight line ...and centrifugal force When you wh,rl a ball around on the end of some string, you feel an outward puO on your hand. But there is no such thing as a 'centrifugal force' on the ball itself. If the string breaks, the ball moves off at a tangent. It isn't flung outwards. E Changing velocity Vdocit) i · pt:ccl in a particular dh\.- ction. So a change in vdocit~ can mean either a change in pccd or a c hange in dh "'Ction, a ho\\ n in the diagram belo\\. Diagram B ho,, , \\ hat happens du ting circ ular motion . If something ha a changing \ elocity, then it has acceleratio n - in the same dir<..>ction as tht! force. So, with t:ircular motion, the acceleration i~ towards the centre of the c ircle. lL ma~ be diffi(:uh to imag ine ~o mcthing accderat ing toward · a point withour gL·lling closer to it , but thl: objccr i · alwa~ · moving inward from the po ition it wo uld hm·c had if travelling in a traighr line. B A I force acts at right ang'es ' to d1rect1on of travel u fo,ce act!>., cf rect10n of travel - 0- 0- -o+-o+- o+- -0+. t.<. '/ 54 Cl ..i 10,·, 0-- -0-~ •· c.. " \, 1 --------- Jly C ngC!S change m speed c.hange in d1 rect on no c.hange n direction no change m speed FORCES A D MOTIO Orbits* Satellites around the Earth A a tcllitc tr~n ·cl ro und the Earth in a c urved pa th called a n orbit, a~ hown bcJow. Gravitati o na l pull On o ther wo rds, lhc satellite's weig ht) provid1.~ lhc centripe ta l fm-cl! needed. \ Vhcn a saLellitc is put inLo o rbil , its s peed is carcfull) c hosen so Lha l it~ pa lh docs not take il further out into s pace o r back lo Ea rth . Heavy satellite nee<l Lhc same speed as lig ht ones. li the n1as · is <lo ublec.J , t\\ ice a n1 uch centripetal force i rcquirc<l. but that i ~ s upplied by the d o ubled gravitational pull o l the Earth. Planets around the Sun The arth and o th er planets m o, ·c in a pproximatch cir ula r pa th~ around thl! un . The centripetal ro rce needed is supplied b) the uns g ra vitatio nal pull. Electrons around the nucleus I n a to rn ' ► ncgati\'ely chal'gcd particle called electrons a rc in o rbit around a po~itivclv charged nuclcu . The a ttrac tion between opposite char ge ( 'Omctimes called a n electrostatic force o r electric force ) pro\·ic.Jcs the cent tip •tal force n c<.~ cd . • A satell te close to the Earth orbits at a ~eed of about 29000 km per hour. The further out the orbit, the rONer the gravitational pull, and the less speed is required. ®0 A piece of clay is stuck to the edge of a potter's w eel. Draw a diagram to show the path of the day If it comes unstuck while the wheel is rotating . E) A car travels round a bend in the road. What supplies the centripetal force needed? In question 2. how does the centripetal force change if the car a has less mass b travels at a slower speed c travels round a tighter curve? 0 nudeus A Model of a hydrogen atom: a single electron orbits the nucleus. (According to quantum theory. electron otbits are much more complicated than that shown ,n this simple model.) A The further a planet is from the Sun, the less speed it has. and the longer it takes to complete one orbit. The time for one orbit is called the period. O what supplies the centripetal force needed for a a planet to orbit the Sun b an electron to orbit the nucleus in an atom? 5 A satellite 1s an a circular orbit around the Earth. 8 Draw a diagram to show any forces on the satelhte. Show the direction of the satellite's acceleration. b · If the satellite were in a higher orbit. hovv would this affect its speed? c· If the satellite were in a higher orbit, hovv would this affect the centripetal force required? Related topics: velocity 2.1 ; Newton·s 1st law 2.6 ; force and acceleration 2.7; grav,ty and weight 2.9 ; electric charge 8 .1: atoms 11.1, orbits and sa tellites 11.4 55 Further questions a i De ·cribc: ho\\ changing. lhe force altccts the acceleration. [2] ii \Vr;tc down, in words, the equation connecting lorcc, mas~. and acceleration. 11 J iii U c the data from the g,·aph to E 1 a \ \trite: down. in words, the equalion connecting speed, distance and time. rt l b A car travd at a , tca,h pccd ol 20 111/s . c~ku late the distance tnl\'cllcd in 5 ~- r21 2 The diagn1m sho\\S the pm,itions of a hall as it l'olk·d down a track. The ball took 0.5 to roll from 0111: po. ition to the nc,t. For C\:amplc, it l'olled [rom A to B in 0 .5 ~ an<l from B Lo C in 0. - s an<l so on . a \\'rite down: i the distance tran~llc<l h) the ball from A to E; [11 ii the ti1ne taken b, Lhe ball Lo reach E. I l] b Calculate the a\·e ragc spt"Cd of the ball in rolling irom A Lo E. \\'rite clown the fom,ula that ~OU use and shO\\ )Olff wm·king. r3l c Explain: l ho\\ vou can tdl from lhc: diagrc.lm LhaL the ball b ~peeding up; 11) ii \\ h, Lhc: ball spL·cds up. rl ] calculate the mas~ of thL' trolk), ( 2) b ketch the gr..tph and draw the line that \\ ould ha\'C been obtained 101· a trollc\ of la rgcr mass. r11 4 A car hJ~ a n1a. ~ ol 900 kg. It ace --lcratc. from re ·t at a rate of 1.2 m/ ·1• a Calculate the lime taken lo reach a ,·docit, ot 30 m /s. [ 3] b Calculate the lorcc rt!qui,~cl to accclernw thi.: car at a rati: ol 1.2 nl/s2• [31 c E\·c n with the L·nginc \\orkjng at full po\\ l'l~ Lhc car's acceleration as Lhc: car goc~ f astcr. \ \'h, is this? (3) 5 The diagram hdo\\ shows some ol the force acting on a carol mas 00 kg. d:.rect1on of motion dn._,ng force light se!ho~ , ,, , ,, at this in tant. [ 11 li \:\'1ite do\\n, in \vords. the L-quation connecting ma s, (orcc and force A . tudcnt n1ea. ur-es the accclcrntion of a Lrollc, using the appar·atus above. The light c en. 01 arc connected to a comput1:r which h. programmed lo cakulate the: accdel'ation. The n?suhs obtained aa·c shown on the accderation- rorce graph. acceJeorationlnvi or State the i1;c the total drag lorcc ,, hen the car is Lnn·dling al constant s~e<l. [ I] b The: dri, ing force is inc1\..'asL-d to 3200 ~ • Find Lhc n:sultant lore<: on the: ca1· a l'9ht sensor / ~~ 2000 N ◄~---,€15 ~ -,.·lii ii.-iiiiii.~kibt ,t,-'-,• -.-~•► tota drag force . E 3 dc-cn.:a ~e 6 accdc:ration. [ I1 iii Ca kulate the initial accdcnHion or the car. r21 Explain \\ h\ the car will c,·entualh· reach a nc,, higher constant spL--cd. ( 2] 3N wn::r:r:r.1i::1r:r.rn:m:r.n::m::~nm:rr., .n ........, , .......,.n..•...•. n .....n,rn ....,,. 1:r,;1~m.11.a~umm.;1:m.11:t:1~m::i.:1,;1~:1mL i: ......... ·····•••.. 1 ;;,., . . . . . . . . . . . . . . . . . . . .·. . . . . . . . • ·•• -- • · · · · • ~ 25 t:r.1:111??r.t:I!?11r:r.::11111r:r:1:111t?r.::1u•1?:r: - - - - - - - - -4N i:: :Ll;:::;:~:::::::::i:f!!:;;:; :i -l;:::~; ·:£1::::~ tt.;1.;..i Jlili..ii.,;UJJllit.i.;.lJI:Il:t.;I;.iJI:J".r:i;..I JiliL a 20 t:r.i;iti:ir.t:itilit:r.i;iiiiir:r.i:1::,ir:::i:iiit:r~ r,, .n ..........,1, ......... '"''"'!Jr........... ,, ......, 1:1,;1;.m:m:.:um.:t::.:1.: ::m•.r..m:11,;1,;1.~1::::L , ......._. ........... 1,:......... 101,•.i:,.• , ...........J,.,L I5 gp flHiii~P.ii;!ii~~i{il!;:fH~µgg~r:µ1~iiii~ iH · □ ••'t•••t i•·.,··•t.J' I"I"""''' ·O ♦••·••t -iJ,···· 1:t:1~111.11.:t:umu•.r..umi.:t:1~m11r.;1,;1:.umL ,,......................c:: ......................, ........... 10 P.::R !::1::ml:::~::::~1 !!::::::~:i::1:Jn:::::· tt,;Ll"""":J~.... ,l'""LUZ-'"'t.;LJ'l"l'"Ll:.J"'''t:. t:J.;I.;.:iiii•.lliiii:iii:;i;iJ1iif:r..1:.:i1i1£li..:Miiii~ OS t:r.::1=:rir.i~ii?iit:r.:;:;;;;r:r.i;itiiir.r.i~:;;;:r: ~'!l' ,•it••··· .,,, .......r, ,,.,..., .n,, .......;-;,...,,. µ•.az .::m:1r.;:.:u:1m:.;1;1. 11:1t:t::.:.m:1r.;:.:1~m::L :auz11;.ru.u:11:.::iu::.::1::.1u::aa.::11~:...w-11u- 1 t 2 3 4 S r0<ce/N sing a scale: drc.1wing (lorc'\amplc:. on graph papl.·r), li nd Lhc re ·ultant of the fon:cs abon:. [3] b Ora\, diagram to ~how how, by changing the direction or one of the force~. it i. po.. iblc to produce a resullant ol i 7 ~ ii I i\. [4] © CUP! this may be reproduced for clilss use SOlety for the purchaser's institute FORCES A 7 This question is about PEED and e ACCEL RATIO . A c)de ll".K"' i 500 metre-.. long. A c,dbt completes 10 lap-.. (that is, he I idc-, completely 1·ound the lt-ack 10 tin1cs). a How man, kilornetn:-.. has the t:\'clh,t f 11 t ra, l.' II cd? b On a,·t..•rage it look lht.: c,dist 50 s~conds lo complt.:ll.' one lap (that b.. lo ride round ju-.,t one....). i \ Vhat \\ ._h tht..• averagt..' -..pccd of the cydbt? [2) ii How long in minuh.-... and s1..'conds did it take the cvdist to complctl! 1h • I Olaps? r21 c '\car thl.' l.'nd of tht..• nan t hL' c,disl put on a purl. During this spurt it look the c, di-,l 2 econd-, lo inc1\.'a~ speed from 8 1nl-, to l 2 nv .... \\'hat "a:-.. the C\ dbt\ ac·cdl't ation during thb spurt? [2) E 8 Thb question is about fORCE and ACCELERATIO~. The drhe, or a car moving nt 20 m 1.., along a stn1ight lc,·d road applies the h1akes. The car dcc:dcraces al .1 ..,Leady I ate of 5 m ,s 1. a How long drn.:... iL takt.: the ar lo slop? [21 b \ Vhal kind or fon:L' slo\\S the car <lo\\n? r I ] c \ Vhct\.' i-.. thb 101 CL' applkxl? 11] d Tht..• rna..,s ol the car b 600 kg. \ \'hat is the ..,i,' or the tot'Cc ~10,, ing the car down? [21 9 How will the graph continue after 9 seconds it sht.: is stil1 lalling? ( ll The gi1 l n1ak1.?s a -,econd jun1p with a large, Jrt..'a parachute. he foils 1h1ough the ail (01 thc..• :-.,1mc time bclot • opening her new pan1chute. How will this affect the graph: <luring the fi1. t fot.ff second-,? [ 11 ii artcr this? (I] E 10 a ketch a ,docity- linlt.: graph for c1 car nl0\ ing \\ ith unifonn ac<.:dct'alion h om 5 m s to 2 5 m .., in I :::; ~t..>conds. [ 3) :-. ' thc..• sketch graph lo find , alucs tor i b the ucc ·le1·ation, ii the tot~I dbtanlc t1·a,cllcd du1ing accekn1tion. ho,, clett.-ly al each slagL' how )C>U usl.'d the graph. [ 4) i 11 day~ < Om/s 7 k~ ~ ~ stone ~3 ·9 Ice A ~lOllL' of mass 3 kg is -,liding aero a rroll.'n pond ..,l a pt.~xl of I0 ,n,~ when it collide~ head on" ith n lump of clay of 111a ~ 7 kg. The stone ~ticks to the ckn and the two slid ' on together ac.ross the ice in the same di, •ction a-.. before. Calculatc the lollo,, ing (a-....,umL' that the,~ is no f, ict ion from lhL' icl.'): a The momentum of thl.' tonL' bdorc [2] the colli ion. b The total mom1.?ntun1 of the ..,tone and clay aft1.:r the c.ollbion. [ l] C The total ma~s ol the ... ton. and clay. I] d The -..pc\?d ol the stone and clay afterthe coll isicm. r A girl \\caring a pa1 achutc jumps lrom a hclicopll!1. he <loci.. nol open lhc pan1chuh! straight awa ,. The tahlL· sho\\ s hl.'r sp..·l.-<l du1ing thl.' 9 seconds al h:r she iumps. 12 Jn lhl' diag1'i.un bdow, somi.:one i ,\,inging a ball round on l he end of a piec(' or ~lling. time m seconds speed in m/s f D MOTION 0 a Copy and compll.'tc the tablL' by waiting down tht..· pcL"<l :.,t 2 seconds. 13] b Plot a glaph of ... pced against time. I 1I c How n1an, :-.c onds a I ter ~ he jumpc..xl did the girl op ·n hc1 par'1chutc? Ho,, doth · results sho,v 't his? [2 I d i \\ hat Im· c pulls the girl down? f 11 [ I] ii \ \'hat (01-c~ act.., upward..,? iii \ \'hich o( tht."c (or c~ i..; largcr: :.1l 3 ..,..: onds? :.1l 6 s..:<:<>nlb? ,LI 9 s..:cond..,! [31 57 FORC S AND MO 10 a \'\' hat name is gin~n to tht.• force needed to make the ball move in a circle? [ 1] b Cop, and complete the diagra1n to how \\ here the ball \\ ill tra, cl if the ..,lling br --aks \\ hen the ball i~ at point X. [2] c Plancb move around the un in approximatch· circular orbit . \\'hat pro, ide the lo1'Ce nece a1'\ for the orbit? [ 1J Use the list below when you revise for your IGCSE examinatjon. The spread number, in brackets, tells you where to find more information. Revision checklist Core Level Extended Level □ A-:, Jor Con.: Lc\'cl. plus the following: C Calculating ace ~leration. (2.1) □ Deceleration b. negative acceleration. (2.1) C Calculating accclcralion from the gradient of a spccd-timt.: graph. (2.2) □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ 1casu ,;ng speed. (2. 1) The difference bct,,ccn spc..>cd and vclocil\'. (2.1) Linking acceleration with changing pccd. (2.1) Reprcs ·nting n1otion U!-.ing dbtonce-tin1c and spt."Cd-timc graphs. (2.2) Calculating speed from the gradient of a distancc..--cime graph. (2.2) Recognizing from the shapt.: of a distancctitne graph \\ hen an object i - -,tationary (at rest) - moving at a ..,lead\ "P ·cd - mo\'ing with changing ~peed. (2.2) Rc..-cogni:1ing acceleration and dccclcr·a tion on a speed-time graph. (2.2) Calculating tht.· distance trc.1n~llcd f ram a specd-tirne graph. (2.2) Ilo,\ the acceleration ol free fall, g, is con tant. (2.4) Measuring torcc. (2.6) Tht! newton, unit of Force. (2.6) \Vcight is a gravitational force. (2.6) Air rcsistanct.: is a form of friction . (2.6 and 2.8) How an object mo\'c jf the force on it arc balanced. (2.6) The meaning of resultant force. (2.7) Tht: rc~ultant of two forces in line. (2.7 and 2. I 3) How a fon:c can change the motion of an object. (2. 7) How forces can change hape and \'olun1e, a~ ,,ell a n1otion. (2.7) The effect!-. of friction. (2. ) ~ing the equation weight - ma~~ x g (2.9) 58 C □ C C □ C □ HO\\ an object fall in 3 UJ"lirorrn (constant) gr~n itational field - ,, ithout air 1 '~i tancc. (2.4) - with air re~i lance. (2.5 and 2.6) Terminal ,·clocitv. (2.6) Re ognizing the diITcrl.!nce between uniform (consLant) and non-unifo,m (non-constant) acceleration from the ..,hape of a peed-timc graph. (2.5) MaS!) a~ n..~i tancc to change in motion (2.7) The link bctw(."Cn fore\ mass, and accelc1·ation. (2.7) Defining the nC\\tOn. (2.7) The di ITcrcncc bet wccn wdght and mas-,. (2.9) Calculating mon1cntum. (2. J 1) C C The link bctW(.'Cn force and n1omcntum chang ~. (2.11) C Calculating impulse. (2.11) C The conscn1ation of momentum. (2.12) □ The difft.:rcncc bctwt.:en ,ccto~ and ..,calan,. (2.13) Adding\ c..'ClOl . u ing the parallelogram rule. (2.13) C Motion in a circle, and ccntdp •tal force. (2. 14) a ' Sharks like thi are verv " cfrcctive hunter . Thei1harp teeth give thcn1 a dangerou bite, although because of their longjav.•'s, their bi ti n g ro ,-ce i · not n1uch n1orc than that of a hun1an. Ho,vcver, \\·hen it comes to divingt sharks heat humans easily. Son1e t_rpc can reach depth.. of o,·er 2000 n1ctre , \\·here the ,vat r pre ·sure i - far too great f01· any hum, n diver. chapter 3 59 Moment of a force It i difficult to tighten a nut ,dth ,our finger . But\\ ith a panne•~ you can produce a larger turning effect. The turning ,ffect i C\ en greater if you increa e the lorce or use a longer panner. The tt1171ing eflect of a foa·ce b called a moment. H i.s calculated like 1his: • A large force at the end of a monH.· nt ol a lorn.· about a point long spanner gives a large fot\.' \.' x p\.'l'JK'ndkular di,tancc..• lrom the..· point turning effect. Below, there are !-,Orne examples of fo1·ce and their moment . ~1oments are described a~ clock,vise or anticlockwise, depending on their din:clion. The mon1enl of a force is also callee.I a torque. It 3m 0 l 3N ., moment aboutO =4N x 3m = 12 Nm (dockwise) 0 2m t - 3N 2 moment aboutO = 3 Nx 2m moment aboutO =3N x 2m ■ 6Nm ■ 6Nm (antidod:w,se) (ant clockwise) 4N The principle of moments 0 Unit of force Force ,s measured in In diagrnn1 A below, the bar i~ in a slate of balance, or e quilibrium. , ore thaL the antidock\\ i c moment about O i · cqu.._,l to the clockwi c moment. One turning cftcct balances the orhcr. In diagl'am B, there arc more Force · acting but, once again, the bar i in equilibtiu m. This time, the toMI clock,, ise monient ahout O i equal to the anticlockwise moment nev-rtons (N) 0 The~e examples illuslralc the principle of moments. Taking moments Calculating the moments about a point is called taking If an object i~ in cquilib,;u m: the ~um ol the dock\\ i,c momenL-.. about any point is equal lo the ,um of th\.' anticloc",,bc moment~ about th ..,t point. moments about the point. A i,- 2 m - - - - 4 m--1 6 p SN IO N 10N _ ___,I ...___~ moment about o 10 N x 2 m =20 N m (dnticlockwi~) s 60 moment about o •5 Nx 4 m :20 N m (clockwise} moment about 0 •l0 Nx2m ;::;20 N m (ant1cloc v1se) moment moment about O about O =8 Nxlm =3 N x 4 m ::: 12 N'n -8 Nm tota moment ;:; 20 N m (clockwise) FORCES A D PRESSURE Conditions for equilibrium Tf a n object i · in equili brium, the force. o n it mu ·t bala nce as w "JI a the ir turnin g enl.!C tS. o: • The s um o f th e fo r ces in o ne directio n mus t equ al the !-.um l01·ce~ in the o ppo ite direc.: Lio n. The pli nciplc o t rnom ent mu t appl). • or th e For e xa mple, in diagram A on the o ppo ite page, the u pwa rd force fro m the ~uppo1·t m ust h " 15 N, to ba la nce the 10 • 5 to ta l downwa rd fo r ce. Also, if ) O U ta ke m o m enL1.o a bout ,u,_\' po inL , for example P, the to ta l doc kwise mo m ent mus t equal the to tal antidoc k\\ ise m oment. \Vhcn taking mo m ents a hou l P, yo u nee<l Lo includ l! the m o m l! nl of the up\\ arc.l fo rce fro m the support . This d oesn't a ri!-.C "he n taking m o m e nts abo ut O because the fo rce ha no n1on1enc a bout th at po inL E Solving a problem £wm111le &-low 1ight, ~omeonl.' of weight 500 , is standing on a plank Clockwise .... or anticlockwise? In the d1agra m below, the SOON force has a clockwise moment about A, but an anticlockwise moment about B. To decide whether a moment is clockwise or anticlod.wise about a point. imagine that the diagram is pinned to the table through the point, then decide which way the force arrow is trying to turn the paper. ~uppol'tl.'d b\ two t1"\..'~tk·s. Calculate the upwa1 d f or "Cl.'S, X and L exerted by the t1-c~tk•.., on thl.' plank. (A... ..,tunc thl.' plank has negligible ,,l'ight.) The s,stcm is in eq uilib r iu m , so the princ iple o f m o m ents a pplies. Yo u can take m o ment · a bo ut an~ point. But taking m omcn L"i abo ut A o r B get rid o f o ne of the unkno,\ ns, X or }'. r- 2m ---- 3m --◄ I I 'x y Taking 1110nw111, about A: clockwise m o ment . 500 :'.'[ · 2 m a nt iclockwis ~ m o m ent =Y = I000 N m 5 n1 As the mo me nts bala nce, - Y m - 1000 o: Y m SOON 200 N From here, there ar ~two me thod o f finding X . Either ta ke m o m ent about B a nd do a Ct\lcttlatio n like the o n e abo\'c. use th c lact that X m u~t <.X}ua l the -oo '1 do wnwa rd force. 8\ e ither m ethod: X 300 '! o,- ® 8 A 1 The moment (turning effect) of a force depends on two factors. What are they? 2 WI at is tl e principle of mor:nents? What other rule also applies if an object 1s in equilibrium? 3 Below. someone is trying to balance a plank with stones. The plank has neghg1ble 'h'eight. a Calculate the moment of the 4 N force about 0. b Calculate the moment of the 6 N force about 0 . -2 rn-;;-2 m ~ · 0 •l m----1! G Will the plank balance? If not, which way will it tip? Y (D What extra force is needed at point P to balance the 0 plank? G In 1/-JhicJ\ direction must the force at Pact? In d agram B on the opposite page: a What 1s U'e upward force frorr the support? b If moments are taken about point P, which forces have clockwise moments? What 1s the total cloc \'Vise moment about P? c Which force or forces have anticlockwise moments about P? What is the total anticlockwise moment about P? d Comparing moments about P. does the p,ioople of moments apply? Related top1cs: fotce, balanced forces 2.6 61 I I I I up ward fOfce on rule gravI1at1ona forces on particles of bei:lm Like othc1 object:>, the beam on the left i n1adc up of lot of tiny particle , each with a mall gravitational lorce on it. The beam balances when u pended at one particular point, G, becau c the gi·a\itational force ha\'C tu11'1ing i:ffects ubout G which cancel ouL Together~ Lhc smalJ gr1l\·italional forces acL like a ~inglc force at G. l n other word ·, the) have a r-c ·ultant al G. This r-c ·ultant is the bcan1' · ,vcight. G i the centre of gravit (01 centre of mass). Finding a centre of gravity upward fOfce on rule G (centre of grav,ty) ._ve,ght (resultan o gravitation~ forces) In diagram 1 below, the card can wing frceh. from the pin. \\'hen the card i relea. ed, the fot es on it tu111 the card until it centre of gra\·ity is n:rtically under the pin, a in diagram 2. \ Vhichever point the card b ~u~pendcd from, il \\ il1 ah\'a)s hang\\ ith its cenlrt:? of gravity \'erlicall) under the pin. This facL an be used to find Lhe centre of gra\'it~. l n diagram 3, the cenu-c of gt1\\"it\ lie · ·omc, here along the plumb line, who e po ilion i marked b) the line AB. It the card i u pcnded at a diflerent point. a second line CD can be drawn. The centre of gi·a,it) musl al ·o lie along thi · line, ·o it is at the point whe1~e AB cro · ·es D. upward force from p n s. centre , 1 g avit -----IOm----- I !~ 6,.s m,. 0 3m , ~ I bar s from I centre of support ; mass forct' I I W(we1ght of bar) 62 t) Heavy bar problem To solve Lhc problcn1, rL"<lraw the diagran1 to show all the forces and di · tancc , a in the lo,,er diagrarn. As g 10 l\Ag , rhc J.5 kg ma · ha a weight ot 15 N. • niforn1' means that the bar's weight i e\·enl~· distrihuwd, so Lhe centre of gra\'il) of Lhe har (b) iL~elf) is al the mid-point, 0.5 m from one end. The bar' weight 1\'' act at thi point. take moments aboul the uppor1. 0. The upward fon:c has no mon,cnL about thi point, but the,~ i an anticlock\\'isc moment of 15 0.2 m and a clocl..·wisc moment o1 iv x 0.3 m. A the bar i in equilibliun1: lx 0.2 m \V x 0.3 m • O\\ 15 N I Exmnple If a un iform bar balancL's, a.., on lhl' left. with a t .:- kg ma~~ a t tadH.·d to Olll' L'n<l, w h al is il~ \\ t·igh l? (g I O , kg) kg 0.2 Q i n ~implc problem , )OU a1-c often told thar a balanced bar ha negligible weight. In more complicated problem , \ ou ha\ e to include the weight. I . I centre{; · gra~ ty 2 1 1 centre ,, o: the bar' weight 1\-' L 10 · FORCES A D PRESSURE Stability c~ntrcot ;ravwty This box is in equilibrium. The forces on it are balanced. and so are their turning effects. With a small tilt. the forces will turn the box back to its original position. With a large tilt. the forces will tip the box over. A box with a wider base and a lower centre of gravity can be tilted further before it falls Oller. If the box abo, 1: b pu hcd a little and then relea eel, it tall back to il~ odginal position. It~ po ition was s table. U the box L pu~hcd much further, it topple-... Tt tart~ to lo pplc a ·oon a"i i~ centre of gi11,ity pas ·es overt he edge o f it · ba I!. From then on, the forces on the box ha, t! a turning t!ffoct ,, hich tip~ ii even furthc:r. A ho:\ ,,ith a wider ba...c and/or a lower centre of gn.1, il\ is more table. 1l can be Lilted to a gr~a tcr angle before iL ta11 co toppJc. States of equilibrium Here are three types of equilibrium: centre of 0 gravity Stabte equilibrium If you tip the cone a httle. the centre of graV1ty stays (N(!tl the base. So the cone falts back to its 01ig:nal position. Unstable equilibrium The cone is balanced, but only briefly. Its pointed 'base' is so small that the centre of gravity immediately passes beyond it. Neutral equilibrium Left alone, the ball stays where ,t is. When moved, it stays in its new position. Wherever ,t lies, its centre of gravity is always exactly over the point which 1s ,ts 'base'. --------'O ___ A He w,11 stay balanced - as long as he keeps his centre of graV1ty CNer the beam. 1 The stool on the right 1s about to topple over. a Copy the diagram. sho\.Vlng the position oft e centre of gravity. b Give two features which \Wuld make the stool more stable. 2 A uniform metre rule has a 4 N weight hanging from one end. The rule balances when suspended from a point 0.1 m from that end. a Draw a diagram to show the rule and the forces on 1t. 0 Calculate the "'-t?ight of the rule. 3 Draw diagrams to show a drawmg pin in positions of stable, unstable. and neutral equilibrium. Rela l ed to p1cs: resultant force 2.7 and 2 .11; mass, weight, and g 2.9, turning effects, moments, and equ llJbr tum 3.1 0 According to the prindple of moments: If a s~tem is in equ1hbnum (balanced), the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about that point. Force and moment essentials distance A moment is the turning effect of a force: moment of a force - force x pe,pendicular distance about a point from the point If an object 1s in equilibrium, the forces on it must balance and also their turning effects So • The sum of the forces in one direction must equal tl e sum of the forces in the opposite direction. • The principle of moments must appfy. Testing the principle of moments 9N ~ ,ead1n9 spnng bal~n<e 0 1m 9N 0.2 m-,_.,--0.2 m--99t- - 0 4 m - -- y 200 g X masso meue rule 2N 3N 4N 400g 3009 mass mass Equipment Force d lag mm You can te t th"' pdnciple of moments by can·ying oul an experiment like Lhe one abo\'C. Hcre, ~1 metre rule has been suspended lrom a :,,p,;ng balance. \Veighl~ ha,l! been hung from the rule and their position~ a<ljuMed so Lhat the s~stcm ~ baJanccd it is cquilib1ium. The second diagram ~ho\\S all the forcc on the rule, including thl· \\dght of the rule it-;cH. (Each 100 g of gaavit, i a · umed to \\cigh 1 . ). E The principle of moments ~hould apply about any point. So, for example, choo~ing point X (and omirting some units for ~implicity): 1 • • The 2 .. and 3 . forces each ha\'e a clocku·i.!,e momenl about X. S0 1 ·um of clockwise moments (2 < 0.2) -'- (3 0.6) 3.2 L m The 9 . and 4 ~ torcc.., each have an m1ridockwi e mon1cnt about . o, ~um ol anticlo k\\ i e moment - (9 x 0.2) +- (4 >- 0.1) - 3.2 , r m The l,,o ·um arc equal, a predicted by the pd nciplc. You could C:\prc:. this t"(' ull in another wa,: calling the clock,vi e n1oment posith·e, and the anticlock,d~ -- moment~ negative, the net moment (comhincd total) i. 7ero. FORCES A D PRESSURE Crane problem Exmnple The di:.1g1·am on the 1ight !'-ho,,:--. .., n,iodcl crane. The crane has a counterhalancc "cighi ng 400 , , whic.:h can he n10,cd fU11hcr or clo~cr to Oto cope ,,ith di l fon.-nt loads. (\\'ith no load or counh: rbalancc. the: top !',CCtion ,,oulc.l balance al point 0.) a \ \'ith thL" I 00 , lo:.,c.l ~hown, ho\\ Jar from O sh ould thL" countcrbalanc:(.' be placed? b \\'hat is th(.• maxi1num load the crane can s:.,fdy lift? 400 N load 100N a To prc\l!nt the crane falling o ver, its lop se ction mus t balance at point 0 . o lhe moment of the 400 1'. for ce (the cou nlcrbalancc) rnu ·t equal the 1noment o l the I00 lorce ( the load ). That follow · fro m the principle o f moment . Let x be the di tancc of the 400 force fro m 0 . Taki11g 1110 111e n 1s <lbo111 0 : cl ock\\ ise mo me nt =- a nticlock,, i~e mome nt 400 1'. · x = I00 2m .\" = 0.5 m o: the counterbala nce houlcl bL" placed 0.5 m from 0 . b Let F be the m axin1um load (in '\). \\'ith this load o n the crane, the countc rbnl ance must p ro duce its m n ximum m o ment a bout 0 . o it mus t be the gr calc~t poss ible di ~tance f m m O - in other wo rd~, I m fro m iL. A~ the crane is in equilibr ium, the principk o l mom e nt~ applie~: Taki11g 111011U!nfa about 0 : clock,, i c moment - anticlo k\, i c moment 400 1\ l m - F 2 m = F 200 o: the n1aximum load i~ 400 K . ®0 0 Centre of gravity essentials 0 Although weight is distributed through an object. it acts as a single. downward force from a point called the centre of gravity (or centre of mass) For an object to be stable when resting on the ground, its centre of gravity must be over its base. If an object is pushed, and its centre of gravity passes beyond the edge of its base, at will topple over. In the d agram on the right, a plank weighing 120 N is supported by two 1m~ 1m -- - 2 m____... I I trestles at points A and B. A man Y.'eighmg 480 N 1s standing on the plank. I centre of I a Redraw the diagram. showing all the forces acting on the plank. I gravity I I / of plane I b Calculate the total clod:wise moment of the lY.'O we19hts about A. I c Use the principle of moments to calculate the upvvard force from tl e we,ght weight B trestle at B. of man of plan' =480N = 120N d What is the total downward force on the trestles? e \l\lhat is the upward force from the trestle at A? f The man now wal -s past A towards the left-hand end of the plank. What is the upward force from the trestle at B at the instant the plan starts to tip? g How far is tt e man from A as the plank tips? In Testing the principle of moments on the opposate page, moments were taken about X. Calculate the moments again, only aoout pomt Y. Are the sums of the clockwise and anticlockwise moments still equal? Relat ed top1cs: balanced forces 2.6 ; moments and equilibrium 3 .1; centre of grav1ty 3-2 65 Elastic and plastic If you bend a ruler slighLI) and release il, ii springs back to its original ·hap(:. Materials that bcha\'c like thi arc e lastic. HO\\ ever, thcv wp bci ng cl~, ·Lie if bent or Lrelched 100 far. Thcv either break or become pern1anentlv de1ormcd (out of ~t,ape). 0 Force and weight essentials force is measured in If you stretch or bend Plo,sticine, it keep ils new ~hape. M,uerial · that bcha\'c like this arc plac.tic . (The materials \\C call 'plastics' \\ere gfrcn lhat name because they are plastic and n1ou ldable when hot.) Stretching a spring newtons (N). Weight is a force. On Earth, the weight of an object is 10 N for each In the cxpcdmcnt bdo\\, a steel pring is stretched by hanging ma~ <.:s from one end. The force applied to the ~pring i · called the load. A g i · 10 /kg, the load i I lore, cry I 00 g of ma hung from the pring. the load is increased, the ~pring tretch more and more. Its e :d ens ion is the diflerence bcl\\'ecn it.s sLn?tched and unstrctched h:ngths. ilogram of mass. _L ~ 40 ---;o·~- -----·r-20 mm y___ j__ c; Cl )( extension 2 N lex1d extens on N mm 0 1 10 2 20 3 30 4 40 58 5 66 et 0 1N load l 30l==:::==~==~ -====:==;;;;;;;;;;;; - 201=====;:~==-I '.:==~=== 2 3 4 5 load! N E Tht: reading~ on the left can be plotted a a graph, a abo\'c. p to point X, the graph line has Lhc e feature : • The line j tt~ight, and passe through the 01igin. • If the load i doubled, the cxten ion i doubled, and ·o on. • Extension + load always ha."i the same value ( 10 mm/ ). • EH~I) I ~ increase in load prcxluc~s the same extra extension ( I O mn1). Mathemaaically, these can be summed up as follo,\s: p lo point X, the c.xLcnsion ii:, propo11ional Lo the load. X i • the limit of proportionality. Point E mark another change in the ~pdng' bchaviom: p to E, the spring behaves elaMicall) and returns to it original length when the load is rt>movcd. E is its ela.c;;tic limit. Bcyon<l E , Che spring is left pcrmam:nll) strcrchcd. FORCES A D PRESSURE Hooke's law* Jn lhe 1660 . Rob e11 Hooke inve~tigaled how pdngs ~nd wires tretched when loads were applil.!d. H e found th at, for man) ma teria ls, the e xten ·io n a nd load wcn: in proporLio n , pro, idcd the d a,;tic limit \\cl~ not l! Xcccdcd: C: ~ C CJ X CJ A nlat(.'rial obeys Hooke\ law if, bl'nl'ath its daslit: li1nit, the (.'\ll' thion b proportional lo the load. load A Extensio~oad graph for rubber teel \\ ire.s do no t l n! tch a muc h a~ stt!d pri ngs, but they o bey Hookc's law. Glass and wood ab..o o bey thl! la w. but rubber <lol's not. E Spring constant Fo r lhc s pting o n the o ppo~itc page , up to poinl X o n the g raph, di\ i<ljng the load (fo rce) b) the cxtcn ·io n alwa~ g i\ c ' the same , a lue, 0 . 1 r-..Jmm. Thi ~ i~ called the spring constant (s)mbo l k): In S) mho b,: F- k xx K no wing k , yo u co uld use thi~ equ ati o n to calcula te the exlens io n produced by any load up to the limit o i pro po rti o nalit). Fo r example. for a load o l 2.5 r : 2.5 - 0. 1 exlen ion Rcarr~ngl!d, chi!-. giYcs: e xtension (on1itting unit for implicil\') 2.5/0 . 1 2- mm Compressing and bending* Ma1eria b, can be compn!ssed as well m. stretched. If th e compr~s~io n is elastic , lhc matc1ial ,, ill re Lum to iL-, o rigina l sha pe when Lhc lo rc cs an: re mo,·cd. \Vh~n a mater ia l is bent, th e applit.xl for cc produce compres io n o n o ne ~ide and s tretc hing o n the o th er: If the clas lic linl it is exccooc<l, the bending b pen11a nent. Thi can happen,, hen a m etal hcet i de nted . A The Onental Pear1Towe< in Shilngha11s CNer half a kilometre high. In high wnds. its top can move by a quarter of a metre. But being efastlC. its steel and concrete structure always returns to its original shape. ® 1 What 1s meant by an elastic rraterial? 2 What 1s meant by the elast;c limit of a material? 3*Look at the small graph dt the top of the page. Does rubber obey Hooke's law? Explain how you can tell from the graph whether thrs law 1s obeyed or not. 4 The table on the right shows the readings taken in a spnng-stretchmg expenment: a What is the unstretched length of the spring? b Copy and complete the table. c Plot a graph of extension against load. Related topic$: forces 2.6 ; mass, we.ght, and g 2.9 d*Mark the elastic limit on your graph. O Over which section of the graph line 1s the extension proportional to the load? 0 What load '-NOuld produce a 35 mm extension? 0 What load '-NOuld make the spring stretch to a length of 65 mm? load/ N length/mm 40 extension/ mm • • Block · A an<l Bon the left arc rc-,Ling on soft ground. Bolh \\dgh LhL" a,nc and L''.e11 the ame lore~ on Llw ground. But the rorcc rron1 block B i pl"cad o,c-,· a larger area, o the lorce 011 each square IIU!tre i, reduced. The pre sure under block B i le ·, than 1haL und ~r blo k A. For a lon~c acting at right angl'-'"' to a .,urtace, the prcs m-c b calculated like thi : F A ( ) and an:a in ~uarc m~th.: (n12). p i e sLu·c i~ mca w·ed in nc,, ton/squa1~ metre(, nl). l /nl j called 1 pascal (Pa): if lorce is mca urcd in Ill:\\ tons lfa lOON [on:-c is pread O\L'ran area or I rn1, Lhc p r'L--s u1\: is rt a 100 J torcc b pread O\'Cr an ~wca of 2 ni, the pre ' urc i II a 100 J l orcc isspr~ad o,~1-an m"l.'a of0.2m2, 1hcprc.-~urc i!-. 11 a 200 t lon:c is spn~acl o, L'r an area ol 0.2 m 2• the pr\~. ~u1'l! is 100 Pa. 50 Pa. -oo Pa . JOOO Pa. For most p1'l!ssurl! ml'a~ur\!menl..,, the p3sca] i~ a , ·e n small unit. In practical situation...,, it i., ohcn more con, enient Lo u~L" the kilopasc-al (kPa ). l kPa - 1000 Pa Redudng the pressure by Increasing the area lncreas;ng the pressure by reducing the area The S[uds on a footba boot ha\'e on y a SITIJII Sl,,;as have a l..trge area to r~uce the prt'Ssuce on the snow so that they do not area of contact with me ground. The prcS~ure ~ir,k in •oo far under the S[uds IS h19h enough fo, lhem 10 sin · into the ground, wh h g ves e;.tra gop. The area under the edge of a ·nife·s blade 1s extremely sma . Beneath 11. the pressure e, I 19h enough fo, the bi~ to P\JSh easily through the mater al Under the tiny area of the point of a dra\mng pin, lhe pressure 1s fat too hfgh f0t the y.•ood to Withstand. 68 I Wall foundations h c1~ a large hofizontal area. This reduces the prt"SSure undern~th so that me walls oo not sin further nto the ground. A load-spreading washer ensures that the nut 1s not pu11ed into the wood when t,gntenC!d uo. FORCES A D PRESSURE Typical pressures 20kPa Pfessufe problems £\·a mph> I The \\ ind prcssun.: on the w;.111 on the right is I 00 Pa. If the wall has an an:a o f 6 111 2• what is the lon.:1.~ on it ? To oh c thi problcn1, , ou need to rearrange the pre_ ure equation: force . p t~ · ure x area - I 00 Pa x 6 m2 - 600 ~ o rh e force on the wall is 600 £ \·m11ph>2 ,.\ conc rete hlock has a n1ass ol 2600 kg. If the hl oc k ml.·asun.:s 0.5 m by 1.0 m b, 2.0 m, what is thl.· maximum prcs~un.• it can l."Xl.'11 when rt..'sting on lhl.' !?,found? (.1= 10 , kg) As g i I O N/kg, t he 2600 kg block ha a weig h t of 26 000 f\ , o the force on the ground i a l o 26 000 ~ - To exert 11zaxi11111111 pt~s ure, the b lock mu ·t be re ·tin g on t h e s ide wit h t he s111alle.,t area. Thi b t h e ide measuring 1.0 m x 0 . - m, as ·hown o n l hc 1;gh1. IL~ area . 1.0 m x 0. - m 0. - m 2• force area 26 000 1~ 0.- m - 52 000 Pa So the maxin1tm1 pre • ure i 52 000 Pa, or 52 kPa . Assume that g - lON/kg, and that all forces are acting at nght angles to any area mentioned. 1 A force of 200 N act s on an area of 4 m2 . a Wha t pressure is produced? b What would the pressure be 1f the same force acted on half the area? 2 Wha t force is prodU<ed 1f: a A pressure of 1000 Pa acts on an area of 0.2 m 2 ? b A pressure of 2 kPa acts on an area of 0.2 m 2 ? 3 Explain ,,-.,hy a tractor's big tyres stop it smkmg too far into soft sod. 4 A rectangular block of mass 30 kg measures 0.1 m by0.4 m by 1.5 m. a Calcula te the weight of the block. b Draw diagrams to show how the block must rest on the ground to exert i maximum pressure ii minimum pressure. c Calcula te the maximum and minimum pressures in part b Relat ed top1cs: force 2. 6; mass, weight. and g 2.9 69 Pressure acts in all directions. A liquid i held in it container b, il~ "eig ht. Thi cau c pre, urc on the containc1; and pt '~"urc on an,· o bject in the liquic.l. The 1ollowing propc11ic apply 10 an, ~tationa1,· liquid in an opl'n container. The exp . .1in1cnts on the l •t t demon lr~uc lh1 ..c of them. Pressure increases wi th depth. Pressure acts in all directions The liquid pu~hc~ on l.!\CI} ~urfocc in contac; t with it , no mau~·r "hic;h \\i.l.Y the .sm fa ct." i!:-. fa cing. For t."xampk·. thl" dccp-M.:a , ·c~sd Ix-lo\\ ha~ to,, ith.sland Lhc t:n..1-..hing effect ol .SL'a waLcr pu,h i ng in on it la orn all idc ·, not .i u t do\\ ll\\ arc.ls. Pre ure increa cs ,\rith depth The dc"p"r into a liquid you go, the gn:atcr the weig ht ol liquid abo\' • and the higher 1h • pre~ lff'"'. Dam:-. are mad' l hick~r al l he bott om to ,\i1 hMand the hig her pr· '!--:-.urc then.:. Pressure depends on the densil , of the liquid fhl' moi~ den-.l' Lhc liquid , the hig hc1 the pres~ur~ .u anv panicuJar c.lcpth. • The pressure at points A, 8, C, and O 1s the same. ► Deep-sea diving vessels are built to wi thstand the crushing effect of sea water whose pressure pushes inv"ards from all direct1ons. 70 Pressure doesn't depend on the shape of the container \ Vhatcvcr Lhc shape or ,\idth, Lhe prc~-..ure al an\ partit.:ular depth is thl: saml: . FORC S A D PRESSURE Useful connections Pressure and weight essentials For calculations hke those below, yoo need to know the connections behveen these: volume (1n m3) density On kg/m 3) mass (1n kg) \l\l'eight On N) g (1 ON/kg) For a force act ing at right angles to a surface: For example, you might know the volume and density of a liquid, but need to find its weight. For this, the equattons required are: dens1 t - mass Y volume pressure - force area weight - mass x g If force is in newtons (N) and area m square metres (m2), then pressure 1s 11 pascals (Pa). From these equations, 1t follows that: mass - density x volume E volume weight - densify 0 g Calculating the pressure in a liquid The conta iner o n the righL has a ba c m~ a J\ . l t i · tilled to a depth I, \\ith a liquid o i den it\' p (G1\.~ k letter 'rho'). To calculate the pre ure o n th • base due tot he liquid , you fir t need to know the weight of the liquid on it: volume o l liquid ba c .. rca x depth - Ah ma~~ o f 1iquid - den~ity x volume So: ,, eight o f 1iquid mass force on ba c /'6JV1 g = pAh = 1~ Ah <..~ = I O \!/kg) depth This fo rce i~ acting on an area A , ~o: pre. ·urc - force area Al a depth /, in a liquid ol den i ty 11. o r, for a change in d epth u./1 , the change in pre Ull: h ~>; g~ II base ared A Example It the den,itv of wa h:r is I 000 kg/m , what i~ thL' pn:ssu, ~ d ue to thL' water ..,t thL' botto m of a swinun inl.! pool 2 m til.·L'p? prcs~ur~ = pgl, = I000 kgtm·' x IO , 1kg x 2 rn g 20 000 Pa 1ON/kg; density of water - 1000 kgfm 3; density of paraffin - 800kgfm3 ·1 In the diagram on the right: a How does the pressure at A compare with the pressure at 8? b How does the pressure at B compare with the pressure at D? c How does the pressure at A compare Wlth the pressure at C? d If the water in the system i.,rere replaced with paraffin, how VvOuld this affect the pressure at B? 2 A rec tangular storage tank 4 m long by 3 m wide 1s filled with paraffin to a depth of 2 m. Calculate: a the volume of paraffin b the mass of paraffin c the weight of paraffin (> the pressure at t e bottom of the tank due to the paraffin In the diagram on the right, calculate the pressure at B due to the water. ·-·A- - - - - - C lm _L ·-· B- - - - - - -0 - 0 Related top1cs: density 1.4: mass. weight. and g 2.9; pressu,e 3 .5 71 can .-_-_-_-_- ---)• air removed by vacuum pump atm<>!>phcnc pr~SUfl' cru!thes can The atmosphcn) i, a deep o cean of air which ~UITound~ Lhl.• Ea11h. ln some \Ut\ ~. iL i~ like a liquid: • It~ pre sure acts in all direc tion . • It~ pr(' ..,ure occoru~s le · a you ri e up thro ugh it (bccau c thcre i le . and k~ ,, eight abo, c). liquid, air can h .. compn:!---..,cd hqum,hcd). Thi:-. make, lhc atrno~phcrc clcm,cr al lo,, er le, d~. The atmosphere ~trctchL~ hund1·ccls nlike :i of kilomctrl:s into ,paCl.'. yet the bulh. of the a ir lie~" ithin abo ut 10 ldlometn:~ of thc E::u·th' .& Demonstrating atmospheric pressure W'hen the a,r 1s removed from the can, there is nothing to resist the outside pressure, and the can is crushed. urfocc. Atmospheric pressure At ('a lc,d, atmo phcdc pre ~urc i about LOO kPa (100 000 ne,,to n~ per quare men "' ) - cquhalcnt to thc \\eight o ten car p1' ing on e,·' I'\ ·quar .. mctn'. But , ou ar ' n't c rush xl b, t hi~ huge prc~sure be ' UU!'IC it i~ match<.-. <l bv Lhc pn: !'\~Ur ' in your lungs nnd hloocl ~\'~tern. Vawum cleaner A fan lowers Drinking through a straw You exp d rour lu gs to reduce th r pressure inside th straw As a ,csu t atmosph r c pressure pushes hq d up t 72 S1raw a r prnssure JVS beyond bag The a•mosp re wshes in, carry ng dust and d rt w th ,t The bag c·s <1s a , rcr. stopp ng t dust nd d , but not the a FORCES A D PRESSURE The mercury barometer Instrument:-. that mca~urc aln1osphcdc prc.s~u, • arc called barometers. The barometer on the right contain the liquid metal n1e1'ClU)'. Atn10 phcrk p1 ~ ~un: ha pu hcd mcrc-ul) up the tube b<.'CaUM! the ~p,lcc at 1hc top of the tube ha no air in it. It i a acuum. At ea le\'cl, atn10 phctic pt\.~ urc ,, ill upport a column of m "t'Clll") 760 mm high, on ,weragc. For convenicncl', cicnti l omctimc de ribc thi a a pre urc of 760 'millimclrc of mel'Clff)'. How~\'cr, it i easily con,erh.'CI into pa.scnl~ and other unit , a )OU can cc below. Barometer The actual value ot atmo pheric pl'c urc ,·aiie ·lightJ) dc:pending o n the weathc1: Rain cloud form in large area~ of lo,,cr pr· ~urc, o a fall in the barometer reading ma) rncan that rain is on the \\'a). Atmo phcric pre urc al o dtX1 'a . .~ \\ ith height abo\'c ea le\'cl. Thi idea i u 1.."CI in the altimeter, an inst1un1cnt fitted in aircraft to 1nc~ure ahitude. • - - vacuum - mercury Standard atmospheric pressure The p1 · m~ that ,dll support a colun1n of met-cur, 760.0 mm high i known as standard atmospheric pressure, or I atmosphere ( 1 atm). It \'aluc in pa.-,cal can be found b) calculating 1he pre ure due to uch a colunu1. At a depth I, in a liquid ot den ity p , the pre ure /~/,,where ~ i 9 . 07 ·1kg (or 10 /kg it Jc accurac\ i needed ). A the dcn~ity of mercury i 13 590 kg/n1', and thl' height or the column is 0.760 0 rn: I atm = 1,t:h - 13 -90 kg/n1' x 9. :)07 '/kg x 0.760 0 111 - - glass tube I l ManometM 10 1 300 Pa Jn calculation , for ·implicity, you can a~~un1c that J atn1 - 100 000 PJ. In weather tot\."'Ca ting, the millibar (mb) i often u cd ns a pre w·e unit. l rnb - 100 Pa, o tandard atm~phctic pre lll'! i approximatdy 1000 milliba, . height d1f erence The manometer an mm of mercury _ L - r = excess pressure A manometer mca~un:s prcsstffc diflerence. The one in the diagram on the right i filk"CI ,dth mcrcun. The height dHJ~tcncc ho,, the exlm pre .su1~ that the g as ~uppl~ has in addition to atmo~phcric pr\! Mn-e. This "'\lt'n p1\:' urc i called the exec s pressure. To find the actual pre urc ot the ga ~upph, you add atniosph tic prcssun: to thi~ ' '\Cess pressure. 1 1 Wnte dOl/m two ways in which the pressure m the atmosphere i~ lil-e the pressure in a hquid. 2 Explain •.-\lhy, when you 'suck' on a straw, the liquid travels up it. 3 If a mercury barometer were carried up a mountain, how 'NOuld you expect the height of tt e mercury column to change? 4 Look at the diagram of the manometer on this page. If atmospheric pressure is 760 mm of mercury: a \Nha t is the excess pressure of the gas supply (In mm of mercury)? b Wha t is the actual pressure of the gas supply [In mm of mercury)? c \-Vhat Is the actual pressure of the gas supply (m Pa)? 5* If, on a particular day, atmosphetic pressure is 730 mm of mercury, what is this a m pascals b in atmospheres c ,r millibars? 6 rhe densaty of mercury as 13 590 k~m3, the densaty of water is 1000 ·,;,m3• and g 1!> 9.81 N/kg. a What is the pressure on Pa) at the bottom of a column of water 1 metre long? b If a barometer 1s made using water instead of mercury. and a very long tube, how high is the water column when atmospheric pressure is l atm (760 mm of mercury)? Related topics: density 1.4; pressure 3.5, calculating the pre$Sure in a UQuid 3.6 73 \¥hen dealing \vith a fixed mas of ga~. there an: always three factors to consider: pre.\5llrf!, 1•0/1111,e, and le111pem1ure. A change in one of these factors always product.-s a change in at least one of the 01 her ·. Often all three change at once. This happen , for example, when a balloon ri 'c · ctuough the atmo ' pherc, or ga.sc · c, pand in the c. lindc, of a car engine. Thi p1~ad deal · \\ ith a si1npler case: how the prcs ' urc of a gas depends on it \·olu rnc ir the temperatutc i · kept constant. The link between the pre ua 'and the volume can be found from the follo,dng experinlcnt. Linking p~essure nd volume {at constant • VVhen this balloon rises, the pressure, volume, and temperature can all change. The equipment for the expe,;ment is .shown in the diagram below left, where the ga~ being ~tud ied is a fixed 111ass of d0 air. The air is I rapped in a gla ·· tube. ll · ,olumc i · reduced in stage by pumping air into the rc ~crvoir o that oil i pu ·hed fur1hcr up the tube. Each time the voluml" reduced, the pre urc of the trapped air i 1nea ured on the gauge. eressure glo~i; tube l( volum~ scale pressure ) auge air rom pump oil of mpera ure) - volume kPa cm 200 so 250 SOO 40 25 20 1000 10 400 reservoir 0 volume/cm 3 50 ua hing the ~•ir \\atnl it up lightlv. o bcfo, taking each reading. \ OU have to wait a IC\\ n1oment~ for the air to return to its 01iginal tenlperature. The gauge actually mea ure the pre urc in the re erYoir, but thi is the same tL'> in the tube be au ·e the oil tran ·mit ' the pre · ure. bovc, you can ~cc some tvpi<.:al readings and the graph they produ c. E Re ·ult~ like chi · ·how that the relationship between rhc pre su1'l." and volume i an inverse proportion. It h.. the c feature : I I TI the volume hal\·e , the pre. ure dnuble , and o on. 2 Pre ·.\ ure x volu111e ulwa \· · ha · the ~ame value ( 10 000 in lhis a ·e). 3 rt pres.\11re is ploHcd again'-;t _J_, the gr"1ph is a straight line volume . . ,·olu111e through the ong1n, as shown on Lhc left. The findjng · can be expressed a a la\\: r01· a h~cd m~ss of g.l ... at con ... tant t1.:n1pcnllun:, the p1 •:-.:-.urc is in\'crseh propo11ional to the, olumc. This is kno\, n as Boyle's la, . 74 FORCES A E Here is a nolhl'r wa~ o f\\ ri ting Bo~ lc's Jaw. If the prl.'ssure o f a ga s c ha nge!) fro m p 1 to p 2 "he n Lhl' \'O]ume is c ha nged from \!1 to V2 : Pressure essentials pressure - j.., a tmo~ phc tic pre 1 a tm Als o: p2 - llli ' pre u1 .. due to 20 m o f \\ a te r 2 a tm . 3 atm 1 atm, V1 = 2 c.: m 3, and \/2 i., to be found. As the tempera ture docs no t c hang e, Boyle's la\\ a pplies. p 1 x \1 1 = p 2 x V2 o: 3 1 Pa - 1 N/m 2. l.'qui\alent to the pn.."Ssm-e Irum a column of water 10 m dtX'p. Tn thi cas ·: p 1 2 Thi~ g in.· s \'2 = I ; \/2 force area 0 If force is measured in newtons (N) and area in square metres (m2). pressure is measured in pascals (Pa): £mmr,/e An air huhhll.! h~,s a \olumc ol 2 (.:m ' whcn rclcu ...cd al,\ depth of 20 m in watc.:-1: \\' hat will ils \·olumc he \\' hen it reaches the su,·fru.:c ? A sume that the LL'mpcrnturc doc~ not change and that atmosphl.'ric pn.-. sun: D PRESSURE Standard atmospheric pressure, called 1 atrnosphere (atm). is approximatety 100 000 Pa. o: (at co nMant tcmpcnllurc) (omiLting units [or simplic ity) 6 , so on Lhc: s urface, the: \'o lumL' o f the bubble i~ 6 en'\''. Ex la"ni g Boyle's law* The kinetic theory. ~ummalizcd on th "' light, e'\pla in: Boyle' · law Jike this. Tn a ga!'> , the m o lecules an: con~tantl) striking and bouncing o ft ~he walls o f the co n1a inc1: The lorce o f the..~ impact'-> ca uses the prl.'. sure. H Lhc \'o lumc o[ the ga., is hah-L-<l, shown below, thc:n: arc t\\ ice as n,an) molL-culcs in a., each cubic 11u! tre. So, c:vcr~ ·econ<l, Lhe1'C a rc t\\ ice: as many impac ts '" ith each M}UaI c mCLn: o l the conta iner wa ll ·. o the pre, ur-c i · doublL-d. A ga~ that cxac tl) obe) s Bo~ le's law i~ called an ideal gas. Rea l gase come d o e to thi · pro, ided the~ ha,·e a lo\\ d e n i~ . a tcrnpcra tu,-c well above the ir liquct\ ing point, and arc not lull of \\ atcr vapom: n k 1he e condition arc n1e t , attraction~ be tween mole ulc affect the ir h --havioua: An idea) ga~ hm, no a tt rac1ions b 'l\\ CCn ils mo lecules. 0 The kinetic theory According to this theory, a gas is made up of tiny, moving particles (usually molecules). These are spaced out with almost no attractions between them, and move about freely at high speed. The higher the temperature, then on average, the faster they move. volume hdlved pressure doubled 1 If you squash a balloon, the pressure 1ns1de ,t nses. HO'..v does the kinetic theory explain this? A balloon contains 6 m3 of hehum at a pressure of 100 kPa. As the balloon rises through the atmosp ere, the pressure falls and the balloon expands. Assuming that the temperature does not change, what is the volume of the balloon when the pressure has fallen to a 50 kPa b 40 ·Pa? 0 0 l he readings below are for a faxed mass of gas at constant temperature: pr~sure/ atm volume/ cm3 4 10 40 a HO'.-v can you tell that the gas obeys Boyle's law? b Use a calculator to work out values for 1/volurne. P1ot a graph of pressure against 1/volume and descr be its shape. Related topics: pr1?S.Sure 3-5; air pressure 3.7; ldnetlc theory s.1: temperature 5.2; water vapour 5.8 75 i n Further qu 1 The diagram ~ho\\~ a pair of nutcr.ickc~. Force~ Fan:- applied lo the handle~ or the nutcrac~ct .. F ----.....~,~ - .......... \\'hat is the pre sur·e on the <lher al tll:pLh of O n-1, JO rn , 20 rn, and 30 in? (2] 3 b At the urfacc, the bell hold 6 m or air. If the bell i IO\\Crcd to a d •pth of 20 m, and no n1orc air i, pumped into it, what \\iJI be the volmne of 1hi: trapped air-? (Assume no change in tcn1pi:ralttrc.) [31 a ~ ---..:..___ E 4 Tht: Iib'ltre hows an e1nply \\ heel barrow "hich "cighs 80 . The op ·rntor pulls upwards on th • handles "ilh a fm-cc ol 20 , to keep Lhc handles horil'ontal. F a The lorccs on th" nut arc bigger than F. E,plain this. f Il b The nul docs not crack. talc two changL"s that could be made to crack the nut. f2] 2 The diagram bdo\\ ~ho,, a uniform metre 1 ule, \\eight U', pi\'Oll--<l at the 75 cm mark and balanc~xt by a lorcc of 2 ~ acting at the 9- cm mark. ,r-----------.1.------r 1 -- 0cm 50cm 75cm 95cm 20 N l. \ [-- - - - - - LSm . a ... ~• M - - - - - .\_ _ _ _ _ _ 2N ~ .A:. ~ • .-el grounc Copv the figurl' and draw a, ro,,·s to how the other t\,o, crtkal force that act on th' \\ hcclbatTO\\. [21 the moment of the 20 , fon:e ahout the ccnLrc of the\\ he-cl A, ii the distance bcl\,ct.•n point~ A an<l M. [3] i forcc about the phot. f21 b sc the pdnciple of n1oments to calculate the, al tu: of iv in , . [21 3 The diving bell belo\\ contain~ trapped air at the ~ame pr~ ~ure as the ,,ater out ide. At the sudacc, afr pre, urc b l 00 kPa. A, the b •JI descends, the prcs!'lure on it incr •,1sc~ b, I 00 kPa f01· evc11 I O m of dcpt h. cab&e from ship upwards pull b Dctcrniine w a Calculate the n1omcnt of the 2 The point marked M. i thl' centre of gr~ vity of the\\ IK-clbarrow. 5 The I ollO\\ i ng re ult!', ,\ ,._-rl.:' obtai ncd \\ hen a pring ,, a ~trctchcd. load IN 10 3.0 4 5 6.0 7.5 length of spring /cm 12.0 15.5 19.0 22.0 25.0 a Use the 1'\:sults to plot a graph of length of spring against loa<l. ( I] b u~l· the graph to li nd the water 6 a i unloaded length ot the ~pring, [ 11 ii c,tcn,ion produ cd b, a 7 .0 · load, [ I] iii load required to incn:asc the length ol the ,p1·ing b, - .0 cm . [ I] A glass ,,indow pane CO\'L"rs an area of 0.6 m 2• The force e~c,1c<l bv air pre u re on the outside ol the glas~ \\indO\\ panl' b 60 000 ~ - Calculate the prc..,sm~ of the ail: \\'dtc down the forn1ula that ,ou u~c and show )Our working . rJl © OUP: this may~ n?produc:~ for class uS@ sol@ly for lh@purchaser·s lnsutul~ b E,plain whv the" indo\\ does not break under this l 01-ce. [ 11 7 A litne enthusiast i lr\ ing to 11\:ngthcn her calf n1u~c1c~. he u~cs the exc1· isc machine below. Her heels apph ~1 for e lo the padded har. This lihs the hca\'y \\Cigh ls. The prcssun.· on thL' ground from stack B is _ _ _ the pre~ urc from ·tack A, bccau..,e the area in contact "ith the ground [or B is _ _ _ tor A. 131 b \\'rite down, in word , th • •quation connc ting pr ' !-ISlffC, for e, and area. C end of horizon al sicel bar F m 0 25 •· .•• padding for bar r11 [f the ,,eight or slack A is -oo ' and the area in contact with the ground is 200 cm 2 , calculate the pn.~ u1~ on the ground i n ~ /c1n 2• [2I 9 The figtu\: sho\\ s a t, re usL-<l on a large earthmoving ,chicle. pivot metal frome tyn. 250 N wetghlS a The centre of grn\ity of the \\eights is at Ora\\ a <liagt"anl to sho\, where and in "hich direction the lorce of g1~\\ it) acts on the \\eight . Labd thb force lV. (21 b The ntHTO\\ ~tccl bar is padded. \ Vhy doc this I •d mon: comfm·tahlc \\hen lifting the\,cights? f2l E c The heels pn:ss again,t l he pad wil h a fon:e rand cause a tu1Tiing effect about the ph ot. Calculate the \alue ol "hen the \\ eighh are in the po it ion hown in the diagram. ho\\ \'Our" orking. I d \ Vhy doc!-1 it b •come hm·dc1· to lift the weights\\ hen thc~ mo\'c to the dght? [21 r r3 8 Three concrete block can be tacked in dirtel\:nt "ho\\ bclo\\. "a, ~, n / I/ A B LI I/ a less than the same as \ \'hen the \'ehiclc is loaded, the art:a of each t, r~ in contact with the gl'ound is a 1 ·ctangle ol klL.., 1.0 rn and 0.5 m. 1 ~tlcuk,tc l he area in m 1 of contact of one l~ 1 • " i th the ground. ii The v •hide ha" four of these t,r·cs. alculatc the to1al an.~a in m 2 of contact "ith l he g1·ound. [4 J b \ Vhcn the \'Chicle is loaded, il \,cighs 100 000 . . l\\ o / a roore than op,· and complck the p~u-agr-Jph bdo\\ using a ph1--a"c lt'Onl 1he bo,es abo,~. Each phrase n1a, be used once, mot ' than one· or not at all. The Iore· o( ~tack on the ground b _ __ the for e ot ~tack B. akulale the p1~s..,ure in :\ 1m 1 c,ertL-<l on the ground b) the l\re:-,. [31 10 A rL"Clangular storage lank ha~ a base mea uting 3 m b • 2 m . The tank i filled with wa1er to a depth of 2 m. The dcm,it, of the wat ·r b J000 kg/m \ and g b l O ~ /kg. Ora\\ a diagram of 1hc tank with the wat 'r in it, and mark all the din1cnsions on) our· dt1l\\ ing. Then caku late the Jollowing: [ 2] a The \olumc ol \\ater in the tank. b The ma~ or \\atcr in the tank. (21 c The \\ eigh Lof "ate1 in the tank (in ~). [ 2) d The p1-c~,urc at the botton1 of the lank. [2] n Use the list below when you revise for your IGCSE examination. The spread number, in brackets, tells you where to find more information. Revi ion <:hecklist Core Level Extended Level □ As For □ Facton. aftccting the moment (turning effect) of a rorcc. (3. 1) Ho,, lo calculate the moment of a □ force. (3.1) □ n1on1 'nt . (3. l and 3.3) □ Apph ing the ptinciplc of moment to a □ balanced beam. (3.1) The conditions apph ing wh •n an object is □ □ □ □ equilibrium. ( .1) The meaning of centre of gra\'it,·. (3.2) Finding the centre of grc.1,~t~ of nat sheet bv c,pcrimcr'lt. (3.2) Ho,, the po it ion of the centre of gra, ity all cc~ tab iii ty. (3.2) Ho,, force can produce a change in i:te □ and shape. (3.4) Ho,, the extension changes with load when a spring is stn:tchcd. (3.4) □ Ho,, to obtain e,ten ion.load graphs b · experiment. (3.4) □ □ □ □ Ho,, to int 'rprct ext 'n ion-load graph . (3.4) Ho,, pre urc depend on force and area. (3.5) Using the equation linlcing pn:ssun:, force, and ar\:a. (3.5) Ho\\ the pre un: beneath the urlacc of a liquid change with depth and den □ it) ore Le\ cl, plus the lollowing: oh ing problem u ing the principle of ol the Jiquid. (3.6) De cribing, u~ing ideas about particles (molecules), how thl! pn~ssun.c? of a gas changes" ith volume when the tcmperalun: i kept con~tant. (3.8) Tc ting the principle ol moment b\ c,p •rimcnl. ( .3) □ The meaning or spring constant. (3.4) □ Using the equation linking extension, load, and the pring constant. (3.4) □ The meaning ol limit ol proportionalit\. (3.4) □ Calculating the pr urc at a pa11icular d 'pth in a liquid: the equation linking pre ·sure, depth, and g (3.6) □ How, ii a gas is al constant tcmper-c.1ture and obcv · Boyle's la,,, pV is constant. (3.9) □ Using the equation p 1 \11 - p 2 \1 2 for a gas al con tant ten1peraturc. (3.9) The iagara Fall , on Lh SACanada border. The photograph ·ho,\' the highc t cction of the fall , ,vhcrc the ,vatcr tumbles over 50 metres to the d,·e•- belo,,v. early three n1illion litres of ,vater flo,v ovl;r the falL every ·econd. MosL of the nerro is ,vast d. but . omc is harnes ·ed b. a hydroelectric po,ver tation \\'luch generate clecllicity for the sun·ounding area. chapter 4 79 Work · J of work IS done v.ihen Jn cvcn:da, language, work might he \\li ting an ~ !-,a\ or digging th' garden . BuL to ...,cicnlist~ and eng inc.:er~. work ha~ a prccb~ meaning: \\·ork is <lone"" hcnc\'cr a lo1·ce make!-. ~omeLhing mo\'c. The greater the forc.:l" anc.J the gn:atL'r LhL' <li~tance moH.-<l, the mon.· \\OI k i!-1 done. , force oH N The 1 uniL o( ,, o rk i Lhe joule (J): l jou)~ or work i-. done when a fOl'Cl." of 1 rlC\\ ton (:"\ ) 11)0\ l'~ ohic l I mctr~ in the di1 cction ol the lorcc. ..ul \\'ork i~ cakulated u ~ing 1hi~ equation: I kilojoule(kJ) 0 - 1000 J (1 o-- J) 1 megajoue (MJ) - 1000000 J ( 106 J) \\01-k dom.· In , n1bol : di,t..illl'l' loll."l' \V F moH.· <l in thL· di1ection of thl' lon.:l' cl For c:\amplc, ir a 4 , force n10\'e~ an obj L'c L3 m, Liu.· wor-k don~ i~ 12 J . Energy A c.:on1prc~sccJ ~pring ha~ energy; so doe~ a lankful of petrol. Both can hl.' u-..c<l lo do \\ork. Like work, cnergj i~ mea~u1·L'<l in j oules (J ). Although people talk about cnerg v being l!,to, cd rn ,~le.. M:"<l, cncrg ~ bn'l a 'thing'. 11 , for cxarnplc , a corn pre cd ~ pai ng stor1..'S J00 ioulc of cncrgv, thi i just a mca uremcm ol ho\\ nuac h \\'Olk oukl be done b~ the pring H the cncI-g) '" "re rclca ed. Encrg\ can be stm"Ccl in <li ffcr- 'nl ways. These arc clcsc1·ihcd on the .._ Particles V1brat1ng in a sohd. The particles have energy because of their motion. ► A fully f exed bow stores about 300 JOUies of energy. 80 oppo°'itc page . To unclcr~tancl th<.•m, ~ ou need to knO\\ the lollo\\ ing: • Mo, i ng obj1..·ccs slor\..' L:ncI'8'- Fo1 c-<ample. a n1ovi ng ball t:an do wo1-k b~ kno cking ~omclhing ovc1 . • 1\1mclial an: made up ot partkk · (atom~ and mok~ tl11..: ·) that a1t: on tanth in motion. For example in a lid, the particll! aa ' ,ibraling. 1f th ~ lid is heat~>d. it!-. temperature rise~. and the pat1idc n10,·1: fa"tc1: ORCES AND ENERGY ergy stores 0 ll ·omctimc · helps to add a label to tht: word cncrID to de ·cribc ho\\ it is being ~t01·ecl. Ht:~ arc the names u~cd lo describe the cliffcn:nt energy stores: Typical energy values kinetic energy of a football when Kinetic energy This i~ energ) ~•on:d h) an object because of it~ motion. 'Kinetic' n1eans 'mo\'ing'. kicked ........................... 50 J Gravitational potential energy Thi i energy tored by objects 1iftcd up,\ard again t the force of gra\'it\. It j rclca cd when the\' fall downward ·. Elastic (strain) ener A ·tretched ru bbcr band ·tore:, cnc1 gy. o doc~ a compn:s ed spring. Chemical energy Thi~ describ ~~ energy ~ton:d in the chemict1I bonds b . . twccn atonl . Fuel tore energy in thi wa,, o do battcric ' and food It can be relca ·c<l b, chemical reaction~ - a fuel buniing for c~ample. Electrostatic energy Il ck:ctric charge auract each other but ate held apart, the) store cnt:rgy. ror more on the forces between chargt:s, sc~ sprt:ad . I. uclear energy An alom ha, a nucleus al its ccntru. This is made up of pa11idcs bound together by strong forces. ln some atoms, if the paniclc~ b "come rcan-angcd, or the nuc1cu ·plit ·. tor xl energ_\' i rdea »d. Thermal energy Jn all material , the particl .. - arc mo\'ing ( ec oppo it .. page-), o the, tore energy. \Vhen a hot ob_ject cool . it particle lo,\ down. ~o ·orne of the torecl encr~ b released - people conunonly called il heat. Thermal energy is n:lah.:d to internal energ . For more on this. ~<..-c spread - . I . Magnetic energy• It two n1agnct attract each other but arc held apan, they More energy. For more- on the force · between inagnetic po)c ·, sec spread 9.1. l n nlan) of the abo\'C, object · or partides ston: energy bt:caust: of their position. The gcncrJl namt: for this is potential energy. 9ravitation<1l potential energy of a skier at the top of a ski jump ...................... 15000 J chemical energy in a chocolate biscuit •.. .. .. ......... .. 300 000 J kinetic energy of a car travel ing at 70 mph (30 m/s) . .. 500000 J thermal energy needed to boil a kente full of water ......... 700000 J energy supplied by a fully charged car batte,y ... ... .... ... .. 2 000 000 J chemical energy m all the food you eat in one day ....... 11 0OOOO0J chemical energy in one litre of petrol .............. 35000000 J Electrical energy? 0 Energy path ays An electric current transfers E\·cay whc~ around us, thing~ an.! rising. fa1ling, speeding up. ~]o\\ ing down. heating. cooling, charging, discharging, bun1ing... In other word • ener~ i being transferred ( hilted) trom one tor .. to another. llcrc arc the four pathway il can take: • Mechan icalh, by a rorcc moving something. • Electrica11y. hy a cun-enl. • Bv heating b ·cau!-tc ol a ten1peraturc diffcr"ncc. • By radiation uch a light wa, e~ and ound wa, e . energy. It doesn't store it. That's why electrical energy doesn't appear in the list of energy stores. How·ever the name is st,11 commonly used when calculating the energy supplied by battery or generator (see spread 8.12). ® 1 HO\,v much \tVOrk 1s done 1f a force of 12 N moves an obJec1 a distance of Sm? 2 If you use a 40 N force to hft a bag, and do 20 J of V.'Ork, how far do you lift it? 3 Express the folloNing amounts of energy in Joules: a 10 kJ b 35 MJ c 0.5 MJ d 0.2 kJ 4 Using information in the cnart of energy values on this page, estimate how many fully charged car batter es are needed to store the same amount of energy as one htre of petrol. 5 a Write down three ways in which the falhng apple on t e nght stores energy. b Using the energy chart on this page as a guide, decide which of the appfe's energy stores has the most energy. Related topics: sctenbfic notaUon 1. 1 ; SJ un1ts 1.2; rorce 2.6; part\cles 5.1-; electrons In c1rcutts 8-4 81 Conservat1on of energy Mone, doe:-,n't disappear when) ou ~pend it. It goe MJmewhere else! Energy i~ ·imilar. ii nl;!\'er disappears. Pcopl~ calk ~1bout 'using ~nergy• but what n!all~ happens i~ thaL the cncrg~ is mo,·cd from one store to another s tore : A stone 1s thra-vn upwards ... ... and fa s to the ground StOr\~ at highest stone point stone falls to 9r01.Jnd moves upwards energy stored in muscles stone hits wall clwm1eo 1net1c energy energy potential k1net1c energy energy The diagn1m abon! shows a sequence of energy cr..msfc~. In th~ last Lransfl'r, cncrro is mo, c<l from a kinetic ~tore to a thermal store. \ \'hen the ~tone hit · the ground, it make rhe pa, ticlc (a1oms and molecules) in the ground mo, c faster, o the ,natcrial wann up a little. During each trJnsfe1; the total quantit) of cnerg~ ta~ · the same. Thi is an c,ample o( the law of conservation of energy: Energy can be s tored or ll'i.\n-..kn-cd, but it c..,nnoc lx· created 01· destroyed. Work and energy essentials 0 Work is done whenever a force makes something ll'IOve. work done ;:::; force x distance moved Things have energy if they can be used to do work. Work and energy are both measured in JOUies (J). 82 Wasting energy The diagram abo\'e shows che energy tran~fe1·s as a simple chain. Jn reality, al difforcnt stagc.o,;, .some encrID i~ trc.1nsfern!d elsewhere. For example, muscles action transfers less than 20Cc of the cncrID stored in )Our food lo a linetic ·LOrc. The re ·t is wasted as thermal energy - \\ hkh is\\ h) ~ ou heat up when you cxcrcbc. And when au object mo,~ through air~ ~omc enettn i tran tern.."Cl to a thermal tore bee au~ of friction (air t~L lance). E,·cn energy tran fen'ed by ound wave:-, end~ up being ~tored thermalh. The ·tone, ground, and su1Tounding~ become a litllc ,vanncr t han bt:!forc. E The diagram al Lhe top of the ncxl pag e s ho\\ show till of Lhc energy from the thro\\cr• · chemical store i · en~n1uall\' transfcn·t.xl to a thcrn,al ·to1"l' although mo t of it b far too prcad out to detect. Dc~pite the cnergv ,/i.. ~ipa1ed (\\'a ted). the la\\ of con ervation of ene11,.T\' till applies. The total qua111i1v or encrgv i unchanged. ORC S therm.:i ~ergy (wasted The arrcH, th ckness represents ,n body) the amount of energy A d1ag·am like tn s 15 called a sa nkey 01agram thermal cmergy wasted because o air rt-Sistanc~) therm I energy gravitational energy stone at h>ghest point ground and stone) (1n energy enetgy stone thr0\•111 upwdtds thenna en~gy MDC stone hits ground Work done and energy r nsferred I n chc diagr'1m on thl' 1;ght, a brick i~ dropped. A~ it fall~ to chc gro und, ii lo~c~ hei g ht anc.l ~pcL-<l~ up. Bi.:ron: il foll~. il h&t~ 20 J or energy in it!-. • , 20 J gravnaiiona! L-----.! potent1a ene-rgy gn1\ itationaJ potc,uial cncrg~ ~tore. \\'hen it about Lo cdkc Lhc ground. all 20 J ha~ bL-cn cran~kn-cc..l to it kinetic More (as..,uming no air •~~i tancc). Looked at in another wa~. 20 J or work ha~ been done by chc fore~ of gravit). \ Vhcnc\·cr woa·k i~ done: work dom: 20J work done 1 50 J of '-\'Ork must be done to hft a vase from the ground up on to a shelf. a When the vase 1s on the shelf, what 1s 1ts graV1tat1onal potential energy? b If the vase falls from d1e shelf, how much kinetic energy does it have 1ust before 1t hits the ground? (Assume that air resistance 1s negl191ble.) c What happens to this energy after the vase has hit the ground? 2 What 1s the law of conservation of energy? 3 On the right, you can see someone's idea for an electric fan that costs nothing to run. The electric motor which turns the fan also turns a generator. This p,oduces electricity for the motor. so no battery or mains supply is needed! 8<plain why this idea wil not work. Related topics: work and enetgy stores 4.1 I fan elecwctty for motOf E The ball on the lch ha~ potcrllial cncrg~ because massm or the Ea11h's ilal ional pull on it and its po~il ion abo\·c l he ground. This is called gravitational potential energy (PE). If the ball rau~. it gains kinetic energy (KE). Both PE and K E can be cakulatcc..l. gr..i\ -----·-········ ,.,;eght mg CalculaUng P The gravitational potential energy of the hall on the lefl L equal to the \\'or·k \\hich would be done ii the ball \\Cl-C to lull to thc gr·ound. A~suming no air resistance, it i al o equal to the work done in lifting the ball a distance h up from the ground in the fin,t place: = mg upward lorce needed to lilt hall = 111g do\\'n\\'ard for con ball h o: \\'Cigh t of hall work done in lifting: ball - force o: dL ta nee moved = 111glz For an obii.."CI of mass 111 al a vc1-iical height h abo\·c the ground: gr-.l\'ital ional poll.'111 ial l'nl.'1-g~ For example, ii a 2 kg ma. gravitational PE - 2 kg --- mglz is 3 m aho\·e the ground, and g i 10 /kg: 3m x JO K/kg - 60 J Calculating KE 0 Units Mass t> measured in !ipeed zero !,'J)eed V ) kilograms (kg). n ·ssm Force is measured in newtons (N). Weight is a force. Work is measured in joules (J). E ergy is measured in joules (J). The kinetic: cncrg~ of thl.! ball abo\·c is equal lo the work \\hich the ball coulc..l do by losing al1 ol iL~ speed. A~suming no air resistant:e, it is also cqiml 10 the work <lone on the ball in incn:asing its S[X-'\!d from zero lo" in I he first place: "ork c..lonc = mass x Useful equations average speed distance moved time taken . gain in speed acceferataon - . = ma.,s acceleration x distan c mo\·cd gain in pel-<l . ' a\'erage ~peed x tm1e taken . lime taken = ma s, gain in peed x a\'erage :-.peed = 111 k time ta en force i-= mass x acceleration ~ight - mass x g (g - 10 N/kg) \\Ork cble- force x d£tanc.e dis ta nee mo,·cd force : , \' l/2 " l/2 111\ ' 2 For an o~iect of mas~ 111 and speed i·: lllC)J8'.I 'NOr done - energy transformed 84 For example, if a 2 kg ma ·s has a speed ol 3 m/s: kinetic energy 1/2 x 2kg x (3 m/") 2 1/1 v 2 32 J 9J ORCES AND ENERGY E Scalar energy n crg_\ b a ~calar qu a nlily: it has mag nitude h i'le) hut no directio n. o )O U d o no t have to a llo w lor dirccti o n when d o ing c ncrg) calc u}a tiom,. On Lhe rig ht , o bject A and B ha ,·c the ·a mc n1a ·• a nd arc at 1hc a mc height a bove the ground. B wa lif1cd vertically but A was nio,·cd up a · m ooth ~lope. Altho ug h A had to be n10 , ·ed further, le · fo rce wa · needed to mo,·c it, a nd the work do ne was the ·a me a for B. · a re ult, bo th o bject ha\'c the a m e PE. The PE (111gh ) dcpcnfil o n the ,·c1tica l gain in height h a nd no t o n the p a rticula r path take n to gain tha t heig ht. t t t .t KE and PE problems •• •• - ---------------------'-~-- Example It t he :-.Lon e on t hl.· r ig ht is droppl.·d. w h at is its kim.· tic cnl!r gy w lll.·n ii h a:-; fallen half-way to till' ground ? ( g - 10 , kg) In pro blem like thi , vou do n't ncct..~til\' hm·c to u~ KE ½ 111v 2• \Vh "n 1hc s to ne fa ll.!-., iL-. f!<l in i n KE is 1.-,qual to it.s loss in PE, so you can cal ula lc that in tcad: heig ht lo ~t by s to ne o: gra,·ita lio na l PE lost hy s to ne . 111gl, KE gained by s to ne o: 4 2m = 4 kg x ION/kg x 2 m = kg ···········1 0J :1 0 J 4m As the ·to ne tarted with n o KE, thi i th e ·to ne' · KE half-wa\' down. Exa111ph.• T h~ tone on l l hl• tig ht slide.:-; down a sn1ooth :-;lo pe. \ Vhat is its .spcl·d w hen it t\.'aChl.·.s thl! bottom? (g- JO :\ kg) This pro blem c:an a lso be so h cd b~ co n ~idc rin g e n e rg~ c hange s. At the lo p o l the s lo pe, the LOne ha.-, cxlra gravita tio nal PE. \\'hen it rcac he the b ou o m , a ll o f this PE has bee n lr..insformed inLo KE. gra\'itati o nal PE at to p o ( · lo pe . 111gh - 4 kg . JON/kg x 5 m o: kinctk encrg~ at bo uo m ol slo pe o: 1/1111 \'l o: Vi x 4 kg x v 2 This gi\'es: V 200 J 200 J 200J • 200J - 10 m/s Sm o th e s to ne's speed at the boLto m of th e s lo pe is 10 rn/ . No te: if the Mo n e fdl vcrticallv, . it ,, o uld s t.ut with the same gra, ·ita tio nal PE and c 11d up\\ ith th e ·a mc KE, ·o its lina l speed would s till be 10 rn./s. ~ @ Assume that g is 10 Nikg and that air resistance and other fnct1onal forces are negligible. O An obJect has a mass of 6 kg. \'Vhat is its grav1tat1onal 0 0 potential energy a 4 m above the ground b 6 m above tl e ground? An obJect of mass 6 kg has a speed of S m/s. a What is its kinetic energy? b \'\'hat is its kinetic energy 1f its speed 1s doubled? A ball of mass 0.5 kg has 100 J of kinetic energy. \l\lhat is tl e speed of the ball? 1 0 A ball has a mass of 0.5 kg. Dropped from a chff top, the> ball hits the sea below at a speed of 1O mls. a What 1s the kinetic energy of the ball as 1t is about to hit tl e sea? b Whal was the ball's gravitat,ooal potential energy before 1t was dropped? c From \-mat height was the ball dropped? d A stone of mass • kg also hits the sea at 10 m/s. R\;p~ot stages a, b, c1nd c dbove to fmd the height from wl ich the stone 'lvdS drOpJX~. Related topks: speed and acceleration 2.1; rorce, mass, and acceleration 2.7; mass and weight 2.9; work and enetgy 4-1- 4.2 85 energy essentials Work .s measured in joules (J). Engines and motor . <lo ,,ork b) making thing~ n,o,e. Petrol and <lic~el engincl) need the energy ~lot cd in lhcia lucl. Eleccdc InotoI rdy on Lhe t..'ncrg) lransJcrTcd from a battery or generator. The human body i~ al~o . _, fonl1 of engine. 1L nL-cds the cnerg, to1\!<l in (oo<l. Energy is measured in joules 0). Efficiency work done = energy An engine doe~ u dul ,,ork "ith ome or the ent"rgv upplied to it. but the rest Ll) w.._,sk<l a thermal enci-g) ( heat ). 1·hc efficienc of an l'nginc 0 Force. work, and transferred can be calculated a lollo,, : Force is measured in newtons (N). E cllicicnc..· v work done force x distance moved 0 Inputs and outputs In any system, the total energy output must equal the total energy input. That follows from the law of conservation of energy. Therefore, the equations on the right could also be written with 'total energy output' replacing 'total energy input'. 0 Typical power outputs washing machine motor 250W athlete 400 W small car engine 35000 W ll!-.d ul ,, ork dmH.' u"d ul cne1 gv ou tpu L total total encrg) input 1.•111..·1~" input For c:-.amplc, if a petrol engine does 2- J of useful ,,ork for C\'cn l00 J oi encrgv upplied toil, then il cllidC'nc, is 1/4, or 2sc.t.. ln othC'I' \\or<l ·• ils useful cncrID ouLput is 1/4 of its total energy input. energy supplied 100 J useful work done efficiency petrol engne 100 J 100 J clcctnc mctr·~ rmk 100 J I 25 J 25% I 3S :I 3S% 90J 90% lSJ 15% Thl' c.:han above sho,,s che efrkiendcs of soml' t~ pical engint.-s and motor . The lo\\ efticicnc, of lttcl -burning engine-, i nol due lo poor design. \\'hen a f ucl buc·n~. it is impo sibll' to tran ·fl'r its thl'1mal cnerg~ to kinetic (motion) cnerg) ,,ithoul wa ting much of it. large car engine 150000 W Power large jet engine A mall engine can do just a much \\Ork as a big engine, bu1 il take longer to do it. The big engine .._«n do \\ Ork al a t~tcr rate. The rate al which \\ork i · <lone' i called the power. 75000000 W 1 kilowatt (kW) - 1000 W 0 Thl' I unit of power is tht.: watt (\\/ ). A power ol l wall mean · that \\Ork i being done (or energ, tran len-ed) at the rate o I jou le per second. Po,, er can hl' c.:akula1e<l a~ folio,\ s: \\·ork done ti llh.: wkcn or power encrg, ll"c.m,kt t t.·d t i m1.• l ak'--· n For example, if an engine doe~ I 000 joule~ o l usclul \\ Ork in 2 econd~. its power output i~ 500 \\ alls (-oo joules per ~econd}. 86 ORCES AND As energy and power arc rdatc<l, there i~ another ,,a~ of calculating the efficiency of an engine: . . dlK' ll'llC\ - . w,d ul po,,e1 output lo lit I pcm, l'l input -------- N RGY 0 The horsepower (hp1 is a power unit which dates back to the days of the early steam engines: 1 hp 746 W (about ¾ kilowatt) Power problems Example I T l1<..· (Tanc on lhc right lifts a I00 kg block of cmH.:n.·tc through a \l'l'lit:al height o l 16 m in 20 s. It the po,~er input to the motor is I 000 \\', what is t ht· dfo: il.·ncy o l thl.· 11101or? On m1h, g i 10 1/kg, o a 100 kg block ha~ a weight of 1000 " · Th ~rcforc, a lorcc of 1000 N i • needed to litt the block. \\' hen the block i~ lihed: workdonc force x distance = 1000 u efu l ,, ork done u dul power output - - - - - - - time tak ~n cFficienc\ x 16m - l6000 J 16000 J 20 t1rn~ ta en 20s 00 \ 16 m u ·dul power output 00 \ V total power input - I 000 \'\' - O. po,.ver input 1000W o the motor ha~ an effi c icnC\ of ~ c.. E.rample 2" The car on the 1ight has a stl•ady spt.·cd of 30 111/s. If the total frktiona l forcl' on the c.u i~ 700 , . what w,d ul po\\ l.'f output does the 1.:nginl.' dt..•li, L'r Lo the d1 i, ing \\ hcds? steady~l"f 30m/s ) A the pccd i lead~. the engine mu t pro, idea for"·arcl force of 700 , • to balance the total hic tio nal force. In l ·ccond, the 700 ~ lorcc mo\'e ' 30 m, o : work done . for c x dbtancc 700 · 30 111 . 21 000 J. A the engine doc:, 2 I 000 J of u cful work in 1 ccond, il u clul po,,cr output mu t b • 2 1 000 \\', or 2 J k\'\'. Problem o thi l) p • can al o be olved with thi equation: usd ul f><>\\·c.- output ® 101 l'.l' · ~rx·cc.J 9 - 10 N/kg 1 An engine does 1500 J of useful work with each 5000 J of e, ergy supplied to 1t. 0 What 1s its efficiency? b Whc1t happens to the rest of the energy supplied? an engine does 1SOO J of work in 3 seconds. what 1s its useful pO\-Ver output? 3 A motor as a useful power output of 3 ~ w. a What is its useful power output in wa tts? b iow much useful work does 1t do in 1 s? c fiow much useful work does 1t do in 20 s? ~ If the power input to the motor is 4 kW. wha t is the efficiency? 0 1· 4 Someone hauls a load weighing 600 N through a vllrt1cal height of 1Om in 20 s. a How much useful wor' does she do? b How much useful work does she do in 1 s? c What 1s her useful power output? 5 A era e hfts a 600 kg mass through a vertical height of 12 m in 18 s. a What w-e1ght (in N) 1s the crane lifting? b What 1s the crane's useful power output? 6. With frictional rorces acting, a fo""'ard force of 2500 N 1s needed to keep a lorry travelling at a steady speed of 20 m/5 along a level road. \t\'hat useful power 1s being detivered to tl e driving wheels? Relat ed to pics: SI units 1.2; force, mass, wei ght, and g 2.9 ; law of conservat1on of energy 4.2; work and energy 4-2- 43 ► Part of a thermal power station. The large, round towers with douds of steam coming from them are cooling towers. lndu ·rdal ~ocicth.: · ~pcnd huge amounts of cncr6~. ~1uc h ol it is upplicd bv elec tricity which com~ from generators in power stations. Thermal power stations ) water ( (condensed steam) thermal energy source boiler turbine-s generator Jn mo t power tations, the generators are tun1ed by turbine . blown round by high pre . ure ·team. To produce tht! team, water is heated in a hoilcr. The lhermal energy come~ from burning fuel (coal, oil, or natural ga~) or front a n uclear reactor. uclcur fud docs nor burn. I L~ energy b rclca ed by nuclear rcat:tion which plil uranium atoms. The procc~~ i · called nuclear fission. Future reactor ~ nla) u c nu dear fu ion: ee 10. 7. On e steam ha~ pa · ·eel throug h the tu1·bine , it is cooled and condensed ( Lumc:cl back into a liquid) so thaL iL can he focl hack lo the boiler. ome pO\\Cr station~ ha, c huge cooling Lowers, wiLh draughts of air up through them . Other · u ·e the cooling effect of ncarb) sea or Ii\(:1· \U\te1: A A turbine ► Block diagram of what happens in a thermal power station 88 fue .. - fuel burners or nuciea, reactor erma energy.. - boiler steam .. - .. rotat on ttnb1n~ - .. elcc:tnaty generator - ORCES AND ENERGY E Energy spreading 0 eH oency Themial power t, tion~ wa"te more energy than they deliver. Mo t i lo l a~ thennal energy in the cooling \\'Uh:r and\\ a ·te ga-.es. Fm· C'-ample, the cfficicnc) of a •~'Pical coal-burning pcl\\Cr stalion is onh aboul 3-r.< - in other word~. only about 35"< of Lhe cncrID in its fuel is Lransfonned into electrical cncrg.,\, The diagram below sho\\ ~ what happens to the 1-cs1: - useful energy output energy input useful power output power input 0 The power output of power stations is usually measured in megawatts (MW) or in 91gawatts (GW): 1 MW - 1 000000 W ( 1 malhon watts) 1 GW - 1000MW (1 billion watts) ◄ Typ&Cal energy-flow chart for a thermal power station. A chart li e this ,s called a Sankey diagram. The thickness of each arrow represents the amou it of energy. 1 energy loss energy floss n bocler5 1n turbines energy oss 111 generators energy to run J)0',4--er statt0n 'E Engineer · try lo make power sLation~ a efficient a~ pos ible. But once cnl.·t-g) is in thcnn.._,I rorm, it cannot all be u ~cd to dri\'c the gcnc1..._,tm ·. Thcn11al cnc1~ i the cnct'g\ of randoml) mo\'ing particle ( uch ru. atom and n1oleculc ). It ha a natural tcndcnc\ to spread out. A it . pread~. it become le · and le~~ u. ef u1. For example, the concentrated \.!nerg) in a hor name could be u~l.!d to mak\.! steam for a turbine. But if thc same an1oun1 of thermal cncrg\ were sp1·cad through a huge tankful of wak1~ it would only ,, aim the water by a f~w degrees. This "arm \\atcr could nol be used a~ an cnerg\ source ror a turbine. District heating• Th 1: tmu cd thc1111al enct'g\ lrom a power ~tat ion do~ not ha\'e to he wa~led. !')ing long ,quer pipe , it con heat home. , olfic~. anc.l lactorics in the local ar\!a. This work~ h~~t if the power slalion is nm at a sl ighl t~ Jowc-r cfl icit!OC) so that hollt!r \\ a tcr is pnxlucc-c.L ® 1 Write down four different types of fuel used in thermal pow-er stations. 2 In a thermal power stat,oo: a What is the steam used for? b What do the coohng tovvers do? 3 The table on the right gives data about the power input and losses in two power stations. X and Y. a Where is most energy wasted? b In what form 1s this wasted energy lost? c What 1s the electrical power output of each station? (You can assume that the table sho'NS all the power losses in each station.) (0 What 1s the efficiency of each power station? turbine power stations These are smaller units which can be brought up to ~~d or shut off very quickly. as the demand for electricrty vori~. In them. natural gas is used as the fuel for a jet engine. The shaft of the engine turns ooe generator. The hot gases from the jet are used to make stec:m to drive another generator. power station X power input from fuel in MW power losses in MW. - in reactorslbollers turbines in generators - in - Power to run station in MW electrical power 0 Combined cycle gas coal power station Y nuclear 5600 5600 600 200 3800 2900 40 60 40 60 ? ? I OUtP-Ul Ill M\,V I Related topics: en~gy 4 .1- 4 .2; efficiency and power 44 generators 9.9; etectnc1ty supply 9.12; nuclear energy 10.6- 10.7 89 0 Energy units The electnc,ty supply industry uses the kilowatthour (kWh) as its unit of energy measurement: 1 kWh 1s the energy supplied by a 1 kW po'Ner source in 1 hour. As l watt - 1 joule per second (Vs), a 1 kW pOYle< source supplies energy at the rate of 1000 joules per second. So in 1 hour, or 3600 seconds. it supplies 3600 x 1 000 joules (J). lherefore: 1 kWh - 3600000 J One effect of aod rain Reactions for energy* \ Vhen fuel bun1 , they combine with oxygen in the air. \ \'i1h mo~t fud , including fossil fuels, the energy i~ released b) this chemical rcacLion: lud -1 oxygen bu, mn1; carbon dioxide \\ater + tller111a/ energy •1.-,e" ".-,1c tt•~,.-, ~..,c- m;:idc- Tht:r"C may be other wa ·te gases a~ well. For examplt!, burning coal produces some sulfur dio:\ide. "atural gas, \\hich is mainl~ methane, is the 'cleanest' (least polluting) of lhe fuels burned in po,,cr station~. ln a nuclear power tation, the nuclear reaction produce no wa tc gn ~ like tho e abo,·c. Howe,t>r, the, do produ e radioactive \\a te. Pollution problems Thc1mal po,\er tation ~ can cau e pol1ution in a \'aJiet, of \\'a\' : • Fuel-burning power ~tat ion put e~tra carbon dioxjde ga"> into the atmo~-ph ~re. This traps the uns energy and is adding 10 global warming. oal-burning power station~ cmil almost l\\icc the amount of carbon dioxide per kJ output compared ,,ith tho c burning natural gas. • nl .. s lo\,·-suUur coal i u l-<l, or dc!)ulfudzation (FGO) unit!) arc fitted, coal-bun1ing power t.._1tion!:. cn1it ulfur dioxide, which is hat111ful to health and cau~e acid rain. • Transportjng fuel can Calk e pollution. For example, there n1ay be a leak from an oil tnnke,-. • The n1dioacLi,·c waMc from nuclear po\\'er ~tation~ i~ highh <langerou~. ll mu t be can-icd away and stored ·afeh in ·calcd cont.._,iner · for nlan) \'Ca1 · - in ·omc ea ·c ·, thou!)aJld!) of) car~. • , uclcar accident a1' rare. But when the) do occur, rndioacti\·c ga and du l can be can-ied thou and of kilometre b, \\ind . Power from water and wind me gcncmL01 · arc Lurnc<l by Lhc force of moving \\'atcror \\'in<l . There arc lhh..'C C\~1mples on the nc~t page. Power chcnl($ like thi · ha\'c nor ucl co~t , and give on no polluting g~c . Ilo\\C\'cr. rhcv can be expcm,hc to build, and need large area. of land. Compared" ith fo , il luel , n1oving water and wind a1--e much le ~ concentrated ource. of energy: 1 kWh of ~weal energy can be supplied US!l\9 ... go .•. 0 S ht,es of 011 (l>utning) ..• 5000 bt,e~ of fast-flowing water (20 ml~) Pumped storage scheme This is a form of hydroelectric scheme. At night. when power stations have spare capacity. power is used to pump water from a lower reservoir to a higher one. During the day. when extra electnoty is needed. the water runs down again to turn generators. Hydroelectric power scheme River and rain water fill up a lake behind a dam. As water rushes dovvfl through the dam, it turns turbines which turn geoerators. Tidal power scheme A dam is built across a river where it meets the sea. The lake behind the dam f lls when the tide comes in and empties when the tide goes out. The flow of water turns the generators. ® ~ - - - - - - - - - - - - -~ power station ~ A coal (1 MW-1 000000W) Wind farm This is a collection of aerogenerators generators dnven by giant wind turbines ('windm1lls'}. (oon-FGD) I 1 ~ B como,r~ cyde gas C nuclear 1800 600 1200 eH,oency (fuel energy ➔ electrical energy) 35% 45% 25% 20 6000 4 0 0 2 5 4 2 3 0 5 3 <l 0 1 WI at 1s t e source of energy in a hydroelectric power station? 2 The table above gives data about f,ve different power stations. A- E. f) Chas an eff1c1ency of 25%. What does U 1s mean? b Which povver station has the lughest eH1C1eocy7 What are tt e other advantages of this type of power station 7 5 E large tidal scheme I power output in MW The following are on a scale 0-5 build cost per MW output fuel cost per kWh output atmospheric pollution per kWh output D wind farm c Which power station cost most to build? d 'A'hich power station has the highest fuel cost per kWh output? e Which power station produces most atmosphenc pollution per kWh output? f Why do two or the power stauons have a zero raung for fuel costs and atmosphenc pollution? Related topics: efficiency and power 4,4; energy resources 4.7- 4 .8, calculating energy 1n kWh 8. 12 gi How energy is used in a typical industrialized coun try industry 30% domestic 25% 1ransport 30% Mo L of che ener~ that we u c corn~ fr01n fuel 1hat arc burned in power tation , fa to1ie , home , and , ·chicle . ~earlv all of thi energy E originally came fron1 the un. To find out how, ~ec the next ~pread, 4 .. The un i~ 7 S'- c. hydrogen. lt 1-clease - ener~ b\ a procc~s caJled nuclear fusion (see ·pr~ad 10.7). One <la), il may bl' po · iblc to ha1 nc ·s Lhi · proce on Earth, but until thi can be done, \\I.: will ha,e to manage \\ ith other re ourcc . 0 Shale gas and fraddng Shdfe gas (see below nght) is extracted from shale by a process called tracking (hydraulic fracturing). High-pressure water is pumped into the rock, fracturing it. and opening up crac s so that the trapped gas can flo-N out Some see shale gas as a ma1or source of energy for the future. Others have deep concerns about the environmental impact of extracting it. 0 Where to find out more For more detailed see information on... spread... hydroelectric energy tidal energy wind energy solar panel energy and mass nuclear fission nuclear fusion 92 4.6 4.6 4.6 5.8 10.6 10.6 10.7 The energy resources we use on Earth can be renewable or nonrenewable. For example, wood is a ~newablc fuel. Once usL-cl, more can be grown Lo replace it. Oil, on thL' other hand, is non-r~newablc. ll Look millions ol \L'a1 to fo1111 in the ground, and cannol be replaced. Non-renewable energy resources Fossil fuels oal, oil, and na1ural gas arc called fos~il fuds: 1heY formed from the remain~ of plants and tin~ sea crcatun.-s that lin~d millions of ycat · ago.They arc a \ 'Cl) concentrated source of cncrg~. Petrol, diesel, and jct lud al\.· all t.·.xtracte<l ronl c1udc oil (oil a it occu1 natural in Lhl' ground) oil and it i the, aw m._llcrial for making mo t plastic . atural gas is the• leanest' of the fo:sil fuels (sec spn:ad 4.6). t\t present, it is mo!'\tl) 1aken from the same underground rock formation~ that contain oi] - the ga~ formed with the oi l and becante trapped abo, e it. Ho\\c,·cr, 0H.·1· the nl'.xl dccacks, more and more gas ma~ be extracted from a roc k called shale ( ec kh). Proble111 \i\' hen fo~!)H fueb burn, their waste ga~e~ pollute the atmosphere. Globall\', the mosl ~criou.s concc1-n i~ the amount of carbon dioxide being produced. There is around 30.(, mon! in the atmosphere coda than th~rc \H\s 50 yca1 · ago, and thcrl: is little doubt that this is ._,dding Lo global warming ( ·c...-c panel on rhc next pagL" ). 1 uclear fuels Mo t contain uranium. I kg of nuclear htcl s101'e a much energy a -5 tonne of coal. In nu lear power !-.tat ion , I he energy i relca!-£d bj fis.."ion, a process in which the nuclei of uranium atoms arc split. Problem!l High ·atcc~ ~tandards arc nccdcd. The \\a tc frorn nudt."ar lud i , ·et'\ da ngcrou and ~ta\ radioactive tor l hou~and ot \ ea, . . 1 uckar power tation arc C'\""pen~i\'e to build, and expen i\'c to decommL ion ( lo e down and di mantle at the end of their working life) . ORCES AND ENERGY Renewab e energy resources 0 Hydroelectric energ A rher fill~ a lake behind a dan1. \Vntcr llowing A global warning do,, n from the k,kc cun1~ generators. By burning huge amounts of fos.s1I fuels. industrial sooetIes are putting more carbon dioxide 1nto the atmosphere than is being removed by natural processes. The extra carbon dioxide is trapping more of the Sun's energy. and there is little doubt that this is causing global warming. The result: more extreme ,veather events. glacial melting. and coastal flooding. Most scientists believe that we have little time left to tackle the problem. Prnble111 E~pensi\'c to build. Few area:-, of the ,,orld are uilah]e. Flooding land and huilcling a clam cau ·e.,. en\'ironmcntal damage. Tidal energy in1ilar to h)<lroclcctdc energy, but a lakL' [ills \\hen the tide come in and cn1ptic wh1..:n it goe · out. Proble111s !-. tor ln·droelect ric energy. \ Vind energy l!nt:rators an.~ <lti, l!n b~ ,, i nd turbine~ ('wi ndm il b/). Problem, Large, remote, wind, itc · arc needed. \Vind ._i·c variable. The wind turbine~ ar\? noi v and can poiJ the land cape-. \Yave energy Generator~ are d1;ven h) the up-and-down motion of wave~ at "ica. Proble111, Diflicult to build - fo,, dc\'icl: have been uccc (ul. Geothermal cner 'Geothermal' mean · heat from the arth . \i\'ater is pumped down to hot rock deep underground and ti c ~a · tcanl. In ar1:a o volcanic acth it\', the Lt'arn come naturally fron1 hot spring . Proble111s Dcl!p drilling b difTicuh and expensive. Solar cnerg (t'ncrgy 1" diated Irom lhc un) Solar panels absorb thi encrro and u c it to heat water. olar cell ~arc made fronl matelial · th..Lt can dc-li\'cr an electric cun\!nt \\ hen the, ab orb the energ\ in light. Proble111s Variable amounLs or sunshine in some countdes. ola1· cell.,. an: expensive, and must be large lo deli, er uscful amounL'i of powl!r. A cdl area of around I O m 2 i · 1'\c-cde<l to power an dccuic kcttJc. Biofucls The car' Juel n1adc lron1 plant or animal n1attc1: The, include wood, alcohol t1un1 ugnr cane, and methane gas fron1 rotting,,·~ste. Prable111-., H ugc area~ of land arc needed to grow plant . Saving energy Burning f():).·il fue~ cause~ pollution. But the ahe1T1ati\'e~ ha,·e theh- own environmental problem~. That is one n:a"ion why we need to he le s wa-..tefu1 ,, ith c-ncrg\' hy u,ing vchick·, kss, and more cfficit!ndy, and recycling mo~ waMc material . Al o, beucr insulation in buildings woukl mean le~ ncL-<l for heating in cold countiies an<l for air conditioning in hot onL~. ® To answer these questions, you may need information from the illustration on the next spread. 4.8. 1 Some energy resources are non-renev.table. What does this mean? Give two examples. 2 Grve lV'IO ways of generating electnc,ty in which no fuel is burned and the energy 1s renewable. The energy in petrol or1ginalty came from the Sun. Explain how it got into the petrol. 4 Describe tVIO problems caused by using fossil fuels. 0 A In Brazil. many cars use alcohol as a fuel instead of petrol. The alcohol is made from sugar cane. wh eh is grown as a crop. 5 Describe two problems caused by the use of nuclear energy. 6 What is geothermal energy? How can 1t be used? 7 What is solar energy? Give t\'YO ways in which 1t can be used. 8 Three of the energy resources described 1n this spread ma e use of moving water. What are they? 9 Give four practical methods of saving energy so that we use less of the Earth's energy resources. Related top1cs: po•,1er stations 4.5- 4.6;energy from the Sun 4-8; solar panels 4-8; nuclear react0<s 1.0.6- 10.7 93 ORCES AND ENERGY Renewab e energy resources 0 Hydroelectric energ A rher fill~ a lake behind a dan1. \Vntcr llowing A global warning do,, n from the k,kc cun1~ generators. By burning huge amounts of fos.s1I fuels. industrial sooetIes are putting more carbon dioxide 1nto the atmosphere than is being removed by natural processes. The extra carbon dioxide is trapping more of the Sun's energy. and there is little doubt that this is causing global warming. The result: more extreme ,veather events. glacial melting. and coastal flooding. Most scientists believe that we have little time left to tackle the problem. Prnble111 E~pensi\'c to build. Few area:-, of the ,,orld are uilah]e. Flooding land and huilcling a clam cau ·e.,. en\'ironmcntal damage. Tidal energy in1ilar to h)<lroclcctdc energy, but a lakL' [ills \\hen the tide come in and cn1ptic wh1..:n it goe · out. Proble111s !-. tor ln·droelect ric energy. \ Vind energy l!nt:rators an.~ <lti, l!n b~ ,, i nd turbine~ ('wi ndm il b/). Problem, Large, remote, wind, itc · arc needed. \Vind ._i·c variable. The wind turbine~ ar\? noi v and can poiJ the land cape-. \Yave energy Generator~ are d1;ven h) the up-and-down motion of wave~ at "ica. Proble111, Diflicult to build - fo,, dc\'icl: have been uccc (ul. Geothermal cner 'Geothermal' mean · heat from the arth . \i\'ater is pumped down to hot rock deep underground and ti c ~a · tcanl. In ar1:a o volcanic acth it\', the Lt'arn come naturally fron1 hot spring . Proble111s Dcl!p drilling b difTicuh and expensive. Solar cnerg (t'ncrgy 1" diated Irom lhc un) Solar panels absorb thi encrro and u c it to heat water. olar cell ~arc made fronl matelial · th..Lt can dc-li\'cr an electric cun\!nt \\ hen the, ab orb the energ\ in light. Proble111s Variable amounLs or sunshine in some countdes. ola1· cell.,. an: expensive, and must be large lo deli, er uscful amounL'i of powl!r. A cdl area of around I O m 2 i · 1'\c-cde<l to power an dccuic kcttJc. Biofucls The car' Juel n1adc lron1 plant or animal n1attc1: The, include wood, alcohol t1un1 ugnr cane, and methane gas fron1 rotting,,·~ste. Prable111-., H ugc area~ of land arc needed to grow plant . Saving energy Burning f():).·il fue~ cause~ pollution. But the ahe1T1ati\'e~ ha,·e theh- own environmental problem~. That is one n:a"ion why we need to he le s wa-..tefu1 ,, ith c-ncrg\' hy u,ing vchick·, kss, and more cfficit!ndy, and recycling mo~ waMc material . Al o, beucr insulation in buildings woukl mean le~ ncL-<l for heating in cold countiies an<l for air conditioning in hot onL~. ® To answer these questions, you may need information from the illustration on the next spread. 4.8. 1 Some energy resources are non-renev.table. What does this mean? Give two examples. 2 Grve lV'IO ways of generating electnc,ty in which no fuel is burned and the energy 1s renewable. The energy in petrol or1ginalty came from the Sun. Explain how it got into the petrol. 4 Describe tVIO problems caused by using fossil fuels. 0 A In Brazil. many cars use alcohol as a fuel instead of petrol. The alcohol is made from sugar cane. wh eh is grown as a crop. 5 Describe two problems caused by the use of nuclear energy. 6 What is geothermal energy? How can 1t be used? 7 What is solar energy? Give t\'YO ways in which 1t can be used. 8 Three of the energy resources described 1n this spread ma e use of moving water. What are they? 9 Give four practical methods of saving energy so that we use less of the Earth's energy resources. Related top1cs: po•,1er stations 4.5- 4.6;energy from the Sun 4-8; solar panels 4-8; nuclear react0<s 1.0.6- 10.7 93 Solar panels TI .~ absorb energy radiated from the Sun and use 1t to heat water: The Sun Solar cells Tt ~ u!.e the erwrgy in sunlight to produce small amounts of elecrric11y. he ood v.-e eat The f animals which fed on pi T Su11 rdd ates enetgy because of nuclear fus,on reactlOl'\s deep inside 1t (see spread rn 7}. I s output 1s equrva nt o that f ,orn 3 1026 electrte hotpldtes hist at ny frac. 10n of this readies the Earth. energy in plants P!antli td e 1n ~nergy from sunl,ght fa ng on lhe1r leaves. Titey use 1t to rurn water and carbon d1ox1de rom the alf m·o new growth Tne process is called phot~tht'Sis. An1ma!s eat plants to get the enNgy stored In them . Biofuels from plants Wood s an rnport.:tnt fuel n many countnes. Wl en -.•100d ~ burned. 11 relei1ses energy tha the uee once took 1n rom the Sun. In some countnes, sugar cane IS grown and formen·e<i o make Fossil fu~ls Fo~ f ue: ~ 1c0ci I. olJ, aoo natural gas) 'WC're tor:med frorn the rem ns oi plants and t ny sea aeatures wt kh l~d many m ltonr. o ye~s ~go lndustnal ~ooeties rety on f o~s,1 fuels for m~t of the1r energy !\'\any po-.-.: ~tr1tiorn burn fo~1I f\A?ls alcohol This can be ~ed as a fuel instead 01 petrol Biofuels from waste Rou1n9 ~nu"".11 a1d p!dnt was can give o me.11.Yle gas ThtS IS similar to natural gas and can be used as a fuel Marshes. rubbish t,ps, and sewage ueatJ I two ·s arc a sourc~ o methane Scrne wc1~ e can abo be used d rooty c3!> fl.>?l by burning ,t Batteries Som bdttl;'t s ,~.9. car batter c,s) have to be 91~n energy by chdrging hem with electrioty. Others are manufactur~ from chem,cals v,,.t,1ch alrec!dY store enetgy 8u1 energy 1s needed to produce the chemicals 1n the f•rst J)Jace Fuels from 01I Many fuels can be extracted from od (crude). These include. petrol, diesel ft.lei. ,e fuel, para m, cen•ral heating 011. bottled gas The tJdes The gra. tat1on.al pull of the Moon (and o a 'es..,er extent. the Sun) creates gentle bu~s 1n the E6rth'S oceans. As the Earth tolc'tes. different places have gh and low tJdes as they pass 111 and oot of the bulges The mo:oon of the tides c.arnes energy with 11 Nudeus of the atom ~d,o ct1\ moter ol!. hMe atoms with unsu1ble nude1 (centres) vmJc:h break up and release ene,gy The matenal gtves off the energy slO'.<Jly as thermal energy Ene,gy can be released more qu ckfy by sphmng heavy nude, (fission). Energy can also be released by pmng light nude, ( usioaj, as happens Ill the Sun Weather systems Tht ~e a·e dn,tm b-/ energy rad ated from the Sun Heated ,n, ns ng above the equotor ea 1ses belts of wind around die Eortn, Winch catry water vapour from the oce~ and b11r1g ram and snow Geothermal energy Deep underground. tt -e me s arc hotter than they are on the surface. The therma enefgy comes from rad,oac11Ve matrwals l')aturally present n lht? ,oc s It can ma e steam for heating buildings°' drMng generators . Tidal energy In a dal el"C'QY .;chcme. an estuary 1s dammed to form an arb 1c1al lake, Incoming odes hll the la~:.e; outgo;ng ll des empty 1t The flow of water In and our of rhe la ·e turns generators. Nuclear energy \n a react()(, nlJdear rss1on react,ons release energy from the nudei of uranium atoms. Thrs heats water o make steam for dnv,ng genera:01s, Wind energy Wave energy Wa"Vt!":. c1,e Cd'J f by the ",nd (c!nd partly by tides) W~ves ca~e d fapid up-and-uown movement on the surface of 1he s~a. This m~ement can be used to drrvc 9enerat0ts. Hydroelectric enugy AA cVt1f (lc1 k,ke form tAnind For t-ntun~. peop e have been dam. Wdter rus,11n9 <10\', \ frorn this la_e ,s ~d to turn generat0ts. The la c 1s ept full by (1V{l( water vJhkh once fell as ,a1n or snow. d US1ng the power of me ._.,.,nd to ITIO't'~ ships, pump water. and gr:ind corn. Today, huge wtnd turbines are used to turn genera to~. Further questions 1 vvound up sprjng batteries connected to motors rotating flyv1heel stretched rubber bands which of the abo\'e change shape "hen their stored energ, is tran ·fen·cd. (2] b* De ·cribt.- how Lhe cnct~ lrom a rotating nywhccl can be tran ~tc.,,l.xl to moving pan of~ child~ to~. ( 21 a talc 2 The diagram below shows a pcnclu lum wh ich was ~leased from position A. i \ \'haL na1ne is used for the encrg\' stored in a compn: · ·cd ~p1ing? [ JJ ii \ Vhat happens to thi torcd energy when the handle of the plunger i rdeascd? r21 E b Calculalc the m~ximun1 gravilational potential enc~ acquired b~ the met.al ball from 1he catapult \\fritc do,\n the formula Lhat you use and show yow· ,,orking. Takt: the acceleration due to gra\'it) to be 10 nlls2• [3) c Explain win the ma.xin1un1 gra\'itaLional potential encrg\- gained by th, metal ball is less than the original ~torcd energy· of the spring. [31 a an1e four r 'nc,\·ablc •ncrg\ ~ourcc~ lhat are used LO genc1·a1c clectricit). 41 ,•• b Most n:ncwablc sources ha,·e no fuel costs. ,I• I • C in~ two other advantages of using I I renewable encrro rather than ro , ·il I ucl~. [2J A • • 8 C c Thc1~ can be problems with u ing renewable encrgv ource . Gh·c one example. ll a How is the energy of the pendulum slonxl al d* II most renewable energ, source~ have no i A, ii B , iii C ? [3J fuel costs, wh\. isn't the dc.ictricit\. thc:v . b En:· ntually the pcndulun1 ,,ould ·top suppl) f n!c? r21 n1oving. E 5 A drop hammer is usc:d Lo dri, ~ a hollo,, sled Explain what has happened to the initial po ·t into the ground. The hammer i · placed cncr~ of the pendulum. [21 in idc the po ~t b\ a crane. The crane lift~ the 3 han1mcr and then drops it o that it fall onto the b~~platc of the post. 4 a 1 r r i------ 1ube suppon ro~ from crane ho lo-.•,1 steel post drop hammer (1800 kg) spnng ground dis1an ce lhc hammcf' falls baseplate A t, pc ol to) catapult con i t o( a movable plunger which has a ·p1ing attached a ho,, n abo\'e. The handle \\'as pullc."<.I down to futly compr·ess the spring and on ndcasc the n1c1al ball or mass 0. 1 kg (weight I ) was projected 0. 75 m \'Crticall).. 96 The hammer has a mass of I 00 kg. lts vclo<.:il\' is 5 m/s just bdon: it hi ts the post. a Calculalt: the kint:tic t:nc1-g) of Lhe hmnmcr ju ·t bdorc it hit · the post. (3) b Ho,, much gravitational potential encr~ i tran fcrrcd from th' ham1ner a it fall.? Ao..su me that it fol ls freely. [ 11 c Calculate the distance the hammt.;!r has fallen. (Assume 8 - 10 [ /kg) [3] © OUP· this may be reproduced fot class use solely fOf the purchase,·s Institute 6 A crate or nlrus 300 kg is rai~d by an dt.'Cttic E 11 a motor through a hdght ol 60 m in 45 . Calculate:: a The,,cightofthccranc(g- 10 . /kg) [2] Most of Lhe c:ncrgv available on Eanh con1c~. or ha cotnc, from the u n. ome enc11:,.'J\ 1\.: out-Cl,.., on Earth -,tore the un' cnct'g\ lrom million of ,cat ago. ~ame one of the!--C resoun:es. rI] b Cop\ and con1plctc the sentence h •low to sa, what tl fuel d~s. [21 A fuel is a material,, hid1 supplies _ __ E b The u clul work donl'. f 2] C Thell ,f ul PO\\ ·r of the n1otor. r21 d Th• •ffi ienc, of the motrn~ ii it takes a (X)\\er of 5000 \ V Imm its ck-ctriciL, supph. r21 7 power rating/ W electrical power appliance \\ hen it rating/kW telev1s1on 0.1 c E\plain the diflct cncc ~t,, e~n I enc" able and non-rcnc,, a blc rucl . [ 1) d Cop\' and con1plctc the lollowing table to 100 electric kettle 2000 food mixer 0.6 gh·e e'\amplcs of some fuels and their uses. The l'it-st one has been done f01· , ou. [ 41 The: tabk abo,·c how the po\\c1· rating of th,~c dccll icaJ appliance-,, a Cop, the table and fill in the blank pace..,. [21 b Lat' \\hich appliance translc1 . th ~ lca'>t amount of cncrgv pet· ~1.><:oncl. [ 1l c late wh ich appliance transfcr~ some of the energy i Ln:cd\·cs to ki nc:Lic enc:r~. [I] d \'\ 'hat happen lo the n:st ol the encrg\? ( I] Explain what, ou undc:1 Land b, the 8 a c \:ame a non-rcn ·wahle crn.:1-g, \\ hich is not blffncd. 1· 'source 12 wood uranium yes r11 yes yes yes hydrogen rocket fuel Cop ' and co1npktc the follo\\ ing scntcncc-, about hou-.ehold clectri al de\ ic ·~. ~c chemical current light ound thermal kinetic In an iron, cncr·gy dcl h cr\:cl b\ a _ __ is transferred to _ _ _ crn:1·gy. b The cnc:rg\ suppl ied to a vacuun1 dcaner is tran fcn·ed to _ _ _ c:ncrg, and a ltn\\anllxl c In a torch, canied b, a cnc:tg). torl'<l in the batten b and -.om ' i\ l hen carried ~\\ a,· b\' - - - \\'a\ cs. d on1c of l he cncrg, supplied to a radio i-. carried awa, b, _ _ _ \\'a,·cs and the rest i~ transferred Lo _ _ _ c:11erg,. ( 9] renewable must be found in fuel burned to the Earth's release energy 01.Jst no I a qaseous fuel a liquid fuel words from th' list bdo\\. {ICh \\Ord may he used once, n101\: than once or not at all. 10 a coal use a renewable fuel a non•renewable fuel 9 a The chemical t.•nc:1-g, stor"L-<l in a fo~·sil fud is tran,tc11'C'd lo thc1mal cnc1-g, \\ hen the fuel i-, bu111c..xl. Dc')Clibc how thi cncr"g\ i then t1,cd to produce ·k'Ctticitvat a po\\Cr~tation. r21 b \ Vhat b the en, it-onn1cntal impact of gcnen1t ing elect 1;cia, using fossil Iucls? [21 fueV energy resource example a solid fuel [ ll resources aT' btn-ncd. description I phi a-,e ,ion-rt!Plen-able ene,~v n ! \Oltrc.·e~. (2] ,plain win• mo~t non-rcne,, able cnerg) b ___ , 13 The lbl belo" contains the name ol omc enc1-g, store . chemical elastic g ra,•itational nuclear The table tibo\ c shows that coal is not a rcm.:,\ahlc fod. It n .>lcascs L'ncrro ,, lu.·n bunled and is found in Lhe Earth's crusl. Cop, and c.:omplctc the t..,ble lor the other lucL encr-m 1\_..,ou1-cl: na1ncd. (2] b i E,plain ho\\ lo ,il fud \\Cl'C prodUCl'<l. rl] il tatc h\10 rea~011s \\ hy \\C should use less fossil fuels. [21 Copy and c01npletc chc: table belo,, b, na1ning Lhc encrg, ,toacd in each one. U c word Iron1 the lbt. Each \\ ord ma) be llM..xl one•, more than once or not at all. (31 a bow about to fire an arrov" water at the too of a waterfall a b1rthdav cake 97 Use the list below when you revise for your IGCSE examination. The spread number. in brackets, tells you where to find more information. R~v·c;· n hecklist Core Level Extended Level □ ru;. (or ore Lc\'cl, plus the following: D How Lhc la,, of conscnation of enL·rgy applie~ in a cric of c nerg, change . (4.2) Ho,, work done depend~ on force and di tanccn10,·cd. (4.1) The equation linking ,,ork done, force, and di tancc n1O,· ·d. (4. 1) The ioule, unit of work and energy. {4.1) The di ffcrcnt en erg) slant!-.. ( 4. 1) The different \\a\'s in \\hich cncrgs can be tr-..1n~fen·ed fron, one ·tore to another. (4. l) The la,, o[ con en·ation of energ,. (4.2) HO\\ en 'l'g\ b tran fcn·cd whenc,·cr \\Ork i done. {4.2) Ho\\ power depends on work done and tim • taken (or cnl!rID transfcrn:d and time taken). {4.4) D Calculating kin •tic en ·rg\ (K ). (4.3) 0 olving problems on PE and KE. {4.3) O Using the equation linking power, energy □ The wall, unit of power. (4.4) O D □ thermal PO\\CI' tation~ (fuel-burning po,,er tation and nuclear power tation ) produce electricity. (4.5) The altcrnathc to thermal powcrMation □ □ □ □ □ a □ a □ □ (PE) {4.3) trc.1n~formcd (or work done) and time takcn. ( 4.4) D Calculating cificicnc, knowing the energy input and cnct'g) output. (4.4) D Calculating ,fficicnc\ knowing the pow •r HO\\ {4.6-4.8) The di ffercncc between rcnc,, able and non-rcnc, ,:ablc cner'ID rc~ource~. (4. 7) D on-renC\\ able cnerro re ource - (o · ii luel - nuclear fuel The advantages and disad\'antagc~ of each L~ pc, including environmental impact. (4.6 4. ) D 1 a □ Rene,, able encrg\ re ource - h, drodcctric en erg\ - tidal ·ne•"ID - ,, ind energy - wan~ energy - geothermal energy - olar cncrg, ( olar cells and olat pane 1~) The ad, antage and dbadvant~_1g~ of each type, including environmental impact. ( 4.6-4. ) □ How high dficicnc, mean., lc. s energy ,,astc<l. {4.7) 98 Calculating gravitational potential enerm D input and power output. ( 4.4) How to inwrprct cncr·gy now diagrams ( ankc\' diagran1~). (4. -) How, in a scrie of cncrro change , energy tend-, to prcad out and bccoine IL-ss u eiul. {4.5) How the un i the ource of en •1~\ for mo ·t ol our energy re ourccs on Earth. {4. 7 and 4. ) H ow cncrg) i~ released by nuclcar fu~ion in tht: un. (4. 7. 4. , and 10.7) Ho,, re carch i being carried out to deYc)op nuclear fu ion reactor for po,, er tatiom,. {10.7) Typhoon aircraft Lake · off. The gl O\V con1e from hot ga e in it _jct engines, ,vhcrc the t 1ncpcrature can reach more than 1SOO °C. At high altitudes, jet aircraft like thi leave 'vapour trail ' acros the skv. Ho\vever, the trai1 · arc not really va pou 1-, bu l n1illion of tiny droplet , fonncd \\'hen ,vatcr \'a pour fr m Lhe engines onden ~e · in the cold atn1ospher . chapt r S 99 ► Water can exist m three forms: solid, hqu1d, and gas. (The gas 1s called water vapour, and 1t is present in the air.) Like all materials, water is made up of tiny particles. Which form 1t takes depends on how firmly its particles stack together. Solids, liquids, and gases E\'cry material i~ a solid, a liquid, or a gas. citmlisL.._ have developed a m oc.ld (description) calJecl Lh~ kinetic theory to explain how solid~, liquid-.;. and ga c · bchtwe. According to thi · theory, mauer i!) made up of tiny paaticlc · ,, hich arc con ·tanth in mo tion. The patticlc-s attract each othe1 Solid Partides vibrate about f xed positions. trongly\, he-n clo~. but the attractio~ \\e-aken if they mo,·c tu11ht>r apm1. Solid A olid, uch as iron , has a fixed hape nnd \·olume. Jt · particles are held clo!-.ch together b~ strong forces of au raction called bonds. They\ ibratc backwards and fo rwards but cannot c hange posiLion~. Liquid A liquid, ·uch a~ waler, ha~ a fixed Yolumc but can now 10 fill any shapt.!. The pa11iclcs an: close together and aCLratl each 01hcr. But they \ ·ibrJte o vigo rou ·I) thaL the attractions cannot hold them in fixecl po!)ition~. and the) can move pa teach other. Gas A ga , such a hvdrogen, ha no fi,ed hape or,·olumc and quicklv fill any pace available. It particle~ an: well ~paced out, and vit1ually free of an) atlrncLion ·. Th'-!v move ahoul ,lt hi g h ~pecd, colliding with eac h other and the\\ alls of their container. Liquid Particles vibrate, but can change pos,taons. What are the particles? Everything 1s made from about 100 simple substances called elements. An atom is the smalle~t possable amount of an element. n some materials, the ·mov,ng particles· of the kinetic theory are atoms. HOVveVer, in most matenals, they are groups of atoms called molecules. Belo\N, each atom IS shown as a coloured sphere. This is a simplified model (descnption) of an atom. Atoms have no colour or precise shape. 00 00 Gas Particles move about freely. 100 Iron atoms ct3 O' c1 er) oxygen ------f).... atom ~ Water molecule-s ,....-hydrogen atom cP c0 co <o c9 Cb Hydrogen mole-cules THERMAL EFFECTS Brownian motion: evidence for moving particles mo kc is made up o f nl illions of tinv bit · of ash or oil dro p le ts. If , ou look a t mokc th rough a micro cope, a~ on th e right , )OU can sec the bit o t mo kc glinting in the lig hl. ru, thcv dlifl th ro ugh the ah~ the\ wobble about in zil!-7ag pa th . Thi cffcct i called Bro\ Dian motion, a lte r the c ienti t Ro bert Brown who fir t noticed the wobbJing, wa ndering m otion o f pollen grain in w ater, in 1 27. E The kine tic theof) e xpla in B rownian motion as lollo\\ . The bit." of s moke an: j ust big eno ugh to be ·~ n. but ha ve so little mass tha t the~ a rc jo:-.tlcd a bout a~ I ho usands of pa rticles (gas molc~ule~) in the s un·ounding air bump into then, at ra ndmn. I ~ m croscope VH!W through glass n·uc,oscope cover _j_ z1g•zag paths of smolce blh smoke C E Energy of particles Thi! pa,;_ick s (al o m s or molecule~) in ~olid~. liquid~. a nd ga~l!~ have kinc1ic i:ncrID because they arc mo, ing. The, a lso ha\'C polcntia] encrg\ becau~e thci r motion keep · the m ·cp a ra tcd and opposes Lhc bonds tr ing to pull the m togcthc t: The pa 11icles in g .. c ha \ ·c the mo~t po te ntial e nerg, bccau ·e the, aa ~ furthc t apa rt. Kinetic energy 0 Energy because of motion. Potential energy Energy stOfed because of position. The tota l kine tic and pote nlia l e ncrgie · o l a ll the a toms or molecules in a m a w1;al is called its internal energy. The hou cr a m a leria1 i~, th l! faster its panid cs mo\'c, and the more internal cm::rgy it has. Il a hot ma terial h in contact with a cold one, the hot o ne cool d o\\11 a nd lo ~ intern a l net-g:), while the cold one heat up a nd gain~ internal e ne rgy. The energy tra n letTcd i kno wn n~ heat. The terrn them1al energy i often u ext for both internal ener~ a nd hea t. ® 1 Say whether each of the followmg describes a solid, a Hqu,d, or a gas. a Particles move about freely at high speed. b Particles vibrate and cannot change pos1t1om. c Fixed shape and volume. d Particles vibrate but can change positions. e No fixed shape or volume. f Fixed volume but no fixed shape. g Virtually no attractions between particles. 2 Smoke 1s made up of millions of tiny bits of ash or oil droplets a What do you see when you use a microscope to study illuminated smoke floating m air? b What 1s the effect called? G How does t e kinetic theory explain the effect? 3 If a gas is heated up, how does this affect the motion of its particles? What 1s meant by the mternal energy of an object? 0 Relat ed to pics: energy 4.1; changing state 5.10; atoms and etemenls 10.1 101 The Celsius scale Sun's centre 15 000 000 C Sun's sur:face 6000 ( bulb ftlament 2500 C bu sen flame 500 C boi gwater 00 C A temperature scale is a range of number.-. for mea~uring the level of hotness. E\'Ct)<Jay Lcmperatun.-s arc n01mally measured on Lhc Celsius calc (somctjme called lhe 'centigrade' calc). Its unit of tempera ture i t he degree Celsius ( C).The number on t he ·calc wc1c ·pccially cho ~en o that pure ice melt at O C and pure water boils at 100 C (under tandard atn10 phelic pres ure of JOI 325 pa als). These are its two fixed points. Temperatures below 0 ha, ·c negative( - ) , ·alues. human body 37 C Thermometers* warm room 20 C Tl!mpcraturc is mt!asurL'd us ing a thermometer. One s imple l) pc is s ho" n bclo\\. The glass bulb conta ins a liquid - either mcr UI) or coloured alcohol - which expand when the tc1npcra.turc ri es and pus he ~ a ·thread' ot liquid f urthcl' along the calc. 0 C melting ice food in freezer 18 °C I quid oxygen 180 C absolute zero 273 C nar,ow tube? Every thennometer depend on ome propertv (charactc1i tic) of a matetial that ,-nrie · with lemperature. For exan1ple, the t he1mometer above contains a liquid who~ ,olumc in reases with Lcmper.iturc. The two th~nnomete,~ below use material~ whose dcclrical propenics , -ary wiLh lcmpcrc1turc. Clinical thermometers like the one befovv medsure the temperature of the human body very accurately. Their range is only a few degrees either side of the average body temperature of 37 4'C. When remO/ed from the body, they keep their reading until reset. All d1crmornctcl agrcl.! at the fhcd point:>. H oweve1~ at other tcmpcraturl: , the\> may not agree exactly becau e their cho en propertie mav not vary with temperature in quite the ame way. d 91tal meter r. A measu,es current and converts to a temperature reading --___. ~~,/"1131.2_~ Q ,j ~ l J fir - - ~ - ~-· l probe contains thenn1stor copporw r battery (inside) suppbes current for thermistor Thermistor thermometer The thermistor is a device which becomes a much better electrical conductor when its temperature nses. This means that a higher current f ows from the battery. causing a higher reading on the meter. 102 e co,1stant6:-\ IH \' e uJ',,probe conta1r¥.> temperatureens.1n9 ,unct10n Thermocouple thermometer 1wo different metals are 101ned to form two 1unct1ons. A temperature difference between the junctions causes a tiny voltage which makes a current flow. The greater the temperature difference. the greater the current. THERMAL EFFECTS What is temperature? Jn any object, the panicle~ (atom · or molecule ) arc moving, o th 'Y han~kineli c 'ner~. The~ mo\·c al \a1:ving ~pecc.b, but the higher the tcmpl!ral\.trc, then - on a\'CJ-jgc - the faster the~ mc>n!. E 11 a hot object is placed in contact \\ith a cold one, a · on the light, there i a tran fer o[ thermal energ~ from one to the othe1: the hot object cool down, it particle lo e kinetic energy. A the cold object heat up, it particle ga in kinecic energy. \ \'hen both object reach the an1e temperature, the transfer of energy ~lops becau~c the a\·crage kinetic energy per particle is the same in both: Ob_icch -.ll the m1u! l<!111perat11re ha\'l." the \tH11e m·erage kiHetic energy J>el f)at1ide. The higher the tc1npcratut c, thl' gn:ater the average kinct ic cne•t-~' per pm1idc. 0 0 0 0 0 0 Q I ~t·' Q 0 0 0 0 o e•n:i~• ,H 0 0 energy 0 0 0 0 0 ,o O l"lll~ c1:u'l() Qi 0 0 0 0 0 Temperature i · not the am1: a · heat. for example, a ·poonful ol boiling water ha C'<acth the an1c tcmpcratur~ (JOO C) a a auccpanful of boiling\\ atcr, but would tot • far le thermal cnerg) (heat ). Absolute zero and the Kelvin scale As the temp ~ra ture tall~. the particle:-. in a material lo ·c kinelic en "rgy and move more and n1 ore slowh. At - 27 C, they can go no slower. Thi~ i~ the loweM tempcralurc the~ b, and it is calll!d absolute zero. The rule of atomic ph)!)ic~ do not allow particles to ha\'c zero cnel'g)', but at ab olute zero they would hav~ the minimum enerro pos ·iblc. In cicntific work, tcn1peratur~ are often mca u1 · d u ing the Kelvin s cale. Its ten1peraturc unit, the kelvin (K ), is the ~an1c i ✓' as the degrc' Cclsiu~. but the scale uses ab~olute zero a~ its :1cm (0 K ). You con\·crt from one scale to the other· like thi~: Kdvin h.·mpl.·ratUt'\.· K absolute zero =======::::=== -273 C Kelvin scale Cd-..iu-. tl'lllPl'lc.llllll'' -------~ 0 C melting ice -- OK C · 273 boiling water 100 °c 0 0 The Kelvin scale is a thermodynamic scale. It is based on the average kinetic energy of particles, rather than on a property of a particular substance. The constant volume hydrogen thermometer conta1 ns trapped hydrogen gas whose pressure increases i.-.itth temperature. It gives the closest match to the thermodynamic scale and is used as a standard against which other thermometers are calibrated (marked). 373 K \ \fhc1 · gn:atcr accw-ac) L rcquia --d, ab olutc tc1u i taken to be - 273.1 - C. ® 1 273 0 100 273 373 Say wh1ct of the dbove 1s the temperdture of b bo1hng water in K c absolute zero m °C d absolute zero in K e melting ice m C f melting ice in K. 2* Every thermometer depends on some property of a material that vanes with temperature. What property is used in each of the following? a A mercury-in-glass thermometer. b A thermistor thermometer. a b01lmg water m C A B higher temperature I01Ner temperature 3 Blocks A and B above are identical apart from their temperature. a How does the motion of the particles in A compare with that in B? b In what direction 1s thermal energy transferred? c W en does the transfer of thermal energy cease? Related topics: kinetic energy 4.1 and 4-3; motion of particles In solids, liquids, and gases 5.1;expansion of Uqufds 5.3; motion of particles in a gas 5.4; heating gases 5,4, thermistors 8.6 103 Kinetic theory II a concrele or ~teel bar i heated, it vohnne will increase lightlv. The effect i called thermal expansion . It i usualh too mall to notice. bul unit! ·s pace i~ left for it, it can p1·oduce enough force lo crack lhc concn.!lc or buckle the ~ted. Most solids ~xpand when healed . o do most liquids - an<l by n'lor~ than ~olids. If a liquid is stored in a s.calcd container, a ~pace mu t be let t at the top to a How for e~pan ·ion. essentialso According to the ku-.et,c theory, solids and liquids are made up of tiny, vibrating particles (atoms or molecules) which attract each other. The higher the temperature, then on average. the faster the particles Vibrate. 00000 0 0 0 0000 O O O 0 0000 0 000 0000000 0 0 0000060 00000000 00000000 00000000 00000000 00000000 OQOOOOQO, 00000000 cold hOt The kinetic l hcoa, c,plain thcrn1al c~pan ion a · follow . \Vhcn, a), a leel bar i heated, it partid~ peed up. Their vibration take up more space, o the har expand ~lightly in all direction .. If the temperature fall-. the revc ·e happens and the material contracts (gets smallt:r). 09mm .-.-1 1 1 : ,___ _ _..._ ....,_-c. o.9mm 1mm ,__ _ _ _~ ..- - c mm 1 brass a umn:um 2 mm 3 mm f ocrec1se n length of a 1m bar for a 1oovc nse 1n temperaturc Comparing expansions The chart on the lcfl ~how~ ho\\ much I meln;! lengths of diflercnl maLc:rials expand when their tcrnpcr.uurc g0cs up h) l 00 C. For grcacer length · and higher rcmpermurc increase , the expansion i · more. \".' hen c hoo ing maleriaL for particular jobs, it can be importanl to know how much the\' wm expand. Here are two exan1ple : teel rod can be u~ed to rei nlorce concrete becau e both n1aterial expand equal!\', Jf the expan ion were different, the teel mighl crack the concrete on a hot day. lf an ordina~ glass dish is put sLraighl into a hot o, en, the out~iclc of Lhc glass expand ' bcfo1e the in idc and the lI-ain c!"acks the gla s. ~ r~, expand ' much lcs · than ordinal"\' gla · ·, ~o ~hould not crack. gap oilers Allowing for expansion ... Gaps are left at the ends of bridges to allow for expansion. One eod of the bridge is often supported on rollers so that movE?ment can take place. 104 . .. and contraction When overhead cables are suspended from poles or pylons, they are left slack, partly to allow for the contraction that would happen on a very cold day. THERMAL EFFECTS Using expans;on current from •o supplf heater OJ11ent narroi.\l tube Jn lhc thcm1omet ~r abo\'c, the liquid in the bulb expand~ when the temperature 1;ses. The tube is n1ade na1To,,· so that a small increase in ,·olume of the liquid produces a large mon~ment along the tube, a, explained in the pn:,·iou~ spread, - .3. 01meta stnp; C())(J l ~e============T', , brass ,n..'cl/ ... hot - b1metal stop ~~ brass brass expands most ln the bimctal s trip above, thin ·tdp~ of two diflcrcnt 1netal~ arc bonded together: \Vhcn heated, one metal cxpanru, more than the other~ which make the bimctal llip bend. Bimctal tlip , arc t~cd in wnic them1ostats - de,'ic~ for keeping a ~tcady temperature. The thennostat shown on the dght is conrmlling an dc..-ctdc heater. More n1odcm designs ofrcn use an electronic circuit containing a thcrmiM01~rather than a bimetal strip. Water and ice* \Vhcn hot ,,ater cool . it contract~. Howe,· •r, when water frc ·ze it e"pand.s ~\~ it tun1s into ice. The fore' of the expan~ion can burst water pipes and split rocks with rain\\'ater trappL"d in rhcm. \Vatcr --xpand~ on fr!C7ing for the following rca on. ln liquid wale•~ the particles (,,atcr molecule..~ ) arc do~c together. But in ice, the molecules link up in a VCI} OJA!n ~trU<.:tur·c that aclualh takL'~ up 1110re space than in chc liquid - a~ shown in Lhe diagram on the right. Ice ha a lower den ity lhan liquid water - in other \\Ot'CI •• eac h kilogram ha a grca tcr ,·olumc. Bcc~m e of it lower d "n i l ,. ic • noal on water. \'\fhen liquid water i cooled , the molecule ~tarl fon11ing into an op , n ~tructun: at 4 C, just before frcc,dng point is rcacht..--d. As a ,-esuh, ,,utcr expands VCI} ~lightly a~ it is cooled from 4 C to O . It take~ up least ~pace, and therefore ha, its ma.,i1nun1 clen~it), at 4 ® 1 Ex~am the follQ'..ving : a A metal bar expands when heated. b Overhead cables are hung with plenty of slack in them. c It \Wuld not be a good idea to reinforce concrete with aluminium rods. d A b1metal stnp bends when heated. e* Water expands when ,t freezes. control l'lOb .& Bimetal thermostat When the temperature nses, the bimetal slfip bends. the contacts separate. and the current to the heater 1s cut off. When the temperature falls, the bimetal strip straightens. and the current is switched on again. In this way. an approximately steady temperature is maintained. 0 0 0 000 0 0 ogoo goigoo0°o ooooooooOoooo o 000ooo 0 oo0 o o 00000 molecules 1n liquid watet molecules 1n ~ 2 This question 1s about the thermostat in the diagram at the top of the page. a Why does the power to the heater get cut off if the temperature rises too much? b To maintain a higher temperature, which way would you move the control knob? - to the right so that ,t moves to,.,-vards the contacts, or to the left? Explain your answer. Related topics: density 1.4; ktnettc theory and particles 5.1: thermometers 5.2; thermistors 8.6 105 essenliatso Kinetic theory According to the k,net,c theory. a gas is made up of tiny, moving partides (usually molecules). These move about freely at high speed and bounce off the walls of their container. The higher the temperature. then on average, the faster they move. thermometer pressure g~uge nlike a olid or liquid, a ga do~ nol nece arily expand when heated. That is because it · volume depend on the onlainer it is in. \\'hen dealing wilh a fixed n1ass of gm;, there an: ah\an, three factors to con~idcr: pressure, volume, and 1crnpcratun.:. Depending on the circumstances, a change in tcn1pcratu1·c can produce a change in pr~urc, or \olume, or both. This . pread deal with lhe effect of a change in temperature. To find out more about the link between the prcs~ure of a gas and its \"Olumc when Lh<! tcmpcralurl;! docsn'1 change, sec ~prcad 3.S. How pressure changes with temperature (at constant volume) l n the experiment on the left. air i · tr-.ippc<l in a nask of £ixcd volume. The tcmpcratu1·e of the air is changed in stages by heating the\\ atcr - or puuing a hottc1 or colder material (melting ice. orc,amplc) in the container. At each Lage, the pres urc i mea ured on the gauge. The table hows some typical reading ·: temperature/ C ~ 20- - 80 pressure I kPa 102 123 trapped a r 140 200 144 165 A-.. lhe temp"rature of the air 1i es, o doe the pres. ure. Thi i!',, becau e the molecules mo\·e fa~ter. Then~ is a greater change in momentum lower temperature IO',ver pressure \\'hen the~ hit the ~idc ' higher tempc,ature ::: faster molecules ___.,. molecules hit sides 111\th greater force higher pressure or tht.• fla~k. ~o a g1·catcr force: The cylinde1 u ed for to1ing ga~ arc trong enough to with tand nny extra pressure due to normal 1i ·es in lemperaturc. 11 i · dangerou · to th1-ow aerosol cans on bonfire~ because 1hcy might burst. Howe\·cr, 1ha1 is mainly because mm\! of lhc liquid propellant in Lhc can turns lo ga~. 106 THERMAL EFFECTS How volume changes with temperature ( at constant pressure) coloured Tn the e\:pednie nl o n the rig ht , trapped ga (air) i~ heated a t cons ta nt pn.:~sun!. Thi · i~ a tmospheric pressure bccau ·I.! o nl~ the ·hort le ngth of liq uid separa tes th e air from the a lmo sphc1·c ouls idc. As the tcmp~r-.llure rises, th e \'olume of the ga~ increases the gas expands. lt0u1d dlr at con~tant pre~su•e <atrr ospt-,C'f Here i an e,pcairncnt lo how the oppo ite d1ccl. Take an empt~ pla tic bo ttle (of the type u~ d for bottled \\ a tcr). rcw the to p on tighth. Put Lhc boulc inn freezer for aboul 5 n1inutes, then ~ e ff you no tice any diff~t~ nce. E Comparing expansions of solids, liquids, and gases At const ant pre~ ·ure, gases e xpand much mon: th an liquid which , in lun,. expand m ore than solids. For e'\ample, fo r the same volume o f material a nd th e same rise in Lemperature (Mat1ing a l roo m Lempcr.itun:): \Va1c r cxpand ~ 7 time a 1nuc h a teel heat1119 .& In this experiment. the Ai r (at con t an t pr~ ut~) expands 16 tin, ~ a~ muc h a.s wa ter. ft is 1hc s lrcng th o f 1he a n ractio m. between the particles (m olc:cules, fo r example) chaLmakes 1he differe nce. ln a solid, the a l tractio ns an: \·er> ·tro ng. lf the tempera tu re d e:-i and rhc p article mo\'c fascer, thi~ has \ Cr~ little eilect o n the ir ~cpar~Hion bccau ·c the) a n: ·o tightl) held togethe r: In a liquid , the a tt rac tio n a, ~ weaker, o lhc C"(pa n io n i grca lcr. In a ga , the a ttraction · arc ext, "mch weak, o the c xpa n io n i · muc h n1o rc. pressure of the gas stays constant. As the temperature increases, so does the volume. ◄ Before its flight, this balloon is filled with cold air using a motorized fan. Then the gas burner raises the temperature of the air to 100 °C or more. There is no change in pressure (it stays at atmospheric), but a large increase in volume. 1 How does the kinetic theory explain the following? a A gas exerts a pressure on its container walls. b The pressure increase with temperature (assuming that the volume does not change). 2 If a gas 1s heated at constant pressure, what happens to its volume? 0 0 Comparing a solid with a liquid, \\'hich \.A'OUld you expect to expand the most when heated? Use the kinet,c theory to explain your answer. Comparing a liquid with a gas. which ,.-.,,ould you expect to expand the most when heated? Use t e kinetic the°'y to explain your answer. Related top1cs: momentum 2.11; gas pressure and volume 3 .8 ; ktneUc theory 5-1; temperature 5.2; expansiOn of solids and liquids 5-4 107 lower iemperat\Jte Very good conductors metals e.g. 0 copper aluminium iron silicon graphite Very poor conductors (insulators) 0 glass thermal energy transferred by conduction All matetial · are made up of tiny, mo ving particle~ (ato m or molec ules). The hig her the lempcracurc, the fa~cer the particles m o\·e. l f o ne end of a metal ba1· is heated as abO\'L', 1hc other L'n<l e\'cntua.LI) bcconlcl) too h o t to touch. 'f'hcrmal cncrg ~ (heat) is tran cn'\XI from the hot end to the cold end a the fo5ter particle pa o n their e ~tra mo tion to particle all a lo ng the bat: The proce-.. L called conduction. i\lon: thermal ene rg) is rran~forrcd c,·ef) second if: plastics • • • rubber Therma conductors and 1nsulators wooo wool om~ materia l · arc muc h better conductors than o thers. Ver") poor conduc to1 arc called ins ulators. Many matctial arc in bel\\ecn the t,, o. water materials containing trapped air wool glass wool {fibreglass) plastic foam expanded polystyrene l he materials above are arranged in order of conducting ability starting with the best. the tcmper.Hurc differen ce across the ends of 1he ba r is increa 1;ed the t:ros ·-sec tio nal ('end-on') area of lhe bar is i11c:rellsed the lcngLh of thl' bar i · reduced. Me ta l arc the be t thermal conductor . No n-m etal ~o lids tend to be p oor conduc ton-i; so do most liquids. G ~1ses arc the worsl o f ~1ll . Muny m a terial, an: ins ulato~ hecausc the~ contain lin) poc ket~ of tr..ippcd air. You use this idea \\hen \ O U put o n lots of la)Crs of clothes to keep yo u \\a1·m. Thea\.' arc ~omc m o r~ c~amplc - at the top of the ncxc page. Yo u can o n1etime~ tell ho\\ well o n1ething conduc t~ j u l b, to uc hing it. A m e tal do or hand]e fed cold because it quickly conduct t hcrmal e ne rg) away from yo ur hand, which is warmer. A p o ly styrene tile led~ warm because it insulat<.-s your hand and slop~ i L lo~ing thermal cncrg~. roos coared with a thin la'('er of wax 'Nhen cold \ <1 uze to tr41p 1<:e & Comparing four good thermal conductors. Ten minutes or so after the boiling water has been tipped into the tank, the length of melted wax shows which material is the best conductor. 108 • This experiment shom that water is a poor thermal conductor. The water at the top of the tube can be boded without the 1Ce melting. THERMAL EFFECTS Using insulating materials A Feathers give good thermal insulation, especially when fluffed up to trap more air. In counL1·ics where buildings need to be h caLc c.l, good insula tio n means lO\\ Cr f ucl bills. Abo\'c a r c ·o mc o f the \\a) s in which in~ulatirlg m~1h: d als a ,~ u ed to ,~d uce heat los~c · from a hou ·e: Pia tic foa m lagging round the hot wa ter lorage tan k. 2 Gia wool or minera l wool in~ulation in the loft. 3 \ V~lll cavity fil led with pla tic roam , b ~ad s, or mineral wool. 4 Do ublc-gla7cd win<lO\\S: two s heets o f glas~ \\ ith air be twee n thcn1. E How materials conduct \Vhen a ma te ri a l i~ heated , the;: pa rticles mo\'C foster·, pus h o n neighbouring partidcs, and sp eed those up too. All m a tc1; als conduc t like this but, in metals, e nc11f\ is a lso Lrans fc rn.x.l by a no ther. much quic ke r method. ele<. trons in fre~ atom electrons ... ' ' . ··o·: . . .. • •• In ato,n , there arc tin~ pa11icle ' called clcctrom. ~to t arc fi n11I) attached , but in n1ctal , o n1c arc 'loo c' a nd free to daift bet we-e n the a to m s. \\'hen a m e tal i heated , the c free electrons pecd up. As they m o ve randomly within the me tal, tht:) collide with a toms a nd make them \'ihra le fa~ lcr. In this way, therm a l e n e rgy i~ ra pidly t rans fcrr<..-'<.I to a ll pa rts. An electtic c ur-rent is a llow o f electron - so 1n cta l~ an~ good electrical conduct01 . _ well a~ good thcrn1al conducto , . 1 Explain each of the following : a A saucepan might have a copper bottom but a plastic handle. b Wool and feathers are good insulators. c A Glass wool aluminium window frame feels cotder than a wooden window frame when you touch 1t. d It is much safer picking up hot dishes with a dry cloth than a wet one. 2 Grve three ways in which insulating materials are used to reduce thermal energy losses from a house. A Atoms in a metal 3 A hot water tank loses thermal energy even when lagged. HO'N could the ,energy loss be reduced? 4 look at the experiment shown on the opposate page. co"V)anng four thermal conductors. a Which of the metals 1s tt e best conductor? b In experiments hkc this, it 1s important to make sure that the test is fair. Write dawn three features of this experiment which make 1t a fair test. Why are metals much better thermal conductors than most other matenals? 0 Related topics: energy 4.1; part1des or matt~r 5.1; temperature 5.2; electrical conductors 8 .1 109 warm coofer water s,n ·s water convectlon cu rent potassrum _ / permanganate crysca's to Liquid" and ga~C'I arc porn- thermal ccmduc ton-., but if the, ar~ fn.~ to circ ulate, they can carry the1-m"1I cncr-ro Imm one place co another \'cry quic kh. rises R colour water Convection in a liquid In the c~pcrinwm on the left. thL· bottom of the bt:akc1 i~ being gcnth heated in one place onl~. A ' the \\;_uea abo,·e the name become ,,a1T11cr, iL e,pancb an<l become~ le ~ den~·. ll ri~c" up" ard a coo let~den er\\ atcr ink!-. and di"plac~ it (pu he it ouc of the,, a,·). The P -!'\ult i a circulating Mrcam. called " convection curTent. \\'h "re the water b heated, i r.,., particle~ (\\alcr· molec ule~) gain cncr~ and ,·ihrntc mm~ r.1piclly. A.., the particle~ cin.: ulatc. Lhc, lrttnsfcr encrg, to othcr parts of Lhc beaker. a Convecti on doe not occ ur the water i heated at the top rathc1 than at the bouom. The ,, arn1cr, les" c.kn L' water !'>l3) ~ at the top. Convection in air Convection can o cur in gascc~ as wdl a s liquid~. For exan,plc, \\at111 air ti~e "hen it b dbplaccd b) cooler, d~·n •r air sinking around it. b~· the un, warm air ri~c~ abo,c the equator a., it i~ di,placcd by cooler, denser air sinking to the nonh and south . The 1':sull is huge con,cction cU1·renh in the Eanh's auno-;phl'r'-.'. 1 hcst cause,, ind, a<:ro s all ocean~ and continent . Con\'cctio n aJ o cau e the on hore and olf hot~ brcct" ,,hicl, ~o mctimc:- blo\\. at the coa Lduring the tm1mcr: H c:Hed Dunng the daytime. m hot sunshine, the land heats up more quickly than the sea. Warm air rises above the land, as at ,s displaced by cooler arr movmg in from the sea. air cools At night, the reverse happens. The sea stays warmer than the land, which cools down quickly. Warmer air nO\v rises above the sea, as it is displaced by cooler air moving out from t e land. 110 cool a r sm s THERMAL EFFECTS Using convection in the home heated watC!r collects in tank air cools hot taps from top down wa,m alf nses 1nsulat1on _ _ , heater or rad ator Room heating Warm air rising above a convector cold watc, supply i i cooJer water hot wat1.:1 ,eturns fro,n bo1let heater or radiator carries thermal energy all around the room - though unfortunately, the coolest air is always around your feet. tobo r Hot water system In the system above. hot water for the taps comes from a large storage tank. The water is heated by a coil of copper pipe: hot water from a boiler flows through this and is recirculated by a pump. In the tank. the heated water rises to the top by convection. In this way, a supply of hot water collects from the top down. The tank is insulated to reduce thermal energy losses by conduction and corwection. Practical systems are more complicated than the one shown. There 1s additional p1pc,,work to allow the water to expand safely when heated. Also, there may be an extra circuit for radiators 1 Explain the tollOY1mg: a A radiator quickly warms all the air in a room, even though air is a poor thermal conductor. b The smoke from a bonfire rises uptNards. c Anyone standing near a bonfire feels a draught. d The freezer compartment in a refrigerator is placed dt the top. e A refrigerator does not cool the food inside it properly if the food is too tightly packed. 2 On a hot summer's day, coast.al winds often blow in from the sea. a What causes th~e winds? b Why do the winds change direction at night 7 Refrigerator Cold air sinks below the freezer compartment. This sets up a circulating current of air which cools all the food in the refrigerator. 3 Some hot water systems have an immersion heater an electrical heating element in the stOf'age tank. In the tank below, should the heating element be placed at A or at B? Explain your answer. _ _ - . 1ohot water taps - - - A--i possible pos,t10ns for heating element co!d v-:ater _,. c:::= 8--' Related topics: wor1< and forms of en!Ngy 4,01 111 On Earth, ,,e are wanned b, the un. It energy trnYel ~ to u in the fo1111 ol electron1agnetic wave . The e include in\'i ible infrared waves «~ well a lig ht, and they can travel throug h a vacuum (empty pace). They heat up things that ahsorh them, so are oflcn called thermal radiation. f '\1\/\/V\/\N light (vlsb ) 'VVWWV\/'v 'V\NVVWV\/\/V\, .A. Thermal radiation is mainry mfrared waves, but very hot obJects also give out light waves. All objcc1s g iH~ out some thc1·maJ rJdiation. The hig her their u1facc Lempe•.._ turc and the gr ~ater their ·u1 face area, tht: mo1'\:' cncr~.~ they radiate per second. Thennal radiation i a tnbaure of diftcrent ,vavclcngths, as ho,\11 on the lclt. \ arm object radiate infrm ,d. But if the, be ome hotter, they al~o emit horter ,,ra,·clengths whi h n1ay include light. That i why a radiant heater or grill starts to g low 'red ho t' when it heats up. Emitters and absorbers ome surfac<!s are better at cmilling (sl!nding out) lhcrmal r'1diation lhan ochc ·. For cxanlplc, a black saucepan cools do\\ n more qui ckly lhan a ·i1nilar white one bee au ·c it emits cncrg) at a fill)ter !'ate. Good emiue, of thermal radiation are al o good ab od>e1 , a~ ho,\11 in lhe chart below. \Vhite or il\'ery urlace~ are poor v.b orbe1 because they reflect mo~t of the• hl.!rmal radial ion a,vay. That i~ wh,·, in hot, ~unny countric~. houses an- often painted white lo keep them ccx>l in~idl!. best ..............................................................V,'OfSt emitters -------r----mall= non•shrny ► This chart shows how some surfaces compare as emitters, reflectors. and absotbe<s of thermal radiation. _ _ _ _ _ _ .Jo..__ ____;_ _ refl ectors v-.10rst ....................................•......•.•......•.•....•.•. t>est absorbers best ...............................................................worst matt black conta:rnng boiling water f Comparing emitters The metal cube is filled with boiling water which heats the surfaces to the same temperature. The thermal radiation detector is olaced in turn at the same distance from each surface and the meter readings compared. 112 comparing absorbers The metal plates are placed r at the same distance from a radiant heater. To frnd out which surface absorbs thermal rad,at,on most rapidly. the rises in temperature are compared. THERMAL EFFECTS The Earth in balance? Tf an object ab orb~ thern,al radiation faster than il radiate , i l heat up. Jf it radiates faster than it absorbs, il cool down. The temperatun;! change until a halan c is ~ached. This is true of 1he Earth, \\'hich is absorbing incon1ing radiation from the un, but also radiating energy into space. \.Vithoul an atmo ·phcrc, the arth' a,crage urface tcmpcratrn~ ,,ould be - 1 t• • Ho\\evc,~ carbon dioxide and \\ater \'apour in the atn1osphcrc trap ome of the incoming energv. s a 1 suh, the av .. rage Mttface tempcrattu'C is closer to I - . Over the l~t 60 years, the amounl of carbon dioxide in the atmosphere has gone up b\ more Lhan ()Gr, n1ainh due to lhe incn.~tLst!<l burning of fossil fuds. s a result, the nows of tht.·1-n1al r-c1diaLion m~ out of balance, and the Ea11h i very ~Jowly warming up. \\'c have global warming. 1 • The atmosphere affects the rate at which the Earth absorbs and emits thermal radiation. More transfers l n n1an, situation , the tran ·fer of cncrg) 1akl!~ place by more than one proce . Here are t\\ o example : • Stand 1n front of this wood-burning stove and you will feel the warming effect of the thermal radiation coming from rt . However, the room is mostly wanned by air that is heated by the stove, then rises and circulates by convection. 1 111hite srlvery matt black Which of the above surfaces Is the best at a absorbing thermal rad1at1on b emitting t crmal radiation c reflecting thermal rad at1on? When a warrn obJect is heated up. the thermal radiation 1t emits changes. Give t\W ways in which the thermal rad atIon changes. Where 1n the radiator of a car engine 1s energy transferred by conduction? 4 In experiments like those on the opposite page, It as important to ma e sure that each test Is fatr. 0 0 • A car has a 'radiator' to stop its engine overheating. Unwanted thermal energy is carried by liquid coolant to an array of pipes. conducted to metal fins, then carried away by air flowing across the fins Only a little of the energy is transferred by rad1at1on. a Write down three features of lhe Comparmg emitters experiment that make ,ta fair test. b Repeat for the Companng absorbers experiment. A hot metal sphere is absorbing SO J of energy every second from a nearby radiant source. Explain what will haopcn tot e temperature of the sphere 1f a lhe sphere 1s radiating 40 J of energy per second b the sphere Is rad,ating 60 J of energy per second. 6 In the solar panel above, why does the panel have a a blackened layer at the back b a net\-vor of water p1pes? 0 Related topics: energy 4.1; global warming 4.7~solar energy 4 .7- 4 .8; thermal energy 4.1 and 5 .1; conduct1oo 5.5; convectl()n s..6. electromagnetic waves 7.10-7.u 113 Evaporation 0 Kinetic theory essentials E\'cn on a cool day, r-.1in puddles can \'anish and wet clothes di) out. The \\atc1· bccon1c an invisible gas (called \\atcr vapour) which d1~ifts a\\'a\ in the ai1: \\'hen a liquid belo\\ it boiling point change· into a ga , thi i called evaporation. It happen, bccau c ome pa11iclc in the liquid n1ove iru.tcr than others. The t nster one near the ~urfa e ha\·e enough energy to escape and form a gn . According to the kinetic theory, every matenal is made up of tiny, moving particles (usualtj molecul s). These move at varying speeds. But the hig er the temperature, then on average, the faster they move. E There arc scn.•ral wa)s of making a liquid evaporate more quickly: Increase the temperature \\'et clothe · <ln a tcr on a wanu dav be au ,c more ol the pa11icle (\\atcr n1olccule~) ha\'e enough enetl-T\ toe cape. In a liquid, attractions keep the particles together. 1 1n a gas, the particles have enough energy to overcome the attractions, stay spaced Increase the surface area \Vatc1· in~ puddle dries out more quickl , than water in a cup because more of its molecules arc close to Lhe surface. Reduce the humidity* TI air is ve1 · lum1id, this means that it already has a high water n1pour content. Tn humid air, wet washing dric~ slo,, ly 6'.:causL' molecule:-; in Lhe vapour rcLum Lo the liquid almost as faM a~ those in the liquid L'S<:ape. l n less humid air, wet wa hing d1ie mon: qui<:kly. out, and move around freety. Gas a nd vapour Of Blo\V air across the surface \ Vet clothe dry fa tc-r on a wind, dav be au, e the mo\'ing air carrie e, ea ping water molecules away bet ore A gas is called a vapour if it can be turned back into a liquid by compressing it. manv of them can return to the liquid. • 0 0 T When a liquid evaporates, faster particles escape from its surface to form a gas. HO'.vever, unless the gas is removed. some of the particles will return to the liquid. O gas 0 0 e 0 O 0 0 0 oi 0)90 ooQ}Oooi oQo o~ooJb 0 0 o0 o 0 0 oo iqod •00q 0Oo0 0 0 Oo0 0 00oO ,00 0000 0 0 0 Oa 0 0 0,-,. 0 .... or:.0O~n ,0r..""O 0 .E Boiling Boiling i · a \'Cl) rapid fonn of evaporuLion. \Vhcn \H1ler boils, as in the photogr._ ph on the left, ,a pour bubbles for~rn deep in the liquid. ·rhl'.~ expand, Ji c, but ,t, and re lea c large amount , of \'apour. ven cold water hu. tin,· vapour buhbles in it, but the!'-ie are squa!'-ihed hy the pn:ssure o l the acmo phere. At 100 C, the \'apour pressu1"C in the bubbles is ~trong enough lo overcome aLmosphcric pressure, "i<> the bubbles start to expand and boiling occur~. At the top of 1ounl Evcn.:sl, whcc-c almosphcdc prL-ssurc i less,,, atcr ,, ould boil at only 70 C. The cooling effect of evaporation Evaporation h~ ~-- cooling ctfect. For cxarnplc, if you \\Cl , out hands, the water on them tarts to evaporate. As it evaporatt~. it take thermal energ) away hum your kin. o ,·otar hands tee] cold. 114 THERMAL EFFECTS f The kine tic them} expla ins the cooling e ffect like 1his. If fas ter part ides c.scape fro m the liquid, lo wer o ne a rc le ft behind, o the tempc.-a tu rc o f the liquid i • le Lha n beto 1 ". (D rcfr,gcrant vapour hqwd Refrigerators use the cooling effect o [ evapo rati on. Jn the refrige ra to r o n the r ight, the procc~ wor~ li~e this: 1 In Lhc pipe in Lhc h~ ezcr compartment, a liq uid called a refrigerant cva porat and ta ke · thc n11a) c ncrgv fro m the food and a ir. 2 The vtlpour is d rawn awa) by the pump, which compressc. it a nd turns it into a liq uid. This rdca...;cs thc1-m a l enc~. so the liq uid heats up. 3 The ho t liquid is cooled as it passes th ro ug h 1hc pipes al 1hc bac k, and the thermal cncrg) is c arried awa) b) the ai r. O, c,-all , therm a l cncrg_\ i · tra ns ferred lro m Lhc 1h ing · in ide the fridge to the a ir o ut ide. weating a l ·o uses the cooling c ffc t of "\ a poratio n . Yo u stan to S \\ ' ~ l if your bod) te mperature rises m o re tha n about o.- C abo ve normal. The s wea t, which is ma in)) wa ter, com es o ut o f tiny pon:s in yo ur skin . rh it evaporates, it ta kes thermal c nerg) rro m your body a nd cools you clo wn. On a hmnid ('clo L"') d~n . \\Ca t canno t c\'a po rate o ea ih. o it i n1orc difticulL to ta\ cool and comfo 11able. Condensation \ Vhe n a ga · c ha nge~ bac k into a liquid. thi b culled condensation. For C'.\a mp1e , cold a ir can ho ld less water \'a po u r th a n wa rm a ir, o if humid a ir i~ s u<ldcnly cooled , some o f the wa ter \'a pour m ay conde nse. It m ay become billio ns o f tin) water d roplets in the air - we sec thes e as clo uds, mis t, o r tog. Or it m ay becom c condcn a t io n o n \\ indo w or o lhe r freezer compartment 0 Changes of state A change from hqu1d to gas (0< gas to I quid) is called a change of state. A change from liquid to solid is another change of state It is called solidification, and water freezmg 1s an example. When ,t happens, the particles continue to vibrate but do not have enough energy to overcome their bonds and change positions. · u iiace . U conde n a t io n h·eez1.: , th e 1 • uh i • fro t. Condensation can be seen ...on m· rors ®0 A puddle and a small bo.vl are next ...as clouds in the sky to each other. There 1s the same amount of water in each. a Explain \Nhy the puddle dnes out more rapidly than the water in the bowl. b Grve two changes that woold make the pudd e dry out even more rapidly. 2 If you are wearing wet clothes. and t e water evaporates, 1t cools you down. How does the kinetic theory explain the cooling effect? ...and as clouds of 'steam' from a kettle (the vapour itself is invisible) 3 Give two pracucal uses of the cooling effect of evaporation . 4• Explain i.-\'hy, on a humid day a you may feel hot and uncomfortable b you do not feel so uncomfortable If there 1s a breeze bl01N1ng. What 1s the difference between evaporation and bo1hng? 6 Why does condensation f0<m on cold wmdo.vs? 0 Related topics: atmospheric pressure 3.7; solids, l1qu1ds, gases, and k1netk: ttleory 5.1; cl\ange of state and latent heat 5.10 115 0 Internal energy If a matenal absorbs thermal energy. its internal energy ,ncreases. For more about internal energy. see spread 5. 1. T a mate1ial takes in theamal energ\, then unles it is melting or boiling, iL, tempen1turc ri.sc ·. Howc\·er, omc material~ ha\·e a greater capacil) for absorbing 1hermal energv than o the 1 . For example, H \ OU heat a kil ogram e~1ch of water a nd aluminium, the water· mu ·t be supplied with nearly fin? tim~ a much enerro a the aluminium for the ame 1isc in te mperature: 1 kg alurNnium - I _. 1 C -- a......... A 900 joules of energy are needed to A 4200 joules of energy are needed to raise the temperature of 1 kg of water by 1 ~ +[J=trJ raise the temperature of 1 kg of aluminium by 1 C. c. cientific all) speaking, \\atcr has a specific heat capacity of 4200 J/ (kg C).Aluminium hu a ~pecific heat capac it\ of o nly 900 J/( kg C). Other ~pc ific heal capacities are ~hown in the table ht>low lefl. Units Energy 1s measured in joules U). Tempera ture is measured in C or in kelvin (K) Both scales have the same size 'degree'. so a 1 C change in tempera ture 1s t e same as a 1 K change. The energy that must be tn1n fen·ed to an object to inc rea ·e its ten1pera turc can be calcula1ed u ing thi equation: L'lll.'rgy lram,k·n-l.'<l mas.., • specific heat L-.tpacily · ll.'mpct ..alur l.' changL' In sy mbols: where 111 i~ the mass in kg,,. is the ~pecific heat capac it) in J /(kg 8 repre ent the temperaturc c/zange in C (or in K). ). and The san1c cqualio n can also be u~L-d to calculate the cncrgv transferred (Spe!Ci°flC heat capacity ,.____JJ _ (k ;;_,g~ Q___ 4200 2500 2100 900 glass 700 steel 500 400 copper E:rnmple If 2 kg of \\ah.•r coob lrom 70 C to 20 C, how much l h~11n;.1l cnl.!1 gy do~s i l Ins~? Jn 1his case. 1he temperature chang e i~ 50 C. o: energy tr~ n~fl'n·cd 111co9 2 4200 -o J = 420000J Thermal capacity* The quanlil) 11u1ss x specifi<: heat ct1pt1c i1,• is called the thermal capacity (or heat capacit ). For c:-.ample, il there i · 2 kg of water in a letlle: thermal capacity of the water 2 kg x 4200 J/( kg C) 8400 JI Thi · rnl'•.u1~ that, Lor each I C rbc in tcrn_peraturc, 400 joull's of l:llCrg_, musl be supplied to the \\'aler in the kcule. A greater mass of water would ha, c a hi gher thermal capacity. 116 THERMAL EFFECTS Li nking energy and power energy power = - . - t11ne So: E energy = power x time Energy is measured in joules 0). PO\Nef is measured in watts NI), Time is measured in seconds (s). Measuring specific heat capacity \Va le r Al) pical e~pc1i mcnt is s hown on the ri ght. Hen!, the beaker con la ins 0. - kg o l wa tl.!r. \ Vhc n the 100 wa tl electric heater b witchcd on for 230 seconds, the tempe1-aturc or the w·c.11cr 1;scs bY I O C. Fro m these figu res, a \'alue for the pccific heat capaci ty of water can be ca lculated: co _r ==•:::=_, ~ply ele<.tr,c heate, (Omitting some o f the unit-. for s implic il) ) e nergy tra nsferred to water - 111c~8 0.5 >-. c x I 0 encrg) s upplied by heate rpower > Lime I 00 x 230 · 23 000 J SO: 0.- XC X 10 23 000 Rl.'a n -angcd and .simpli fied , this g ives c: 4600 so l he s pcci fie hi:al capacity of wa ter is 4600 J /(kg ). water gives out Thi nicthod m,1k •~ no a llowa nce for an\' then11al cnergv losl to the beaker or the s unn undings, so the value of c is o nl v approxim ate. , ______ thetmal energy \ I / .,,, Alun1inium (or other n1etal) The mcthcxl is as abo\·c, e , cept that a block of aluminium i.s used ins tead of wa ll.'r. The block has holes drilled in iL for the heater and th »rmo mctcr. As be fore, c is calculated fro m thi ... equa tion: power x time - 111c T (a~ uming no therma l energy lo c ) Storing thermal energy Because of iL-.. high s pecific heat capac ity, wa ter i~ a \'cry useful s ubMa ncc for Moring a nd can-)ing thern1a l encrg\. For example, in centra l hea ting ~ys tcm.s, wa lercan i cs therma l energ, fro m the bo iler to the racliat01·s around the house. In ca r· cooling syste ms, wa ter ca n;cs u nwa nted th cr~mal c ne rID fro m the e ng ine lo the ra dia tor. ig ht stcn-age heaters use concrete blocks to store the rm a l cncrg~. Ah hough concrete has a lO\\ er pecific heat cap aci t) tha n wa te1·, it h, m ore clcnse, so the same mas~ takes up lc~s s p:ice. Elec1r-ic heating clem ent hent up the block O\'ernight, u ·ing cheap, 'off-peak' ckcltici t\' s upplied th rough a s pecial me ter. The hot blo ks release therma l e nergy through the day a lhcv cool down. ® r l water ta es in thermal energy I boiler • Inmost central heating systems. water is used to carry the thermal energy. The speo·t·1c heat capacities . . of copper and water are given . G If, in part b. the copper 'lh-ere replaced by water. in the table on the opposite page. 1 Water has a very high spec1f1c heat capacity. Give W/0 how much thermal energy i.vould this give out? A 210 W eater is placed m 2 kg of water and switched on for 200 seconds, a HO\N much energy is needed to raise the temperature of 2 kg of water by 1 °C? b How mudh energy does the heater supply? c Assuming that no thermal energy 1s wasted, what is the temperature nse of the water? practical uses of this. 2 a How much thermal energy ,s needed to raise the temperature of 1 kg of copper by 1 °C 7 0, If a 1Okg block of copper cools from 100 °C to SO hO\v much thermal energy does it give out? cc, 0 Relat ed topics: density 1.4; thermal energy 4.1 and 5.1; Internal energy 5.1: temperature 5.2; eleclr1cal power 8 .12 117 \•V ater can be a olid (ice), a liquid, ora go. · alled water n\pOtff (or cmpc,raturc/ teanl). The e are it three pha cs, or tatc . C Solid to liquid 20 lqu:d mcl· ng 0-4------....,;;;,--. tme Kinetic theory essentials If ice from a cold freezer i · put in a warm room, il o.b~orb the1mal enerID, The graph on the lch ho\\ , \\ hal happen to it tcn1peralut-e. \ Vhile n1elting, the ic\! g~ on ah orbing energy, but it · temperature doe not change: it tay at O lhe tnelting point. The energ, ab orbed i called the latent heat of fusion . l l i needed to eparate the particle~ o 1hat the, can tornl the liquid. If the liquid changl: back to a olid, the energy L re lea_ed again. O , 0 Accordrng to the kinetic theory, materials are made up of tiny, moving particles (usually molecules). In solids, the particles are held together by strong attractions. 1ln liquids, they have more energy and are less strongly held. In gases, they have enough er1er9y to overcome the attractions, stay spaced out. and move around freely. 330 000 J + 1 kg ICC 1 - Tee ha a pecific latent heat of fu ion of 330 000 J/kg. ThL mean chat 330 000 joule of energy mu t be tran ·fen "d to change each kilogram of ice into liquid water at the ame temperature (0 C).for an, kno\\ll ma ~. 1hc encrg)' tran ·fcncd can be calculated u~ing thi · equation: ----------- Jn ~vmbol : l.'11L'l"gY trun~fl.'n l.'d mL For example, if 2 kg of ice b melted (at 0 C): energ\ transfen·cd - 111L - 2 kg x 330 000 J/kg - 660 000 J *Mca uring the specific latent heat of fusion of ice In the expedment on the lelt, a J00 wal t heater b witched on for 300 ccond . B, \\dghing the water collected in the beaker, it i found that 0.10 kg of ice ha melted. Fron1 the c figure , a ,·alue for L can be calculated: - - - f unnel 0 6 0 -beaker (Omitting ome of the unit for implicitv) energ\ tran"ifcn·cd when kc- 1nelt ml - 0. 10 L energ) ~ upplied b) heater power x time I00 \ , 00 - 30 000 J o: 0.10 L - 30 000, which give L - 300 000 o the . pecific latent heat ol fu ion of ice i 300 000 J/kg. Thi n1ethod n1ake no allowance tor an, thermal energy received fron1 chc funnel 01 ~urroutH.lings, o the ,aluc of Lb onh approximarc. Linking energy and power energy pOVl/er = - ,-im_e_ 118 So: energy - power x lime Energy is measured in joules (J). Power is measured in wans r,N>. Time is measured in seconds (s). THERMAL EFFECTS Liquid to gas If you heat \\Utcr in a keu1c, the temperature rise until lhc \\ate1· i boiling at 100 C. then top ri ing. II the kettle i left ,,itched on, the water ab ·orbs more and more thermal energy, but this just tum · mor~ and mm ol the boiling water into tcarn, till at 100 C. The energv arn-.orbed i~ called latent heat of vaporization, Mo t b needed to eparatc the pa11icle o that thev can forn1 a ga , but on1e i required to pu~h back the atn1osphe1~ a!'! the gas fo1-n1~. r~ 2 300000 J + i g v1ater (1 qu d) _( - 1 kg { water vapour '- (steam) -) ) \._~ *\Vatcr ha a specific latent heat of vaporization of 2 300 000 J/kg. Thi means that 2 300 000 joules of energy mu~t be transfen·ed to change each kilogram of liquid water into tcmn at the an1c tcn1peratme (100 C). To ca_lculate the energ) tran tcrrcd when an, kno\\ n n1a o( liquid change~ into a gas at the same temperature, \Ou u ·c the cquaLion on the oppo itc page. Ho,,c,·e1, l i now the ·pccific latent hc~,t ot 1•apori:.atio11. ~A jet of steam re!ec1ses latent heat when it condenses (turns hquid). This idea can be used to heat drinks quickly. * J\1.ea wing the specific latent heat of vaporization of water In the expciin1cnt on the dght, the can contain boiling \\ate1: \\'hen the LOO watt hcalcl" ha~ been switched on tor -oo ·econds. the change in the ma balance' reading ho\\ Lhat 0.020 kg ol water has boiled away. l· rom these figures , a \aluc (or L can be calculated: (Omitting some of the unit for ' in1plicit)) cne1-g, lran~tc1 red when watc1 is ,aporizcd . 1ul - 0.020 l t.•ncrg) supplied by hc-all:r power ~ time I 00 \V >- 500 ~ o: 0.020 l 50 ooo. \\ hich gi\'CS L 2 500 000 50 000 J o rhe specific latent heat o( \'aporiLaLion of water is 2 500 000 J/kg. This n1ethod makes no allowance for an\ lhern1al energy lo ·t to the sun·ounding , so ,he \'aluc of Li onh approximate. Specific latent heat of fusion of ice -= 330 000 J/kg; specific latent heat of vaporization of water - 2 300 000 J/kg 1 Some crystals were melted to form a hot liquid, which 2 Energy as needed to turn water into water vapour was then left to cool. As 1t cooled, the read ngs in the (steam). How does the kinetic theory explain this? table below were taken. J* Hoi.-v much energy 1s needed to change a What was happening to the hqu1d between 10 and a 10 kg of ice into water at the same temperature 20 minutes after it start~ to cool? b 10 kg of water into water vapour at the same b What 1s the melting point of the crystals m C? temperature? 4* A 460 watt water eater 1s used to boil water. Time/minutes Assuming no thermal energy losses, what mass of Temperature/'( 90 75 68 68 68 62 58 steam t.-v1II 1t produce in 10 minutes? Related toplc:s: kinetic: theory and thermal ene<gy 5.1; evaporation, bolUng, and condensatk>n 5.8 ;. electrical po~r 8. 12 119 Further questions 1 Expl~in in tcn11. of molecule : a the process or C\'aporalion l b wh) the p1~ ·ur' ot the air in idc a car t) re i ncrcascs \\·hen the car· is dri\'cn al high speed. r21 2 Which of the follo\\ ing describes pat"t ides in a . olid al roon1 Lcmpcraturc? A Close together and stationary. B Clo c togct her and vibrating. C Close together and mo\'ing around at random. D Far apal1 and n1oving al random. I J] r the un. At the same time, it emits thermal radiation into space. E a H the average Lempcralurc of the Earth's surlm:t: \\C~ lo sta-,. stead\,\\ hat wou]d Lhis tell you ahouL the two radiation flows? r21 b \Vhat clTcct does th~ atmosphere ha\'C on the thcnnal radiation emilt(.~ by the Earth? [ I] c The t..:\'idcncc suggests that Lhe Earth's avcn1ge surface tempcnuur·e is slowly incrt.•asing. \\'hat docs Lhis Ldl you about the two r·adiation Hows? [21 5 a The table gives the mdting and boiling points Ior lead und 0\'.Ygcn. 3 Jn sunn) countdcs, some houses ha\·e a sola1· boiling point heater on the roof. It wm111 up water lor th, house. The diagram below shows a typico.l a n&.1 ngcmcn t. in C lead 327 1744 o~g_en_ . __ _ 2_ 19_ _ ..__ _ 18_3_ _ tank for network of At 450 C will the lead be a olid, a liquid or a ga ·? f 1] li At 200 C \\ ill the oxygen be a olid, liquid or a ga ? ( 11 E b The graph ho\\ · ho\\ thl' tcn1perattu\: ot a pure ub tancc change a it i heated. i stonng heated water a \ i\'h~ is the pand in 1hc solar heater hlack? r 4 The Earth absorb them1al radiation from ~' j temperature/ °C 300 I 200 100 .. , 400 [Jl b \i\'hy is there an insulating lay ..,. behind Lhe panel? [ 11 C Ho\\ dcx.~ the water in the tank get heated? r21 d On avcragl!, each square mctr~ of the sola1· panel abo\· .. n:x:ci\'es I 000 joules of energ) from the un e,·cn· second. Use this figure to calculate the po\\~r input (in k\ V) of the pand if i Ls surface an!a is 2 m 2 . 21 E e The solai· heater in the diagram has an clTicicnc) of 60"} (it wastes 401l, of the ·olar en 'l'g\' it r 'ccivcs). \ \'hat area of panel would be needed to ddi\'c1· thennal cne1·g~ at the san1e rate, on a\'erage, a a 3 kW electric imme,~ion heate1·? [21 f i \ Vhat ar' the ad\'antage of using a solar heat -'r i nstcacl of an [2] in1mc1 . ion healer? ii \rVhat ar~ the disadn1ntagcs? [21 ~ SOO J I 0 i t what lcmpe111tu1'C doc the ub tanci: boil? [ lJ ii ketch th" graph and mark with an X an, poinl where the.: sub ·tancc exi t ~ both a liquid and ga at the same tim •. [ l l c i AH substance · con i t ol particle ~. \ \'hal happens to the m·crag .. kin cl ic energy of the ·e particles as the sub Lance change · from a liquid to a ga ? [ l] li Explain, in term · ol partick·~. why energy mu~t be given to a liquid i( it i to change to a ga~. l2] 6 The diagran1 on Lhc next page ho,\ a rdrigL'rato,: In and around a rcl1igcrato1; heal is tran forn:d b, conduction, b, convection, and "'OUP: this may be res,roduced for c:lass 1,1~ solely ror'the purcha5er's tnstltute 120 AS b\' evaporation. Decide which pro e~~ b n1ainly rcspon..,ibl • for the heat tran..,fcr in ct1ch or lhc c,ampl ~ list(..~ at lhe lop ol the nc\l page. a refngeran (vapour) refrigerant (I quid) rc<'ZCr comoartfl'l('nt coo ng b c fins e 8 a b c d e Thl!rmal cm.:rg) is abs01·bL-<l as liquid 1· •frigerant change.., to ntpour in th • pipc\\or·k. [I] C-001 ail" sinking from th • f1 • '"/ ~r compm1m •nt Lrnnsfc1 . thcrn,al energy fronl the food. rI ] Th •rmal encrg, is lost to the outsid1.: ai1· t h1·ough the ooling fins ;,1t the back. [I] Some thcn11al energy lrom th 'kitc.h 'n enter~ the n:·f1;gc1ator· through it~ outc1· panels. [1 l ome the1·mal 'ncrg\ enter~ the rclrigeaator c, en time thl.! clom is opcn(..-d. [I] 7 Th 1: d iagran1 below shows a hot wa t1:r storage tank. The water b heated b, an electric immc1·sion h1:ate1 at the botlom. hot w ater outlet water- - - coot w ater in!et Hu,\ could thc1ma) cnerg,· loss from tht.' tank be 1~ducc.:d? \\' hat matl.'rial~ would be suitable for tlw _job? [2] b \\'11\ i the.: ht.·atl.'r placL-<l at the bottom of thctank1~thcrthan rhetop? [2] c The heater has a power output of 3 k\\'. i \ Vha1 doe" the 'k' stand ror in 'k\\''? [I] ii How much energ) (in jou1l's) docs the heater de1 in.:r· in one .second? [I] iii HO\\ n-luch energy (in jouks) dol.'s the heatc1 de1in~1· in 7 n1inutcs? (21 The lank holds I 00 kg of water. The specific heat capt1cit) of water is 4200 J/(kg C). i Ho\, much cncrg) (in joules) is nceckd SA I S to rabc th • t •mp 't«lurc or l kg ol water b) I C? fIl ii How much energy (in joule..,) b needed to 1·aisc the a\·crage tcmpcratlffe of all [2] th ' ,, ~Her in the tank bv I C? iii If the heater is s\\ itched on fo1 · 7 n1inute.s, what i the a,·eragc aisc in tcmpen1tur' of th • \\ ater in the tank (a~sun1ing lhat no heat is lo t)? [2) The diagram bclo\\ ~ho\\!'- at, pc or heat "t· used in ~ome school . - warm air out fins hot water-.=~mlllmllmmlfl:==:>+-warm water r----.-..._ ,an - cold a r in Hot \\ater is pum~d itum the boiler into pi~s inside the heatc1: fin.., at\.' attached to tho c pipes. Cold air i th"a\\ n into the base oi the heater b, an elccta ic ran. a \\'1n arc fi11s allache<l 10 the pipt•s in idc the hcatca ·? [ 21 £ b 600 kg of water pass through the heater e, er · hou,: The temperature or the ,,ate,· lalls b, 5 C as it p~ses through the heatl'r. Calculate the amount oi IK·at enca-g} transfcrn.:d from the \\atcr c,·en hour. The specific hL·at capacit, o( water i-, 4200 J /(kg ). [31 9 The graph bclo,, ho,," how the tcmp..:rature of some liquid in a beakerchang~d as it \\as heated until it was boiling. a 80 :emperaturerc ~~ i.,- 60 I/ 40 / V 20 I 1 2 3 4 5 6 7 tlfllc/minvtcs a \ Vhat \\a~ thl' boiling point or the liquid? I l] b tate and c,pl~1in what dilier "nee, it any, tht'rc \\Ould be in the final tl'mpcratu1~ if the liquid \\ ~\!'- heated n1on: !--trongh. [2] tate one diHe1 ·nee bet\\Ccn boiling and [l] c, aporation. 121 ASU SA I S Use the list below when you revise for your IGCSE. The spread number, in brackets, tells you where to find more information. Revision checklist Core Level D The kinetic theory of matter. (5.1) D olid , liquids, and ga cs and th • motion of D □ D D □ □ D D □ D D □ □ □ D D □ □ 122 their par1icles (e.g. molecu lcs). (-.I) Brownian motion. C. 1) Ho" an inc~ase in tcmpcrc.1ture incn.:ast:s the internal cnerID of an object. (5.1 and 5.9) The rndting and boiling temperature of water. (5.2) The link bctw"'~n tempcrattff .. and the n1otion of particles. (5.2) Absolute zer·o, the lowl:!st possible ccmpcraturc. (5.2) Converting temperatures bct\\ccn cc and kch in. (5.2) Ho\\ mo t olid~ and liquid c'\pand when h1.~tcd. (5.3) Problems caused b~ thermal expansion, and the uses or thermal expansion. (5.3) How the p~ssun: or a gas is caused b, the motion of its particles (molecules). (5.4) \i\'h, p~ · urc incrc~c \\ ith temperature tor a gas at con tant \'olumc. (5.4) \r\'h, \·olumc incrca~c with tcmpcratur .. For a ga, at constant pressur·e. (5.4) Good and poor thermal conducton-.. (5. -) Convection cun-cnts and why they occur. (5.6) The nature of thermal radiation. (5.7) How dHtcrcnt urfacc con1parc a-., en1ittc1 , rctlcctor , and ab 01--bc1 of thern1al radiation. (5.7) E\·cnda) use. and •ff1.>cts of thermal conduction, com ection, and n1diation. (5.5-- .7) E\'aporalion: the cause and cooling cflcct. C-.8) \ Vhat happcns during condensation. (5.9) Extended Level ru, for Cot\! Lc\'el. plu the follo\\ ing: D How th • propcrtie of solids, liquid , and gases depend on the motion and an11ngemcnt of tht!i1· par'licles (e.g. molt!culcs) and the forces between them. (5.1) □ Temperature and the a\·crL1gc kinetic energy of particle. (5.1) D \ Vh) Bro\\ nian motion occur . (5.1) D \ Vhy thcrma] c,pan ion occu~. (5.3) D How th-' expansions of solids, liquids and gases compare. C- .3 and 5.4) □ How gas pre ·sure is caused b\ particles colliding with urfoces. (5.4) □ Explaining why, when heated (at con tant pre u11.!), ga c expand n1uch more than liquid , and liquid n1or • than olid . (5.4) D \iVh, some materials ar' better thcnnal conductors than othcn-.. (5.5) □ How the tcmpcraturu of an object (including the Earth) depends on the ratc at which it is absorbing and emitting encrg\ carried by then11al radiation. (5.7) □ The differ·nce bet\\C ..n '\aporntion and boiling. (S. ) □ Factor~ affecting the rate at which a liquid e\'aporate~. C .8) □ \\'h~ e,aporation has a cooling eflecl. (5.8) □ Specific heat capadt and it mcasurcn1cnt. (5.9) □ ing the equation energ_\ tran'lfcn'-!d = 111cD8 (5.9) This tree frog from A ·ia uses the large, innatable sac under "" it throat to an1plify the sound of it ~ voice. Onl ' the n1alc can do this, and their calls can travel ten tin1es f1.11~th r than ounds fron1 other fr,og . The ound itself i generated \Vhen air from the ac is blO\\"n pa~l l\vo stretched membrane~ in the botto1n of the frog'.. n1outh, n1aking then1 vibrate. chapter G 123 If you drop a ~tone into a pond, ripple.. pread ac1·os" lhe urfacc. The tin\- wan.~ cam• cncnn:. e,_ as •\'OU can tell fn>m ahc mo\·cn1cnl!'\ the, • cau!'\e al the water's edge. But there i. no no\\ o1 water aero the pond and no matter is lransferrcd. The \\'U\'C effect is just the rc~ult of up-and-do\, n motions in the water. Drawing waves ~ 0 \r\'a\'e are not onh found on wmer. ound tra\'el a~ \\'i\\'es, o doe.-, lighl. \ Va\'C~ can also travel along ~trclched ·pring:-. likc tho e in the e,perin1cnt~ bclo\\, The c- show that thet"' are t,\o main tvpc of \\' U\~. Transverse waves Transverse waves can be drawn as abcwe. Waves can also be drawn using lines called wavefronts Think of each wovefront as the 'peak' of a transverse wave or the compression of a loogitudioal wave. Examples of... transverse waves electromagnetic waves: radio waves. microwaves, infrared, light, ultraviolet, X-rays, gamma rays 0 \r\fhen the end coil of the piing i mo\'ed idewa,~. it pull the next coil ·idc\\ ay · a fraction of a ccond latc1: .. and ·o on along the ·pring. ln thi wa,, the ~ide\\a\~ motion (and it encr~) i pa ed from coil to coil. and a travelling \\'a\'e effect j produced. The to-and-fro mo\·cments of the coil are called o cillations. \\Then the o~cillation~ ate up and down or hom ~idc to side like tho e above, the wa\·e arc called transverse, aves. In trans\'CI c wave , the o cillatjon arc at 1ight angle to the dirt:ction of travel. Light wan!S arc trans,c1 ·c wa\'c ·, although it js electric and magnetic tield \\ h ich o,cillate, rather than anv nla tcrial. Longitudinal waves ,_ _ __.) d ect o o' WiJve t a~ longitudinal waves sound waves 0 Seismic waves ... are earthqualo..es waves: P (primary) waves can ttavel huge distances through tt e Earth. They are longitudinal. S (secondary) are sJower. They are transverse. Surface waves" are the most destructive. They shake the ground from side to side. E Mo\'in the end coil of the ~pring backward and fon.vanls also produces a tra\'elling \\ a,e effect Howe\·cr, the wa\'c arc bunched-up ·ections of coils with ~trelchcd-out ·ection~ in between. These M!CLion~ are kno\\ n a~ con1pressio11s and rarefactions. \'\'hen the o cillation arc back\\ard -and-(01,,ard~ like tho~e above, the wa\·es are called longitudinal wave . In longitudinal waves, the o~cillation arc in the direction of t1~wcl. ouncl wuve~ arc longitudinal \\'U\"CS. \A.'hl!n you . (l\:ak, compn:ssions and rarefaction tr~\\'cl out through the ail: 124 WAVES A Describing waves D SOU OS --+ On lhe d g ht , trans\'erse wa, es a n: being sent a long a rope. H er '" arc o m c o f th e term u~cd to d e c libc the c and o ther wave : Speed The pccd o f the \\a,·e i mca urcd in metre per ccond (nlh:,). Frequency Thb b th l.! nun1her of wa, ·cs pas.sing any point per second. The I unit of h-equenc, i the hertz (Hz). Fo r example, if the hand o n the ri ght makes four oscilla tions pe1· second, the n four wa\'CS pass an~ po int per ccond , and the lrequcnc-,. i 4 Hz. The time lo r o ne o c illatio n is called the period. It is equal to 1/fr •qucncy. If the lrcque ncy is 4 Hz, the period i I /4 (0.2- ). osc:1 at1on wavelengtt I I ( > wavelength \Vavclcngth Thb i the di ·ca n c between an, po int o n a wa\'c and the equiva lent point o n the ne xt. Amplitude Thi i th e n1aximun1 di tan ce a point m o\'c fro n1 it r~t positio n when a \\m c passc:. The wave equation The sp " xl, frequency, and w,l\'dcngth of any. et of wa \' "s ar ~ link<.xl by Frequer cy (in Hz) is the number of osc1llat1ons thi equatio n: per secood. Penod (in seconds) 1s the time for one oscillation. frequcnc, . ., w,n dcngt h frequency - Tn S.)mhols: \' { ,. (i~ 0 Greek 1"t t •r /a,11hda) 1 . d peno when~ ·pccd is in m/s , f1'l.'quc:n c) in Hz, and wan:lcngth in m . The fo llo" ing example s hows wh~ the equatio n works: The waves on the right are travelling across water. Each wave 1s 2 m long, so the wavelength is 2 m. - - 6m - -..., One second later... 3 waves have passed the flag, so the frequency is 3 Hz. The waves have moved 3 wavelengths (3 x 2 m) to the right so their speed is 6 m/s. Therefore: 6 rrJs (speed) = 3 Hz (frequency) ® 2m one !.econd later (wavelength) 1 The WJl/es in A below are travelling across water. a Are the waves trc1nsverse or longitudmaf? b \/I/hat 1s the wavelength of the v.1aves? c Wha t is the amplitude of tl e wJl/es? d If two waves pass the flag eve<y ~ond. what 1s i the frequency ii• the p0 r od' G Use the wave equation to calculate the speed of the waves m A. f What 1s the wavelength of the waves in diagram B below? 0 If tt e waves i, BI ave tt e same speed as those in A, what 1s their frequency? I Relat~d topics: SI u nits 1.2; perk>d 1.3; speed 2 .1; speed of sound 6-4; freque,icy 6.5 The properties of wa\·es can be studied using a ripple tank like thl' one below. Ripples (tiny \\a\'es) arc scnL acros~ the surface of water. Obstacle are put in their paLh to cc what effect arc produced. lamp stroboscope (sp1nnm9 OtSC) lO vibrating 'free1e· the block to wave motion produce ripples - --~'2.lll wave shadov,s on screen Reflection 11 > 11 11 .I 1 A \·ertical surface is put in the path of the waves. The \\'a\·cs arc reflected f rorn the surface at Lhc same angle a the~ ~tri kc it. Refraction npples slew., in sha ow water ~ ) C i 7' i p,ece of p'~tic A tlat piece ol pla l i mak~ l he water n1orc hallo\,, which lo\\ the wa\'es down. \\'hen the wave called refraction. 126 low, they change direction. The eflect i WAVES A Refraction can be explained as follows. Thl' wan'!-. kL>cp o~cillating up and down al the ~amc rate (frcqucnc~ ), !-.O when Lhe~ slow, the \\'a\·ehunts dose up on each other. That [oJlo\\~ fron, the wave equation on the right. A · Lhc frequency i · unchanged, a decrease in ·pecd nu1 ·t cau ·ea decrea c in ,,-a,·dength . From the la ·t diagram on the oppo itc page, , ou can ec that H the wavefront do c up on each othe1~ t h 'ir direction of travel n1u t change, unl --~ thcv arc lra\'eJling al dght angle~ to 1hc boundary. D SOU OS 0 The wave equation speed - frequency wavelength I I I (mls) (Hz} (m) distance number of distance per oscillations bel'Neen second per second w~efronts Diffraction ◄ Diffraction of waves passing .. through a gap. The size of the gap affects how much diffraction occurs . • Diffraction at an edge Diffraction mainly ocrurs at each edge. Longer wavelengths 'NOUld produce more diffraction. The wa,c · bend round the idc of an obstacle, or ·prcad out a they pa through a gap. The cftect i called diffraction. (E) Oil fraction i onl) ·ignificanl if the b~c of the gap i!-. about the ·amc a~ 'i' the wavelength. \<\'id •r gap: produce k~s diflrac1ion. Wave evidence ound, light, and n1clio signals all undergo n~ncclion, n:fn1ct ion, and diffraction. This suggest!\ that they travel as \\a\C!-.. For example: a Lighl reflect ' lrom min-01 : ound reflect from hard urfacc . b Light b ·nd when it pa c~ from air into gla or water: c ound hend~ around obstacles such a: ,,all!\ and huildi.ng~. which i~ \\ h) you can hear around corners. d Light spn:ads \\'hen it passes lhrough tin, hok·s and slits. This suggests that light \\'a\es must ha\'C 1nuch shorter \\'U\"dengths than sound. c omc radio signal can bend round very Jargc obstacle · ·uch as hill . Thi uggc t that radio \\ ave mu t have long ,, m dcngth . ® 1 Say whether each of the effects b to e above is an example of reflection, refr~tion, or diffraction. 2 On the right, waves are moving towards a harbour. a What will happen to waves stnkmg the harbour wall at A? b What 'hill happen to waves slo\ved by the submerged sandban at B? c What will happen to waves passing through the harbour entrance at C? ~ If the harbour entrance were wider, what difference '-''OUld this make? w 1/C C harbour I 1) II B submerged sandbank Related top1cs: waves and the wave equation 6 .1; reflection of sound 6-4; Ught wa~ 7.1; reflection of light 7.1- 7.3; refracbon of hght 7-4; and 7.6; radio waves 7.11 and 7.12 <CD 127 \¥hen a loud ·peaker cone vibrate~. it mo\·es fo rward ' and backwards \ 'Cl)' fast. This squashes and slJ·etc hes the air in front. As a r~uh, a series of comprcs~ions ('squashes') and rdn:fae tions {'stn:Lchcs') lra\'d out through 1he ai1: The ~c arc sound waves. \¥hen the) reach )Our car ·, thcv make yo ur ear-dt1.1m~ vibrate and ou hear a o und. compressions loudspea er (h 9~X'f pre-;w e A waveleng • • v brc1t ng cone The nature of sound waves ound ,vavc arc cau cd by vibrations Anv \'ibrating object can be a V raref act ur s ower pressurt?) 0 out e of ound wave . well a loud peake r cone , e\:ample include \1brating guitar strings, l he vibrating v.ir i rn,ide a trumpcl, and the \ibruting prongs of a 1uning fork . Also, when hard obj1xts (such as cymbals and stcd drums) arc struck, the~ \ ·ibr.itc and produce sound \\ a\·cs. Wavefront essentials For convenience. waves are often drawn using lines called wavefronts In the case of sound waves, you can think of each wavefront as a compression. ba tery a:.r removed •" :uum pump ) .A Sound cannot travel through a vacuum. When the air is removed from this jar. the bell goes quiet, even though the hammer is still striking the metal. (The rubber bands reduce the sound transmitted by the connecting wires.) Sound ,vaves are longitudinal waves The air o, c illate backwa rd and E forwa rd a che comprc. ions a nd rarefoc l ion pass thro ugh it. \ hen a compres.1.;ion passl!s, the air pn.~ssure rises. \Vhen a rarefaction passes, the pressure falls. The distance from one compression lo the nc., t is the wavelength . ound waves need a n1atcrial to travel through Thi matclial i called a medium. \Alithout it, the re i nothing to pa o n any os illation . ound an not tnl\·d throu gh a \'Uc uum (completely e mpty pace). Sound waves can travel through s-01ids, liquids, and gases Mo~t sound wav<.."s reaching )Our car ha\'e travelled through ait: But )OU can al o hear when ·wimrning u11dc1"'atc1~ and\\ all~. windo\\ , doo1' , and ceiling c an all tran mit ( pa o n ) ound. Sound waves can be reflected and refracted ( ee the next spread , 6.4) 128 WAVES A Sounds wa\.•es c an be diffracted You can hear !-.Omt.•onc through an op--n \\inc.lowe\t.:n if,ou annot ~t!C them . That i~ be tiusc sound w.nc. arc cliffr&1CLl'd bv c\·er'\'cla, objects: the, sp1·L·ad through gap, or bend round ohMacle~ or ~in1ila1- ~izc to their \nn·dcngth (t, picall, from a few ccntimctn:s to a few rnctrcs). D SOU OS sou, d waves ~ } J,..,tophooe ~ ~- Displaying sounds ou nd wan:~ can be: displayed gr&1p hicalh using a microphonl' and an oscillo~cope a~ on the right. \\'hen ,otmd wave~ •ntcr the microphone, the~ make a cryMal or a mc1al plalc inside i l \'ibr..1tc. The \ ·ibration-. arc changed into clc trical oscillations, and the o. cillo~ opc U!--C~ the 'to make a ..,pot oscillate up and down on thi: .scn:i:n. It mo, <..~ th~ ~pot stcadih si<lcwavs al the sam ~ tim ', pmducing a,,~\-· ~hap-c ct1l1cd. " 'avefonn. The waycf onn is r~ally a gra ph show1ng ho\\ the air pn:"i'-1.-111! al lhc microphon' varic., \\ill, time. ll i" nor a pictm of the~ound \HI\C~ thcm!-.d\'t.'!-.: .sound wa\'C:-. are 1101 tnm!-.VCr~c (up-and-down). Reducing sounds Hard su1facc~ ti'nt..~• sounds and <:.'an cause echoes (sc · ~pread 6.4). Jn larg~ room~ an<l hall~. the M>l l mate.-ials in c.:u11aim,. c.:arpt:L"-. and pac.lckd furniture hdp n:duce tht.." probll.!m b~ ah. orbing the cncrg~ in sound wan.>s. The h1ick~. ,,ood, and stcd us •<l in buildings arc all good trnn~n1iucrs of ,ound wan.•s. To !'.top unwnntccl sounds gL'lling in or pa.~~ing from one room to the nc'\l, pan •I~ back,d \\ilh foam or fibr~wool can b .. used lo cul do\\ n sound t ran~m i~sion. A 1r you hve near an airport. double (or even triple) glazed wandows are essential 1n situations hke this. Glass is a good transmitter of sound waves, but glass sheets with an air layer sandwiched between let much less sound through. ® 1 Give an example which demonstrates each of the following : a Sound can travel lhrough a gas. b Sound can travel through a liquid. c Sound can travel through a solid. 2 Explain each of the following: a Sound cannot travel though a vacuum. b It 1s possible to hear round comers A Loo ing hke giant mushrooms. these acoustic diffusers hang from the ceiling of the Albert Hall in London. Made of fibreglass. thelf job 1s to scatter reflected sounds so that echoes don't spoil the music being performed below. 3 a Sound waves are lor>g,cudmal wave:s. Explain what 0 this means. If sound waves are long1tud1nal, why are transverse (up-and-down) ·waves' seen on the screen oft e oscilloscope abov~ when someone whistles into th mrcrophon e? 4 What happens to sound waves 1f they strike a hard surface. such as a wall? Related topics: atr pressure 3 .7. longitudinal waves 6 .t ; diffraction 6.2; loudspeaker 9 .5 129 ► Sound is much slower than light so you hear lightning after you see it. Sound takes about 3 seconds to travel one k lometre. Light does it in alm:>st an instant, so a 3 second gap between the flash and the crash means that the lightning is about a kilometre away. The speed of sound Sound wave essentialsO Sound waves are a senes of compressions ('squashes') and rarefactions ('stretches') that travel through the air or other material. Speed of sound through... air (dry) at o~c air (dry) at 30 C 0 330 m/s 350 m/s water (pure) at O C 1400 m/s concrete 5000 m/s In nil~ the speed of ound is nbout 330 metr~ per sc ond (ml·), or 760 mph. Thur h, slower than Concorde but ubout four tim~ fa-..ter thun a r..icing cur. The speed of sound depend on the temperature of the air* oun<l wa,c · tra,cl ta ~tcr through hot air than through cold air: The peed of ound doe not depend on the pre ure of the air• If ntrno phedc p1~su~ change~. the speed of . ound ,,-u,·es tay · the . nme. The speed of ound i different through different material ound wave · tnn·el faster through liquids thnn through gase~, and fa.-.;te ·t of all through solid~. There are omc examples on Lh~ )l;!fl. Measuring the speed of sound The pl'ed of ou nd in air can be rnea u, "'d a hown below. A ound i made b.,, hitting a metal block or plate with a hammer.\ hen the control unit receive~ a pul e of ound trom microphone A, it tart the do k. \ \'hen it receive~ a pulse from microphone 8, ic stop!-, iL If Bi 1.00 metre lurth r awav from the ~our e ol ound than , and the clock record a time of 3.0 millisecond · (0.00 s): - 1.00 n1 - 330 m l~ 0.003 s microphone microphone A B ~l-+mt::::P-+-t-rH ~..:t+--~ I ..,.,.......,......_ I 1 I, ' I ' control 0191tal WAVES AND SOU OS Refraction of sound* Dis ta nt train an<l tra [fic o f Len ·o u nd Jo u<lcr (a n<l clo ·er) at nig ht. The rca ·o n b Lhis. Duling th e nig ht Liine, when thl: ground cool ~ quickly, a ir la \ Ct nl"a r lhc gro und becom e colder than tho c abo\'c. ound wave tra\'d m ore 'lo wly through this colder a ir. As a re uh, w a \'C lcavin~ the g ro und tend lo bend back to wa rds it , instead o f prendin g up\\'a rd .... bending e ffect like this, ca used b, a c hange in s pee d , is called refraction. Echoes sound Hard ~urfaccs uch as wa ll~ n:ncc t so und wa\'cs. \ Vhcn \ Ou hear a n echo, ) O U ar c hcaiing a n:flcc tec.J o und a horl time after tht: 0 1ig inal so und. l n the dfag r am 0 11 th e rig ht, the ·o und has to lra\'cl to th e \\ a ll a,u/ b,1ck again. The Lime it ta k~ j the echo time. ~peed o f ·o tmd dista nce tra, elled tin1c ta ken Echo-sounder This measures th e d epth o f wa te r under a bo at. It sL'ncb pu]sc!) o f ~ounc..l wa,L's to,, ards the '\Ca- bed and n1ea~u~~ the ec ho time. The lo nger the Lime, th e deeper the wa ter ( cc s pread 6.6 ). • Radar* Thi u c the ec ho-~o unding: p1·inc iplc, but with micro wa\·c in~lead of ound wa ve . It d e tect th e positio n o l a ircrah or hip bv mea ·uring the 'echo lime~• o f microwm e pulse. retle led fro m the m . Parking sen~ors* These scl o fI \\'arning biceps \\'hen a car is gctti ng too close to a n obstade. o mc ,,o rk likt: radar; som e use sound pulse~. Assume that the speed of sound m air is 330 m/s. 1 a \t\lhy do you hear lightning after you see 11? b If hghtrnng stri es, and you hear ,t 4 seconds after you see it, how far away is 1t? Does sound travel faster through a a solid or a gas? b* cold au or warm air? 3 ~/heo sound waves change direction because their spe~ chang~. what is this effect called? 0 ~ \ l 'f I> J echo time • ® r'0 ~-~ 2 x di tnnce to wal1 Tf the peecl of o und i kno wn, a nd thee ho time is m easured accura tel), the dis ta nce Lo th e wa ll can be calcula too fro m th l;! a bove equa ti o n. The princ iple is used in sc, ·cral dc\'ices, induding lhc follo,, ing: • sent sound ~ ,eflected I I I I I CQtla I heard 0 Aship is 220 mettes frorn a large chH when 1t sounds its fogt orn. a \AJhen the ect o 1s t eard on the ship, how far I as the sound travellro? b \.Yhat tu, e delay is thete before the echo 1s heard? c The st ip charges its d stance from tt e d1ff. When the echo time ,s 0.5 seconds, how far 1s the slup f,orn the cliff? Related topi cs: refract10n 6.2; sound waves 6.3· edlo-soundtng 6.6; speed of light 7.10 and 11.5; mlcrowai1es 7.11 and 7.12 131 0 Sound wave essentials Sound waves are a senes of compressions ('squashes') and rarefactions ('stretches') that travel through the air or other material. velength Frequency and pitch ound \\a\c are cau eel b, \'ibration ~- foa c,amplc, lhc rapid, backward -and-forward~ oscillalion ot a lo ud peakcr cone. The number of oscillation~ per ~econd i , cull-:d the frequenc . ft i , measun!d in hertz ( Hz). If a loudspeaker· cone ha~ a rrequenc~ of 100 Hz, il is oscillating 100 Limes per second and g i\'ing ouc 100 sound wa\·c-s per second . Different frequen ic ~ound different to the ear. You hear high frequencie as high n otes: mu~ician ay that the) ha\·e a high pitch. You hear low frequencies as /o u· nole ·: they have a low pitch. The human ear can dele t frequencie ranging from abou t 20 H7 up lo 20 000 H7, although 1hc ability to hear hig h fn:qucncie. decn:a!-)~ wilh ngc. frequen~ high upper l1m1t 20 000 Hz of hearing whistle high note (soprano) low note {bass) low drum note 10 000 Hz 1000 Hz 100 Hz 20 Hz 1000 Hz = 1 kilohertz ( Hz) 64 Hl 128 256 Hz H2 512 H? 1024 Hz Octa ves* Mu~icaJ scales arc based on lhcse. lf Lhc pitc h of a nole incc~asc by one octave, Lhc 1n.-quenC) double , as shown on the kc~ board above. Thj ~ kc, board i tuned to s cicntilic pitch. Ba n eh; and 0 1 he ~lra norn1alh u e frequencie thal di Iler s lig htlv from tho e s hown. The diagra m bdow ·how what happe n , if two ~•eady noLc ·, an octave apan, an! picked up h~ a microphonl! and displayed on the screen of an oscilloscope. As Lhe higher note has double the frequency of Lhe lower note, the pcab occua· twice a often and arc only half a tar apa 11. ► The w aveform on each screen as a graph showing how the air pressure vanes with time as the sound waves enter the microphone. The honzontal line is the time axis. 132 ill is sound has a higher pitch (and trcqu ncy) .. than this sound WAVES A D SOU 0 The wave equation Thi equa tio n applie.., l o sound wa\'e : ,pee<l Jn ")mhol : frequL·nc, > w.nelenglh \' OS { ,. (i~ Greek letter la111bda) For e xa mp1e, if the ~peed o f ound in air i 3 0 m/ : s ound wa\'cs of frequenc) 11 0 H/. have a wa,elength of 3 m ; ound wa\'~ of fr equency 3 0 H'l. have a,, a\'e]engt h o f I 111 ; so the lziglwr 1he frcquen \ , the s hor/t1r the \\avclenglh. Why the equation works If 11 O waves are sent ovt in one second, and each wave ,s 3 m long, then the waves must travel 330 metres in one second. In other words, if the freq uency is 110 Hz and the wavelength 1s 3 m, the speed ,s 330 m/s. Amplitude and loudness ampl tudc t }➔ ) ) ) J>) The ound · displa)Cd on the osc illoscope sc n.:cns a bo\'<: ha\'c the ·arnc frequency. but one is louder than the othe1: The oscillations in the air arc biggl'r and the amplitude of the \\ a\'eform is greater: fund~rt ,ental frtlquency oun<l \\'aves can} energy. Doubling Lhc anlplitudc means 1hat fo ur times as much enct-g) is deliYered per ·econd. QuaUty* o n a guitar docs not wund quite the same as n'lidcJJc Con a piano, an<l ib waveform looks dHTcrcnL. The two sounds have a dil fcn: nt qua lit or timbre. Each ·ouncJ has a rrong fundamental frequenc , gi\ ing middle C. Bul other weaker frequencies arc mixed in ai-. well, a.'-\ shown on the Tight. ThL'sc arL' cal1c<l overtones, and the) differ fron, o ne in-.trumcnt lo another. \\'ilh a s\'nlhe:,,izer, \OU can select which frequ~nc ics you mix together, and pro<luc:l· the sound of a guitat~ piano, or an~ other inslrumcnt. ~1iddlc ® Assume that the speed of sound in air is 330 m/s, 1 Here are the frequencies of four sounds: A: 400 Hz 8: 150 Hz C: 500 Hz D: 200 Hz a \"Jhich sound has the highest pi tch? b WhtCh sound has the longest wavelength? c• Which two sounds are one oc tave apart ? 2*Why does a piano not sound quite like a guitar, even if both play the sarne note? 3 A sound is pie ·ed up by a microphone and displayed .. 9"'~ the anal waveform as a waveform oo an oscilloscope. How woold the wavefOJm change If a the sound had a higher pitch? b the sound was louder? 4 lt e lower hmit of human hearing is 20 Hz; the upper hmit is 20 000 Hz. a What 1s the upper limit in kHz? 0 What 1s the wavelength at the lower limit? G What 1s the wavelength at the upper limit? Related top1cs: speed 2.1.:waves and the wave equauon 6.1; sound waves 6 .3; speed of sound 6.4 133 Sound wave essentials 0 Sound waves are a sen<?s of compressions ('squashes') and rarefactions ('stretches') that travel through the air or other material. freQoency/Hz . humans upper hmrt for •• , . dogs .•. bats The human ear can d etect ound up to a trequenc, or abo ut 20 000 J f z. ound · ahove th e range ol hun1 a n h earing are called ultra onic sounds, or ultrasound. Here are ~ome of thi: us.:~ of ultrasound: Cleaning and breaking• avcle~t The number of waves per second is called the frequency. It is measured m hertz (Hz). s ing ultrdsound, delicate machinery ca n be deaned\\ ithout di"n,antling it. The machine!") is i1nmc1 ·ctl in a tank of liquid, then the , ibr.uions of high-power ult.ra ·ound arc u ·cd to di~lo<lge the bi, of dirt and gre-ill)c. Jn ho pital , concentrated beam o l ultra ound can be u ed to bre ak up kidney tone~ and gall !'>tones ,,~thout patients needing urgery. E Echo-sounding hip~ use echo-sounders to measure the depth of wa ter beneath them. An c ·ho-sounder sends pul.scs of ulLr·asound downwards towards the sea.bed, then measu~s the lime Laken for eac h ec ho (reflected sound) to l'cturn. The longer lhe time, the <lec_pl.'r the watc1: For c:-.a,nple: It a pul c- of ultra ound ta ke~ 0.1 c ond to travel Lo the ea-bed and return, a nd the peed of ound in wa ter i 1400 n1/ : <li tancc travdlcd s peed x lime = 1400 m/s x 0.1 - 140 m But the ultra ound has to tnl\'el down and bnck : o: depth o f water Vi 140 m = 70 m M.o l ec ho- o unde1 scan the area beneath them - the, ~weep their ult1·a ~o und beam bac kward and forwa rd~ and r om ide to ide. A computer displa, the depth informa tio n as a pic ture o n a cree n. sea-bed ► This bat uses ultrasound to locate insects and other objects in front of rt. It sends out a serres of ultrasound pulses and uses its specially shaped ears to p1Ck up the reflections. The process is called echo-location It works Ii e echo-sounding. 134 WAVES A E Metal testing The echo- ounding principle can be u. cd to detect flaw in m etals. pulse of ultraso und is sent thro ugh the meta l as on the ,;ght. If then ! is a naw (tiny gap ) in the m e ta l, /WO rcnccted pulses a rc pic ked up h) the <lctcc.:tor. The pulse rcn cctc<l fro m the naw ret urns first, foJlo wecJ b) the p ulse rdlcc tcd fro m l he fa r end of the meta l. The pube~ can be db,playecJ m,ing a n o c illo cope. The trace on the ·cr~~n i a gra ph ·howing how the a mplitude(' trcngth') o the ult ra:-.ound \ -atic:., \\ ilh time. D SOU OS pulse pulse pulse sent reflected reflected out from flaw frO'll end t e osolloscope Scanning the womb The p r~"gna n t n1other in the photogra ph below i having her womb scanned h) ultra ·ound. Again, the ech o-sounding princ iple i~ hc ing used . A Lru nsmiuer sends pulses o f ultra., ound into the m o thc ,·'s bod). The tn.1ns millcr a lso a cts as a d e tector a ncl pic k s up pulses ren ccte<l fron, the bah) a nd <li ffcc\:nt la) er~ ins ide the bod). The ·ignab a n:: p roc-.: ·ed by a co mpute r; which put a n image on the c-rec n. metal / unde,r test ·ing ultra o und i n1uch akr than u ing X-rav becau c X-ra\' can cause cell d amage inside a g r O \\ ing ba by. Also, ultraso und can distinguis h bcl\\ <!Cn differe nt 1aycr:-. of soft tissue, whic h a n o rdin al> X-ray mac hine ca nnot. ◄ An ultrasound scan of the womb. The nurse is moving an ultrasound transmitter/detector over the mother's body. A computer uses the ref ected pulses to produce an image. ®0 0 0 0 What is ultmsound? Give two examples of the medical use of ultrasound. a Wht1t is an echo-sounder used for? b Hov~ does an echo-sounder wor ·? To answer this question. you wall need the information on the nght. A boat is fatted with an echo-sounder which uses ultrasound with a frequency of 40 kHz. a What is the frequency of the ultrasound in Hz7 b If ultrasound pulses ta e 0.03 seconds to travel from t e boat to the sea-bed and return. how deep is the water unde, the boat? c \.Yhat is the wavelength of the ultrasound m wc1ter? ~peed _ distance travelled time taken speed of sound in water - 1400 m/s speed - frequency x wavelength (mls) (Hz) (m) 1 kilohertz (kHz) - 1000 Hz Related topics: sound waves 6.3~speed of sound and echoes 6,4; rrequency 6 .5 135 b Someone i · cuu ing <lo,,n a tn:c with an a.,c. ThL·\ hear the- L'Cho of LhL· j mpact of the a,c hitting the tree alter 1.6 . \,\'hat sort or ob~tack could have i cau. ed the echo? [ ll Further questions 1 Lee and am an: pla)ing with a ball in the pa1·k. nfo1·Lunateh Lhc ball I inishes up in the middle of a pond, oul of n .•a ch. ml ii Y p c Lee thinks that hiuing the watcr,\ith a stick will mah.• \\·a,·cs that will push the ball to the olhL·r side. a \\'hich two of Lhcse words best dcscdbe the \\a\·e that arc crcah:<l on the water urface? The speed of sound is 330 m /s. How far is Lhe tn:c frorn the obstacle? \\'hat is Lhe c.liffcn.·nct: bct\\Cen the sound \\ah.' in b and lhc \\ater \\an: in a . (21 3 The figur.. how. an o. cillo cope tl";lCC for a sound wa,·e product.."C.I h, a loudsreaker. "~ / '\ circular lougitt1dbu,I plane pre. ,w-e .. / V " '\. '\ V Im 11s1 ·er,e r21 b Lee: hils the \\all!r surlacc n:gulad~ so LhaL \\a\'cs travd out Lo the ball anc.l hc\ond it. i \ Vhat happens to the ball? l 1J Sam thro,, a tick" hich hit the ball at P . ii am L ucci.: tul at n10, ing the ball across l he pond. L1..'C b not. E:xplain wh,. c i E 2 a i ii r21 Lee hils Lhc water surfoce rcgula.-1,· "ilh the slick 20 times in I O seconds. Calculate the frcquer1c, of the waves. 12) ii a Cop\' the figure and draw the trace for a louder ound of the amc pitch. E h It takes Irot h ol a second (0.02 s) for the" h o]c t1·ace to be produced. Th~ wa\'C tra\'el acros the pond at 0.5 n1/s. Calculate the wa\'elcngth. [41 The \\'a,·c in the shallow tank of waLcr shown in the Iigun: mo, cs at 0.08 m/s towards the let t. 4 a f2l how that the h~qucnc, o[ Lhe sound produced b~ Lhc loudspcakL·r is I 00 Hi. DctcnninL· the\\ a,·dcngth in air ot the ound produced b, the loud. pcaker: (The ~pecd or ~ound in air is 330 m /s .) [31 J\ sound wan: tr..a\'dling through air can be rcprcscnlc:c.l as sho,, n in the diagram. A displacement of air partte ~ 4--- MM-----..N 14 ~-.or--#-::.:+-"T""- D lilJII ---r-- distance from source \\'hich distance, A, B, C, or D . r~prescn LS: 1--- tank i one "~"•e1cngth? ii the amplitude ol the wa\'c? How long doc it take- lor the wm c to t"Ctuni to th1: po ition XY, but mo\ ing to the tight? [3] 136 ~ OUP. this may be reproduced ror class use solely for the purchaser's Institute l2I WAVES A D SOUNDS A I ight polyst, renL' ball is shown hanging E b ThL' cone of a lou<lspL'akcr is \ibrating. The <liagra1n ~how~ ho\, the air partick..., au.• spread out in front or t hL' cone at . _, Cl..'I tain time. \Cl"\ dose lo a loud J'A..'ake1: The loudspeaker gi\c.., out a sound of low Ii "-'<JUl'nC) and the ball b sc.~n to ,ib1 ale. a E'Xplain ho,\ the sound from the louclspcakcr cau-.cs the hall to mon: us dcscrilx.-<l. 121 b Explain what will h appen to the n1otion of the cone of the loudspeaker when: i thL' sound b made louder [ 11 ii thl..' pitch of the ound i-, incrca e<l. [ l J c CalcuJatc the h'-?QUL'nc, or a ound "hich ha... a wa,dcngth or o,c; m and tr;\\cls at a ~pc x1 or 40 m /s in ait: \ Vritc do,, n the fo1111ula I hat you use and show your working. [ 31 1 P is a con1pn.· ss ion, Q is a ntrdnct ion. 1 Describe ho\\ the pn:ssurc in the air change irom P to Q. f 2] ii Dc-sc1 ibL' thL' motion of the ai1· iii p~11 tick-... as the sound wave pa"""'"-"'"""· 121 Cop\ th' diagram of nir pnrticlc-. nbo\ • ~ncl 1nark and label a dh.tancc equal to one Wah.• ll!ngth or the sound \\a\·e. r11 5 11,e lollo\\ ing an: all exampk·~ of wa, emotion: hght waves X-ra sound waves seismic P-waves seismic S-waves waves in ripple tank a or thl.' I o<l j meta rw 2.4m hammer Transverse waves h How an: ~is111ic wa,·l.'s produced? [ hl' sound \\".._l\ e Lll the othc1 cnd measui~d ekctron icall.). \Vlitc out thL' abo,e in the fonn of a t.._lbk like tlfr,: Longitudinal waves E 7 The figu1 '-.ho\,~ a n1ctal rod, 2.4 m long, being ... t, u k a sharp blow al one end using a ligh L hammc1·. The Lin1c i nten al between the impact ol thL' lmmn1er and the an·intl of rour mca-.u1 •mcnts of the time int •nral arc 0.44 ms, 0.50 ms, 0.52 ms and 0.46 rns. a Determine thl' an.,.,nue \alue oi thl.' rour 0 [6 I [21 c \\ hen son1L-onc fill.'s a stai·ting pistol, they he.u~ an L'Cho 0.4 .., I.Her bccau~ soml' of the ~und \\ aH.·~ tU\: 1\:fk~·ted h,· the \\all ol a building. U thL' spL-cd o[ sound j., 3 ,0 1n -., how fora\\a\ i, the ,,all? [11 n1L"asurL'mcnts. b HL'nce cakulatl..' a value lo,· the spel..'c.J ol .sound in thL' nxl. [ 4] 8 a A microphone is onncctcd to an os illoscopc. \ \'hen dil lcrcnl sound,, A, 8, and C. at\: made, thl.'sc arc the \\a,efm·n1s ~cen on lhL' sct\:en: 6 137 WAVES AND SOU DS E 9 hr-jsound wa,·cs arc high f n:qucnc, a Comparing sounds A and B, how would longitudinal wa,es. X-r-ass arc high frcqucnc, thcv sound diOcrcnt? [21 b Com paling ound A and C. how would tran-;\'CI C "a\'CS. a Explain the difl ~rcncc bct,,ccn tran , c1 c the, ound different? [2) and longitudinal ,,a,c . f2] c \ \'hicl, ound has the high<.--st ainplitude? [ll b The diagram sho,, an ultrasound probe d \\'hich sound has the hight~l frequenc, ?[ 1l used to obtain an image of an unbor-n baby. e The speed or sound is 330 m/s. If sound A hru. a frequcnc~ o( 220 Hz, ,, hat is it wavelength? [2) ~ f \ \'hat b the h-cqucnc, ol sound C? (2 J ultrasound probe c Gin~ two ,~ru.ons whv ultrasound and not X-ray-, arc u cd for thb in,estigation. [2) De clibe one induo,trial u c of ultrasonic r21 Use the list below when you revise for your IGCSE examination. The spread number, in brackets, tells you where to find more information. Revision checklist Core Level □ \r\'a,c motion and wa\'cfront . (6.1) □ \ \'a,c tran for energy. (6.1) □ The diflcr-cncc bclwc ·n tran~\' 't--SC and ,,a,·c , longitudinal with C'\amples ol each. (6. 1) □ The meaning of wan~lcngth. (6.1) □ The meaning ol an1plitudc. (6.1) □ The meaning of [requcnc,. (6.1) □ The hertz, unit of lrcqucnc,. (6.1) □ The •quation linking pccd. lrcquency. and wa\'clcngth. (6.1 and 6.5) □ Demonstrating these wave effects in a ripple tank: • n:flcct ion - ref r-Jction - <liHraction through a gap and at an edge. (6.2) □ Ho" refraction i cau ed b, a chang' or waY' speed. (6.2) □ Ho\\, in a ,;pplc lank, a changc in W,l\ c spL-cd is caust-d b, a change of depth. (6.2) □ ound \\a\'cs arc produced by, ibrations. (6.3) □ ound wm c.., are longitudinal wave . (6.3) □ \ \'Jn sound \\a,c, need a medium (material) to travel through. ( 6.3) □ Di p]aying wa,·efonns on an oscilloscop ~. (6.3 and 6.5) □ Mt:asm;ng the speed of sound (in air). (6.4) □ Ho,, the I dlcction of sound causes cchoc . (6.4) □ The frcqucnc · range ol ound wa\'c . (6.5) □ The link b •tw<."Cn fr•qucnc, and pitch. (6.5) □ The link between amp] itudc and loudness. (6.5) □ Vhal ullnL~ound is. (6.6) \ 0 Extended Level A.., for Co~ Level, plu the follo\\'ing: □ How ,,a\'clength and gap i,e ancct diffraction through a gap. (6.2) D Ho" waYdcngth afl<."Ct~ diffraction at an (.xlgc. (6.2) D \Vhat compressions and rarefactions an.•. (6.3) □ Ho\\ the pcccl of sound is diftc~nt in solid-,, liquid\, and gases. (6.4) D omc n1edical and indu trial u <."- or ultrasound. (6.6) D cha-sounding: n1easur-ing depth or distance b, timing ultrasound pulses. (6.6) A rainbO\\' forms a· the Sun shine - on ,-a indrop .. The raindrop , acting like tiny pti n1 , are plitti ng the \\'hi le sunlight into its different spectral colour ~and reflecting thcn1 back. Becau c th Sun i behind the ca1ncra and tht:: rain ho\\' app ars Loe .. tend to th ·ea, rain mu t be fa1ling bcl\veen the can1era and the cloud , in th background. eh pter 7 139 ► If you can see a beam of light, this is because tiny particles of dust, smoke, or mist in the a rare reflecting some of the hght into your eyes. For \OU to ee omething, lig ht mu~t enter \ Otar eye . The Sun, lamp , laser , and glowing TV creen all emit (send out) their own lig ht. They a re luminous. Ho wever, m o t object · are non-luminous. You ee lhem onl~ because daylighL, or other lighL, bounces off lhcm. The~ re nect lig ht, and somi: of il goes into your eyes. You can ~cc rhis page because it retlccl ligtu . The" hire part · reflect mo t light and loo k bright. Ho,,e\cr, the black letter absorb neady all the light triking them. Thev reflect ,·ea, little and look dark black surface paper Diffuse reflection Regular reflection Absorpt,on Transm,ss,on M.osl urface are une,en, or conlain pa11id~ thar ~cauer light. k. a re ·uh, the\ refle t light in all dire tion::,. The renect ion i diffuse. llowcvec minu 1 are mooth and hiny. \Vhen they reflect light, the reflection L regular. Transparent materials like glass and water let light pass right through l hem. They transmit light. Features of light A This solar•powered car uses the energy in sunhght to produce electricity for its motor. 140 Light is a form of radia tion Thi~ means that light radiates ( ·prcads out) from iL ource. In diagram~. lin called ra s aac u eel to ·how which wa\ the light i~ going. Light travels jn straight lines You can ·cc thi if you look at the path of a sunheam or a laser hcam. RAYS A Light trans[ers energy Energy i~ needed lo produce lig ht. 1a1eria ls gain c ne rg ~ \\ hen Lhcy ah ' orb lig ht. f o r exan, ple, solar cells use the cnc1-g) up plied b) ~un ligh L Lo gcncrarc c lcctri cit). Light travels as ·w aves Lig ht rndiah! · fro m it · ource rathe r a -.. dpple!-1 s pn!a d across lhe s urf ace o l a po nd. Ho,, l.!,·e1·, in Che case o l lig ht, Cht! 'tipples' arc Lin\', \ ibra ting , de lri a nd m agne ti c fo rces. Light wm L'S ha\·c \\a\denglhs o l less than a tho u -,andLh of a millimetre (sec below). Like o ther,, a,·L~, the) can be diflractcd ( L~ ·prc•jd 6.2), but Lhl" cffet:l i · too ,n all to no tice unk '' the gap a1 ' , ·e t') nan'O\\, for example, a in a fi ne mc ' h. o m c c fl ect · of lig ht are bcsl cxpl~inecl b) thinkin g of lig ht as a trcam of tin\ 'ene rgy p a rticles'. c icnti~b. call these pa r1iclcs photons. Light can travel through empty pace Electric a nd 1nagnctic d p plc~ d o no t need a n1atcrial to tra, el thro ug h. That i ,, hy Iight c an reac h u fron1 the un a nd ~ta 1 . D Wave essentials AV S 0 With transverse wa-ves, ike light, the osc1 at1ons (vibrabons) are at nght angles to the direction of travel. Frequencies 0 Light is the fastest thing there is Jn a \ 'Ucuum (in space , for c ...:an1plc), the ~pcL' d o l light is 300 000 kil o m e t~~ per ,eco11d. No thing can tra,d ra~ter th an thi . The ~pL'L-<l o f lig ht seem · Lo be a uni\'cr a] pL'c d limil. Light Wcftll1S have extremely high frequenoes Knowng the speed of hght and the, the frequency can be Wavelength and colour calculated us,ng the equation V = f X ). (See 6. 1) \ Vhcn lig ht cnrcrs the eye, the bl'a in ·cnsc <.litlcn.: nt wa, clcng th ~ as For example: frequency of ... di ITct\!nt colour . The wa \'clcng th rang(' from 0.000 4 mn1 (\ iolct lig h L) to 0.000 7 ni m (red light), a nd white lig ht i m ad e up o f, JI th e \\'in e le ng th in thi-.. rongc. 10~1 sou rce emit a n1i ~1ure o f \\ a \de n g th!-1. tri Ho we\·cr, lru ers cmil lig ht o f a s ingll! wa \ ·cle n g lh ancl o lo ur. Lig ht like chis is c alled monochromatic I ig ht. red light = 4.3 x 1O1~ Hz VIOiet light = 7.5 x 1o14 Hz 0 Y In SI umts, the speed of hght has an exact value of 299 792 458 mls 3 x 108 m/s is a useful approximate value. ◄ light from a laser is monochromatic (single wavelength and cdour}. Here, laser light is being used to measure the deflection of the rotating blades on an experimental jet engine. ® 1 Give two examples each of obJects which a emit their own hght b are only visible because th(fy reflect hgl t from another source. 2 \"It at ,evidence 1s there that light travels 1n straight hnes? 3 What happens to light when ,t stri ·es a wtute paper b black paper? 4 If the Moon is 384 000 km from Earth. the Sun is 1SO 000 000 km from Earth, and the speed of hght ,s 300 000 rn/s, calculate the time ta ,en for hght to travel from a tt e Moon to the Earth b the Sun to tt e Earth. 5 Comparing red hght with violet. which has a tt e longer wavelength b the higher frequency? What is meant by monochromatic hght? 0 Related top1c-s: speed 2 .1; energy 4 .1; colours in white llght 7-4; electromagnetic waves 7.10; photons 10.10 The laws of reflection \ Vhen a ray of light ·trikcs a mirror, it b rdlccted a~ ·hown on the kft. The incoming l'a) i · the incident ray, the outgoing ray i the reflected ray. and the line at right angles to the minor· urlacc i called a normal. The n1inor in t hi ea~ e i a plane mirror. Thi ju~t mean that it i a Oat min'Or. rather than a curved one. ~/ / ////,✓,,,/// ///////// n'IUrOt There are t\i.·o laws of renection. They apply to alJ L~ _pcs of mi1,ur: 1 The angle ol incidence i equal to the angle of reflection. 2 The incident rav, the reflected l'a\ , and the no1mal all lie in the , ame plane. 0 Definitions Angle or ,nc,dence: this is the angle between the incident ray and the normal. Angle of ,ef'ection: this is the angle between the reflected ray and the normal. Put another \\a\, lighc is rcncctcd at the same angle as i t ani,·cs, and the two ray~ and the normal can all be..- drawn on one nat piece of paper. Image in a plane mirror Jn the diagram above, light ra, are coming fron1 an object (a lamp) in front o1 a plane min-or. Thousands of ray · could have been drawn but, fm· simplicit), only l\\'O ha\·c been sho\\ n. After rt>ni:cLion, :some of the ray~ c:ntc:r the: girl's e_)e. To the: girl, che) scenl to c.:onll.' from a posit ion behind the mirror, o that i whc1~ she sec:~ an image of the lanlp. Dotted I inc · have hL-cn drawn to how the point where two of the reflected ra) , appear lo come from. The doued line are ,w1 ray . The image seen in the min'Or looksexactlv the same as the obje t, apart from one important difference. The image is laterall in,·erted (back L<> f mnt). • The word on this vehicle as laterally inverted so that at reads correctly when seen in a dnv1 ng mirror Real and virtual images In a cinema, the image on the SCI\..-Cn i called a real image becau e 1-a, from the projc tor focu~ (meet) to lonn it. The image in a plane n1iITor i not like thi . Although the 1-a\ appear to come from behind the mirror, no rays actuall\' pass th1'0ugh the image and it canno1 he formed on a screen. An image like this i~ called a ,irtual image. RA S A D AV S Finding the position of an image in a mirror The po~itio n o f a n image in a pla ne min~or can be lound b) cxperin1ent : X obie,ct pir Put a mirror upright on a piece of paper. Put a pin (the object) in front of it. Mark the positions of the pin and the mirror. up one edge of a ruler with the image of the pin Draw a line along the edge to ma1k its pogtion. Then repeat with the ruler in a d1fferent position. Take away the mirror. pin, and ruler. Extend the two lines to find out where they meet. This is the position of the image. in The re ult of the expe1i ment can be checked like this. lt a ccond pin i put behirni the mino r, in the po itio n found for the image. the pin hould be in line with the image, a hown on the sight. And it hould tm: in Iinc when you m O\ 'C \'Our head from ~idc to ~ide. ic ntificall~ ~JX--a king, th e, ~ should he no parallax (no n!la ti\ 4! m ovem ent) between th e ~ccond pin and the image whe n you ch a nge your \ ·icwing positio n. If there is n: latin.· m on: m enL (para.flax), chen the tw o ar~ no t in Lhe ~amc positio n. SCC.0 ncf P,I n •I ,, .:> nwr0t 1mageof objeCt pin Rules for image size and position If a second pin is put in exactly the same position as the \ Vhen a pla n ' mi rror fo m1s a n im nge: image of the first pin, it shoufd stay in line With the image, wherever you viev,., rt from. • • The image i the amc i1c a the object. The in,agc i~ a far behind th .. mi,,-01· a~ the obicct i in fron t. • A line joining t.."'qUi\·alc nt po ints o n th e o bje t a nd image p a~~c~ thro ug h th e mirror at rig ht a ng le~. Q---11-- -u- 1 /1..--, - -( \ I ,--\a mage ob,ec ® 1 a Copy the diag,arn on the right. Draw in the image 1n 1ts correct pos1t1on. C) The image cannot be formed on a screen. What name 1s given to this type of mage? 0 From the object arrow's tip. A. draw two rays which reflect from the mirror and go into the person's eye. (0 Can the person see an image of the arrow's tall, B? V 8 ,>,,, ,, ' ' ""> mirror If not, why not? E)Aman stands 1Om in front of a large. plane mirror. How far must he walk before hers 5 m away from his image? R@lated lop1cs: reflect1on or waves 6.2; real and virt ual images formed by lenses 7 .7 - 7.8 143 E Finding an ;mage os;tion by construction In the diagrams below, 0 i · a point objecl in lront of a p lane ( □ at) mit1'01: H l't'C a1·c 1wo method · ol finding che po ition o the irnagl' b~ geomeuic con t1uc1ion u ing a protractm: In M.ethod 1. you deduce the po ition h·om the path ot t,vo ra~ , but lethod 2 i impler! .Wetl,od I obJec 0 / / / / / / / / / / /'(.3 / / / / / / / / / / / / / / / / / / / / / / / / / I I E ob.ect o-•--I I 0!I '////1 @ equal d stances //////'.1////////,/ I I k» I - - - ·• image 144 Fron1 the object. 0, draw a t'a~' which ttikes the n1iffor at an angle of incidence or 35° (or value of your own choo~ing do e lo this). 2 omarucl a normal (a line at right angles lo thl' mirror's !-.Urfacc) at Lhc point when~ the ray strikes chc min·or. 3 Ora\\ the 1·cfk:ctc<l ray from thb point, so that the angle of rdlcclion is equal to the angle of incidence. 4 Repeat tep l to 3 for a econd 1,n with an angle oi incidt:ncc of 55° (or value ol vour own choo ing clo e to thi ). 5 Extend the two reflected rays backward~ until they inter. ect (meet). The point of inll!rsc Lion, I, h, the image position. Metl,od 2 This me1hod is illu lrated on the left. l Lu e · the fact lhat the po it ion of the in1agc behind the mirrol' matche!> 1ha1 of the object in front. From the object, 0, draw a line which passes through the mitTor' ~urfo.ce at right angle ·. Extend thi line well beyond the min·or. 2 Mca!-.urc the distance from the objc L to the mirror: 3 Al an equal distance behind I he mi1Tor, n1ark a point on the cxtcnckd line. Thi · point, 1, i · the image position. RAYS A E D WAVES Reflection problem E.xm11p/e A hori/onlal ray ol lig ht ~trikl.'s a plant.' tnill'or who~l.' su1 face i an1?.lcd at 5.=i lo the g round, a~ "ho\\ n bdow ldt. a \\'hat b. thl' an gll' bt.'l\\'l'"-' n thl' rclk-cll'd 1..,y and the g round? b If the mitTor b n:-anglcd to rdlcct the ray \CrticaUy upwards , what b the new a nglc hcl\H,'Cn the sudm.:c or the mirror tind the g ro und ? b a mc,den r~y ground Jn th e d iagram a ho n ! left, a ngle~ a, b , a nd c ha ve a ]~o h t."Cn la be lled to E a hdp \\ ith th e caku] a Li o n . The inc ic..lc nt ra ~ is p arallel to the grounc..l, so the a n g le bc twcc n th e 1~ flec Lcd n ty a n<l t he ground is cqua] to b c. A the incid e nt rav i parallel to the gro und: a B u t: a b 9 0° S o: b Reflection essentials 0 normal 55° I I ,ingle of I angle of r ,Cldence I reflcctton 35° A~ Lhc a ng le o f ,·c necli o n - a ng le of inc id e nce: c - b o: c 3Thcrcfo re: b - c 70 I / modent ray o, th ' a n g le betw ee n the rcnectc d n 1y a nd the grou nd is 70°. b, a nc.l c: a ll no w h.._l\ e new valut: ·. A bd ore: <l -r- b 90 and c b. .\ i · the unkno\\ n angle between the tuiacc o l the n1i11'0r and the gi'Ou nd . It i , equ a l lo a. The s itua tio n i b s h 0 \\11 a bo ve rig h t, whe n.~ a ngk~ ,,,//////////////////,// tl, mirror When light is reflected from a mirror, the angle of incidence is equal to the angle of reflection. A-:. the ray i r ~flc ted vertically: /, + c BuL: a b 9 0° o: a - 4 5° I 90° o IJ and c arc both 45° Therefo re: x - 4 - o o, the a n g le between the s urface o f lhc mirror a nd thc ground must be cha nged to 45°. ® You will need a ruter, protractor, and sharp pencrl. 0 In the daagram on the nght, two rays leave a point object 0 and strike a plane mirror. a Ma e an exact copy of the diagram. b Measure the angle of mc1dence of each ray. c Draw in the two reflected rays at the correct angles. d Find where ti e image is formed and label 1t. e By drd\-v1ng or calculation, work out what angle the mirror \\'Ould need to be turned through so that ray 8 is reflected back the way ,t came. I I I II »_..,__,._ _____-.,_____ 20 mm ( //// Ii t' / / / / / / / / / / / / / / /( / / / / / / / / / / / / / 111 )l 10mm 30 mm Related topics: reflection or waves 6 .2 145 The 'broken pen' illu~ion on the lert occur~ becau e ligh1 is bent b,· the gla"i"i block. The bending cft ect is c alled refraction . The diagram below show how a ray of lig ht pa.,..sc , th,-ough a glass block. The line al rig hL ang le~ to Lhc side of the block is called a normal. The ray is refr'1 c lcd lo\\'anls lhl' n01mal when iL enlcr~ Lhc block, and away from the no ,ma l when iL leave ~ it. The ray emerge parallel co its o rig inal dirlX tion (pro\'i<lc<l the block ha ~ pm llcl ~idc~). L Rclraction would a L o occur if the gla.-. were replaced with anothe r tran pare nl n1ate ri~I . uch as wate r or acrylic pla:-,lic, althoug h the an gle of refrac lion \\'oulcl be !-.lig h1ly different. The material thaL lig h1 is l1~,·clling through i~ caJle<l a medium. 0 Definitions Angle of rncadenee: this is the angle between the 1nc1dent ray and the normal. Angle of refraction: this is the angle between the refracted ray and the normal. nmmal I I ,nodent r J, mole of 1 Cl'"'nce 1 1n I ar glass 10( glass I I I ray cmc,91,; I parallel o 1a 'e 1of refraction = = = = =~ -=-= incident ray ½ ½ J~ • ray Real and apparent depth* / Becau e o f refrac tion, \\ ~,er (or gla · ) look le s deep than it re, lly i . fts apparenl depth i~ less lhan its real depth. Thb diagram shows why: h9h1 wavL'S gher ~d - ,~ :~... ;~;~d:of beam t ~ slow do,.vn first :'~ ~ ~ hght reftactcd Tappdrf pebb t dppe s to rea dept be here dept I water l "'--------~ Why light is refracted cienti t e"plain retraction ru follow . Light i made up of tinv wave . The. e truvel mo r~ lowly in gla.,s {or water) than in a ir. \ Vhen a light beam pass~ from air inlo g lass, a.s ho,, n on 1hc lelt , one !-tide of the beam is s lo\\'cd b~forc Lhc 0 1hcr. This makes Lhc he--~nl 'hend'. RAYS A E Refractive index medium ~---- l n a \ acuum (empty space ), the s peed of light is 300 000 km/·. In ai1; it i cllcc Li\'clY the amc. Howc\'cr, in gla , light low to 200 000 kin/ . The refractive indc of a medium i · dclincd like this: -,peed of light in\ ,u.: uurn ~pt·t•d of li~ht in mc..·dium o, in the ea e o f glas~: rdracti\'c inde~ 300 000 kntl 200 000 km/ 1.- omc n .: frac tivc indc~ \ ·aluc~ arc gi,·cn on the right. The medirnn \\ iLh the highe~r rcfracth e indc:-.. h as lhc grea1e~1 bending effec t on ligh l bccau ' e iL low · the light the 1110~1. refractive index diamond 2.42 glass (crown) 1. 52 acrylic plastic 1.49 (Perspex) water 1.33 A The above figures are based on more accurate values of the speed of light than those used on the re~. The refractive index of glass varies depending on the type of glass. Refractive index also vanes slightly depending on the colour of the light. Refraction by a prism A pri n1 i a triangular blo k o l gla · or pla tic. The ide o f a pri m arc not pa ra llcJ . , when light i 1·cfracted b) a pti n1, it come out in a dil fen: nt directio n. It i deviated. If a narrow beam o f white light is pru.scd through a prism , iL s plits inlo a range of colour ' called a spectrum, as ' h O\\ n below. The effect i called dispersion.it occur because white is no t a single colour but a mixtun: o t a ll the colorn of the rainbo\\, The pli m •~ Iract~ each colour by a different a mount. D WAVES Seven colours? 0 By tradrtoo. there are seven ·rainbovl colours. The seventh. indJQo. is between blue and violet. This idea came from the Anoent Greeks who thought that seven was a special number in the Universe - which is why \Ne nO'N have seven days in a week. ◄ Most people think that they can see a bout s,x colours in the spectrum of \1Vh1te light. However, the spectrum is really a continuous change of colour from beg nning to end. Red light is deviated (bent offcourse) least by a prism. Violet light is deviated most. However. here the difference has been exaggerated. ® For questions 1b and 3. you will need to refer to the table at the top of the page. Assume t hat the speed of light 1n a vacuum 1s 300 000 km/s. glas~ 1 a Copy the diagram on the right. Draw in and label the normal. the refracted ray. t e angle of ;ncidence. and the angle of refraction. CJ, How would your diagram be differen t 1f the ray was passing into wa ter rather than glass? 2 a When white light passes through a pnsm, 1t spreads into a spectrum of colours. What is 0 the spreading effect called? b Which colour is deviated most by a prism? c Which colour is deviated least? Calculate the speed o f hght in wa ter. Related topics: refracUon of waves 6 .2; colour and wavelength 7.1; light waves 7.1. refraction calculations 7.6 147 0 Refraction essentials The bending of hght when it passes from one medium (ma terial) to another is ea lled refraction It is caused by a change in the speed of the light The in idc udacc oi water, gla , o r o ther tra1r parcnt materia l can ac t like a pcrfec l mi1Tor, depending on the angle at which the light trike it. Tht: diagram~ below show whal happen , to three rays l1:aving an undcn.~;a ter lamp at different angle~. Angle c is c alled the critical ang le. Fo r angles of incic.h:nc1.: greater than Lh is, there i~ no refr..tctcd ray. All the light i · rcncctc<l. The eflec1 is ea Uc<l total internal reflection. , ·fracted ray I\ no cfract1on refrd ed ray ar I water ,I 1 re lcctcd ray , = ong1e of 111ctdence c.mgle of mc,dence grea:er than c c = cnt1cal ong'e The ray splits into a refracted ray and a weaker ref ected ray. The rays sphts, but the refracted ray only There 1s no refracted ray. The surface of the water acts hke a perfect mirror. iust leaves the surface. The \'alue of lhe c titical angle de pend o n the material. For example: critical angle pnsm water 49° acrylic plastic 42° glass <croVv'll) 41° diamond 24° Reflecting prisms In lhe diagrJnls bdo,, , in idc face o t pri m arc being used ru, miJTor~. Total internal reOeclion occu1 becau~ the angle of incidence o n the fa ce (45°) is greater than lhe c rilical angle lor glas or acr ylic pla:-,tic. prcsm • Periscope This 1s an instrument for looking over obstacles Prisms reflect the light although they can be replaced with mirrors. A Rear reflectors (on cars and cycles) Binoculars The lens system m each 'barrel' The d1rect10n of the 1ncom ng hght ,s produces an ups1de-dovvn image. Reflecting reversed by lWO total internal reflectJoos. pnsms are used to turn 1t the oght way up. RA S A E D \ AV S Optical fibres Oplical fibre. an: \Cl"\ Lhin. nc,iblc rud~ made of ~pc ia l gb. 5 or tra m,parcnt pln.-.tic. Lig hl put in at o nl.! end i.., totttl intcmalh renectcd until it com e!-. o ut of lhL' <>l hc1 end, a!-. ~hown bdO\\. Altho ugh some light i~ ab. o rbed by the fibre, ic c.:on1cs out almo~L ~ bdght tL~ it go ~ in en:n if Lht: fibrl! is ~ \ l!r,il kilon1e1n.~ long. ( Fo 1· m o1\..' o n optical ribn.: . ~c ~P• ·ad 7. 12.) A Single optical fibre In the type shown above, the inner glas.s core 1s coated with glass of a lower refractNe index. Bundle of optical fibres ProV1ded the f b<es are in the same pOSttJons at both ends, a picture can be seen through them . .A. Optical fibres can carry telephone calls and internet data. The signals are coded and sent along the fibre as pulses of laser hght. Fev.rer booster stations are needed than with electncal cables. .A. This photograph was taken through an endoscope, an instrument used by surgeons for looi...1ng 1ns1de the body. An endoscope contains a long, thin bundle of optical fibres. ® 1 Glass has a critical angle of 41°. Explain what this means 2 a Copy and complete the diagrams on the right to show where each ray will go after ,t stnkes t e pnsm. b If the prisms on the nght were transparent triangular tanks filled with water, "'~uld total internal reflection still occur? If not, why not? 3 O Grve n.vo examples of the practical use of optrcal fibres. b Give rwo other examples of the practical use of total internal reflectt0n. A / Related topics: refraction 7.4 , catculat ng the cr itical angle 7.6; optical fi bres In commumcat1ons 7.12 149 Refraction essentials \\' hen light is n:fr:.,ctcd, an inc.-casc in the angle of incidence i produces an increa e in the angle ot retraction r. In 1620, the Dutch cientbt \ Villebrord Snell di co\'ercd the link between the t\\o angle : their sim_, \ arc alwa~·!', in propo11 ion. normal I I glass \ \'hen light pa~~c from one medium into another: -..m I ~in r A light rif,f bends as rt enters a glass block The bend g effect is called refraction. It occurs because light waves slow OO,\l'I\ when they pass from air into glass or other medium (see spread 7.4). Passing from glass back in to air, they would speed up again So, if the ray in the diagram were reversed, rt 'NOuld pass back into the air along the same path as it came in. Thi~ i. known n~ Snell's law. rt is illustrated b) the c example.: I= ar gass r s,n 5 Sin O = • Measuring refractive index To f1nd the refractive index of, say, glass, yoo coud drect a rill (from a r<ff box) at a glass block, mark the positions of the incident and refracted rays. measure their angles, then use the equation on the right. A sem1-<:wcular block is useful for experiments hke this. If the ray passes through point O below, no bending occurs at the circular face, so it is easier to vary and measure the angles. 6Q& 10° s,n 45 071 s,n 28° = OA7 0 26 W 15 1: sin 60 sin35° 1S 0.87 = o.s'7 • 1.5 Refractive index The n.:fracti\'c index of a ,ne<lium is dt:fined like thi~: . , l ~l">l't.'d ol light in ,acuum 1\.· f ract I\\.' 1n< l'~ - - - - - - - - - - - ~pi.:cd of light in mi.:dium In a ,acuum, the !>~cd o( light i 300 000 km/!, - and cftc th eh the an1e in ait: In gla~ , it drops to 200 000 km/-. o. the refractivl? index oJ gla~ b 00 000 km/ ~ 200 000 km /s, which b 1.5. Thi. i. the ame a thl.! value of sin i + sin,- in the diagram~ above. Hen: i an altL'matin~ dt:fini1ion of refractive index: ,m I ~,n ,£w1111ple Light ( in a ir)~, rik\.·s Waler at an anglt.· of int:idcnC\.' of 45°. II t he I l.'fracth c indt.·x of water is 1.33, " hat is tht: angle of rd rac tion? Applying the ahove cquati()n: 1. 3 ~in 4 - "' ·in r Rearranged, thi. give sin r in 45°/1.31. \ \'hen calculated, thb gh·es sin r = 0.532. o the angle of refraction r is 32°. RAYS A D AV S Calculating the critical angle refracted I I ray I refo,cted I I no ref ,ac110n I I I I I , i::r IOtal r •fleeted internal rdy reflection c II cmte:al angle ang'e of 1ncideoce angle of incidence greater than c '£ In the diagrams abon_., ray~ ar'l! tran:lling rom gla~~ towards air at dificrent angles. \\' hen the angle o[ incidence is greater than the critical angle, there i no 1-cfrL c ted ray. All the light i renc ctc.:d. There b total internal reflection. Knowing the r ~fn 1ctin! index of a n1atcrial, the c ritical angle can be cakula1cd. For example: On the .-ig ht, the n1iddle diagrjJll abo\'c has been 11...xlrawn "ith the ray direction ,~vc, ed. Thi time, the angle o[ iucideuce i · 90°. a nd angle c i no w the angle or refrllclio11. H the refrac tin~ index ol gla i 1.5: rcfrac ti\'e inde, rem-rangi ng: in 90° in C in c - _ I_ 1.5 I ·in C ( a · in 90 - I ) 0.67 A Compare this with the middle diagram at the top of the page. ·o c, the c ritical angk of glas ~. - 42°. • otc: thi fig ure diflcr lighth from that in pn:ad 7.3 bL-cau~c a impli 1ed value for the t\!lractive ind ' X of gla~!-111'. been u ~din the calculation. ro m the abo\'c calculati o n, it tollo \\ that the c ritica l an gle col anv medium c an be ea) u lated u ing thi equation: ----~ For a medium o f refrac li\'c index 11: Stn C: -,, ® To answer these questions. you 'NIii need a calculator (or set of tables) con taining sane values. 0 f) 0 The refractive index of water 1s 1.33. Calculate the angle of refraction if light (in air) strikes water at an angle of incidence of a 24° b 53°. A transparen t mateoal has a reftactive index of 2.0. a Calculate the critical angle. b If the refractive index were less than 2.0, 'NOuld the critical angle be greater or Jess than bef o,e? Diamond has a refractive index of 2.42. lihe speed of hght ma vacuum (or ,n air) 1s 300 000 ~ m/s. Calculate: a tl e speed of hgh t in diamond b the cnt,cal angle for diamond. A When a diamond is cut the facets (faces) are angled so that they produce total internal refl ection. Reflected light gives the diamond its 'sparkle'. Related topics: refraction and refractive In dex 7.4; total Internal reftect k>n 7.5 151 Lenses ~nd light and form images. Then.! arc two main type~ of lens. The diagr-an'l on the left show · son1e example:-. of each. convex lenses Convex lenses The ·c a1 c th ickc tin the middle and thin round the edge. \ hen ra\ parallel lo the principal axi pa s l hrough a conve:-. len., they are bent inward . The point F where thev converge (meet) is called the principal focus . Tt · distance from the cenln! of the lcn · i · the focal length. A con\'cx ll!ns is known as a converging lens. concave lenses Ray · can pass through the len in either direction, so there i · another principal fo u~ f' on the opposite side of the I.en!-. and the same disrancc from iL Concave (d iverging) lens Conv~x (converging) Ions F' pnoopal a);1s focal length How lenses bend light 0 Lenses are made of glass, plastic, or other transparent material. Each section of a lens acts hke a tiny pnsm, refracting (bending) light as it goes ,n and again as it comes out. Expensive lenses have special coatings to reduce the colour-spreading of the prisms. 152 I )I focal length Concave lenses These are thin in the n1iddle and thickest round the edge. \Vhen ray~ parallel to the principul axi · pa~~ through a concave lens, the) at·e ~nl oul\\'ar<l!-.. The principal fo u~ is tht! point from which the rays appear Lo diverge (spread out). A conca\'c lens is a diverging lens. Real images formed by convex lenses In the diagram bdow, ra)S from a \'Cry distant object arc being brought to a focu b~ a corn ex Jen~. Ra~~ com'-" from all point on tht." object. However, for implicit,, only a e\\ t'i1~ from one point ha,c been hown. Together, the ray fot111 an image which can be picked up on a creen. An imuge like thi b called a real image. It is formed in the focal plane. In a camera, a con\'cx lens is u~cd as below to fo1m a real image on an electronic sensor (or in older <.:amcras, a piece of film). The image in rhc eye i formed in the ·amc wa~. RAYS A The 1·a)s from a point on a \ 'Ct) distanc o bjec t are cflcc Li, d) parallel , so the image pru.sc lhro ugh Lhc ptinc ipal locus. H owe\'cr, fo r an o bj cc Lat an~ other di tancc, che iinagc j-, in a diliercnt po iLio n. You can predic t "hcr·c a con\'c~ lens \\ ill for m an itnagc b~ <lrJ\\ i rlg a ra diagram. There ar\? two exampk lx.-lo,,. Each ha the e lcature : • Fo r im pi icit,, lc:t\· arc dt'a\\11 h·om ju l o ne po int o n the o bject. • The ray u cd an: the standard ray d~ c tibcd o n the light . The c an: c hosen h-'caus .. it i!-, '--'a S\ to work out \\hen! the) go. Onl~ two of them a rc nccc.Jcd lo rind wh cr·c rhc image i~. • For simp]ic it~, rays an: s hown bending al the line rhrough Lhc middle of the lens. In r~ alit), bending Lake · place at eac h sudacc. D WAVES 0 Standard rays In rdy diagrams. any t'NO of the following rays are eeded to fix the image position and size: 1 A ray through the centre passes straight through the lens. convex lens 2 A ray parallel to the principal axis passes through F after leaving the lens. Lrnag~: tea. verted. d:.m1nished (smaller than ObJCC.I) 3 A ray through F' leaves the lens parallel to the principal axis. image: rca. inverted, enlarged (larger than obiect) The ra, diagram abo,e ho w that a the o bject i m o\'ed to\\ard the lcn , the image becom es bigger a nd further aw~\\. A film projcclo r u c a con,·c , len to lorm a mag niHed, r..:al image o n a creen a long wa) awa, from it, a in the lower diagran1. ® 1 a Which of tt e lenses on the right is a convex lens? b Which one is a converg ng lens? c What 1s meant by the p,;ncipal focus of the convex lens? d What 1s meant by the focal length of the convex fens? 2 a If a convex lens picks up rays from a very distant object. where is the image formed? b If the object is moved towards t e lens. what happens to the posi tion and size of the image? 3 Draw a ray diagram hke one of those above, but with the object exactly 2 x focal length away from the lens. Draw ,n and descnbe the image. A B R@lated top1cs: mirrots 7-4; refraction by a pt1sm 7.4; camera and eye 7.9 153 Convex lens as a magnifying glass I I ,..- ~ ~. ,I ,,; 1r I~ " ' r V' - I \E) If an objec t i~ clo ·er Lo a convex kns than A Thick, bulging convex lenses have the shortest focal lengths and make the most powerful magnifying glasses. Thin convex lenses have longer focal lengths and are much less powerful. rhc principal foeus, the 1"''1)S nc\'cr con\'crgc. In tcad , they appear to come from a pos ition behind the lcn . The image h, upright and n,agnific<l. It i · called a virtual image becau e no ray ac tuall) meet to to,,n it and it cannot be picked up on a . c reen. U ed like thi , a on,·e'\ len. is otten cnlled a m agnifying glass. Drawing accurate ray diagrams Problems li"-.e Lhe one bclo,, can be solved by doing a r.1 \ diagram a · an accurate scale d1-a,,ing on graph paper: Ewmzple An obic-ct 2 cm high ~tand~ on th1..· pt incipal ..,xis at a di:-.t~mcc or 9 cm from a con, c, lt.•n:-,. If the local length of the kn..., j..., 6 cn1, wlmt i!'> the itnagc•~ po~ition, height, and t)pl.!? For accurac) , )OU need to choose a scale that makes the diagram as large as possib1c. In the drawing bdow, 1 cm on Lhc paper n:pn:senls 2 cm of actual distance. \Vhcn the final mca ·urcments are scaled up, Lhe~ how Lhat the image b 18 cm from the lcn ·, 4 c n1 high, and real. i cm repre!>ents 2 c.m ----- ~----------...,..-~ F' image: real. n,-erted. 18 cm fron-, ens. 4 154 ,m high RAYS A D WAVES Estimating the focal length of a convex lens* You can find an approxin1ate \'alu ' fo1· Lhe focal lcng lh of a con\'e'\ len hy forming an image of a dbtant window (01· other· distant bright objec t) on a scn.'Cn. Rays from the window arc almo. t parallel, :,,o the image is close to the principal fo<:u~ of the lens. Therefore the distance from the image to the Jen i · app1u ximatel~ the ame as the focaJ length. Convex lenses in a telescope* objective (long focal length) distant object eyepece (short focal Ieng ) virtual image formed by eyepiece The tclcscop' aho\'C ( hown without it tube ) u c two convc'< lcn c . The objective forms a real image of a dh,tant objec t - in this ca~e the Moon - just inside the principal focus of the eyepiece. The in1age ac t~ as a close object to this lens, \\h ich forms a mag nified \iJ"Lual image of it. The eyepiece is being used a · a mag nii~ ing glass, but it i n,agnif~ ing an image of the object rather than the object it ·ell . The linal image i up ide down. 1o t bi noculai - l\\ o LelcscopL' idL'-b~ - idc - ha\'c pri ·m in thcn1 to turn Lhc image Lhe tight way up ( ec p1 "ad 7.5). I I I Images formed by concave lenses* I Tn the diagnm1 below, two ~tandard ray have b !en u~ 'd to how how a concan: lens form~ an image. \Vhercvcr the ohjec l is po~itionccl, the image i~ alwa\s small, uprigh t, and virtual. I I I I ~ / ,, '\ - I I I I ----------•~----- --------F I • A concave lens forms a small, upright virtual image. image: v1rtua. upragt t. smaJler than obJect ® 1 a An obJect 2 cm high 1s placed 12 cm away from a convex lens of focal length 6 cm. By doing an accurate drawmg on graph paper, find the position, he1g lt, and type of image. b The obJect ,s moved so that it 1s only 10 cm away from the lens. Use another drawing to find t e r (N,/ pos1t1on, height, and type of image. 0 Where should the obJect be placed if the image formed by a convex lens 1s to be a Vtrtual, and larger than the object? b real. and t e same size as the object? c real, and larger than the obJect ? 3-Ol:scribe ho.v you could quickty find an approximate value for the focal length of a convex lem Related topics: virtual image 7.2; binoculars 7.5; focal length and ray d.agrams 7.7 155 0 Convex lens essentials F~ ~ Thecamera ~ 14 focal length Real image An image formed by rays that converge. It can be picked up on a screen. Focus Any point where rays leaving a lens converge. If the rays entering the lens are parallel to its axis, then they converge at the principal focus (Foo one side of the lens, F' on the other). Rays from a point on a very distant object are effectively parall~. For sunptic1ty. only one set of rays has been shO'Ml from one point oo the obJea. sensor This U"ies a con\'cx lens lo fonn a small, in\·ertcd, n.!al image on a sensor (or in older cameras, a piece o[ photographic film) at the back. The image ·cnsor is a light~sensiti\'c microchip containing millions of microscopic olar cell!). \ Vhcn the !)huuca open , th~c capture the in1age a ~a panc111 oi decu·ic charge which can b... tored a data on a memorv card. This cnn be proce ed lo produce the final in1age on a . creen or in ptint. The human eye* Like a camera, this u. es a con\'ex len!-. y tern to fom1 a small, inverted, n-al image al Lhe hack. The light is mainl~ con\'erged b) the cornea and Lhc ,,atcr\' liquid behind it. The lens, which is nexib]e, is used 10 make focLL'iing aclju tmcnts: its ·hapc i · changed b) a ring of mu ck·s. The image is formed on thl-" 1ctina, \\hich contains o\'cr lOO ,nillion light-scrn,iti\'c cell . ignal~ fronl the e cell are ent to the brain along the optic ncrn.•. c1 hary muscles 156 cleat Jelly RAYS A D WAVES Correcting defects in vision Snort sight Long sight Correct.mg short sight Comx.11ng long sight E \Vith ma ny people, changes in the s hape of the eye arc not e nough to produce harp focu!-.ing on Lhe retina. To ovcrcon1e tlu: proble1n, ·pcctadc · or comac t lc n ·c h a, ·e to be \\' OJ1l. hort sight In a s ho n - ightcd eye, the lem. cannot be m ade thin e no ugh fo r looking a t dbta nl oh jccts. o the rn)s a re hcnt in,, ards too much . They con, c ,·gc befon .~ the~ reac h the re tina. To correct the fa ult, a c011c:cn·e (di\'erging) le ns is placed in. fro nt of the eye. Long ight In a lo ng-sig hted eye. the lc n canno t be made thick e no ugh (or looking a t clo c o bject . o the ra -,. arc not bent inward enough. \\' hen th ~-,. reac h the re tina, the\· have s tiJI not met. To con-c t the fault , a cmwex (con,·erging) lens is placed in f m nt of the "' ,._ From n1iddlc age o nward , the eye le ns bcco1ne I ncxible a nd lo~cs it a bility to accon1moda le for ohjects a t difl ercnt d ista nces. To o vercome this difficulty, some ~oplc wear bifocals - s pectacles \\'hose lenses ha\'e a l op part for looking a l cli~t anL objl!CL"i a nd a b ottom pa ,1 [or clo~e onl!~. lf the ~pccta c1es have prog ressive le1t!-.Cs, th e changeove r is gradua l. ® You i.\llll need mfo,mat10n from tl e previous spreads, 7.7 and 7.8. on how and whe,e a convex lens forms an image. 1 In most cameras, the lens can be moved in and out to make focusi, g adjustments. If the came,a on the opposite page is to take a picture of a obJect about a mette in front of 1t. will the lens need to rnoved closer to the sensor or further away? 0 0 0 A This person's eye has been fitted with a plastic lens because the natural lens has developed too many doudy patches called cataracts. A short-sighted pe,soo cannot see distant objects clearly. Why not? A long-sighted person cannot see close ob1ects clear1y. Why not? What type of spectacle lens or contact lens is , eeded to correct for a short sight b long sight? R@lated top1cs conveJC lenses and raydtagrams 7.7-7.8 157 0 Wave essentials Waves radia te {spread out) from their source. They are a form of radiation. w~eogth J "I With transverse waves as above. the o5e1Dat10ns (vibrations) are at right angles to the direction of travel. The number of waves sent out per second is called the frequency. It is measured in hertz (Hz). Atom Lig ht wa\'es belong lo a \\'hole fomil~ of electromagnetic ,~•aves. Thest: ha,·e several features in con1mon. For example: • The~ c an Lt"a\'d through a vacuunl (for example, space). The~ t1-a,cl through a vacumn at a pc.:e<l o( about 300 000 kilomctr~ per econd. Thi i u ualh called the speed of light, although it is the . peed o f all electromagnetic wa \'e.. (The e,act \'Ulue i 299 792 45" ml .) • They are transn :rsc \\·a,·es - their o cillations are at right angle · Lo tht! din.-ction ol tra\'cl. It i~ dcc tri c and mag netic riel<ls Lhat arc osc illating. noL ntaterial. • The~ lf"jnsfcr encrg '. A soun:c lo cs energy,, hen it radiate d ectromag neLic wm~. A mate rial gains cncr61y \\hen it ab orb them. The electromagnet;c spectrum The full rc1ng c of electmmag ncLic: wan!s is called the electromagnetic spectrum. ll is s hown in che charl on the opposite page. The r ange or wavdengLhs j huge. At one end ar~: the lo ngc:,t radi o \\ a\'cs wiLh wavelength o f cvcral kilometres. AL the other end are lhe ·ho rtesl gan1ma ra-,.~ ,, ilh wa\·clengths o f le, than o ne- billionth of a n1illimetrc . electrons Where electromagnetic waves come from* A In an t1tom, the electrons have negative (-) charge and the nucleus has positive h-> charge. Electromagnetic waves are emitted whenever charged particles oscillate or lose energy. All mauer i!-. made of atom!-.. Aton1 are thcm:-,elve:-i made up o f a central nucleu_~ with tiny particle~ called electrons orbiring around it. Tht! nudc us and the elec tro ns arc dcc Ldcall) c harged. onlCL i mcs, electro ns can escape fro,n their acon,s. For c~amplc, when an clecuic c urrent pa · ·cs thro ug h a wire, the current i · a flow of frl-c elec tro ns. lect rornagneti c waves are cn1itted (sent out ) \\ he never charged particlt!s O!-.Cillate o r lose e ncrg_ in some way. Fo r example, the vibrating acoms in a hot , glowing bulb filament cmil inrn1rc<l and light, and an o sc illating det:rric c un·cnL e miL~ radio wa\'cs. T he hig her the fr~quency o t oscillation, o r the g reater the enl'rg) c hange, l hc ·ho rh:r the 0 (!) wavelength of the clcccromagnctic wa\-.: · produced. Wave equation For any set of mc:>Ying waves: speed :::: frequency x wavcfength You may need information from tl e next spread. 7.11. (m/s) 1 Give three properties (features) common to all electromagnette waves. 2 Put t he following in ord er of wavelength, star ting wi th the longest: ,nfrared ultraviolet X-rays red light violet fight microwaves 3 Name a type of elec tromagnetic radiation that a 1s visible to the eye b is emi tted by hot objects c 1s diffracted by hills d can cause fluorescence e 1s used for radar f can pass through dense metals. A VHF radio station emits radio waves at a frequency of 100 MHz. a What is the trequency in Hz? b What 1s the 1.-:avelength? (speed of radio waves - 3 x 1OS m/s) c What is the wavel~ngth of rad o waves from a long-wave transmi tter. oroadcasting at a frequency of 200 ·Hz? (Hz) (m) If the speed of the waves is unchanged, an increase in frequency means a decrease in waverength, and \lice versa. 1000 Hz = 1 kilohertz (kHz) 1 000 000 Hz = 1 megahertz (MHz) O RAYS A D WAV S The electromagnetic spectrum wav~length fr~uency Hz m ty~of electromagnetic radiation ex3mpl s, uses, and effects 10' loogv...,~ long-distance AM radio ~um wave lcxa1 AM rao.-o sho<lwave amateu• rad o 103 lo! 10 radfo waves Vr-:F UH TV bfoodcas~ mcrowcl\'CS mobile phonM; TV and commuruca oos sat hies. t ~ l:nb, Wi-Fi; raoar, het1ti:\9 tffect used ,n mic.10-.•,·a.-e ov~ns 1011 1011 ,4ld t hc~ters and gnlh TV ,emo:e (Ot'IUO secunty alarms and laq>s 'l;ght' pu'se$ Ill op·,c f bres onty type of rad tJOn vis•~ to~ <!'ft causes tanrmg. 1n cancer. and eye oa ,ge causes fl00<escence ultraviolet (~k~ some chemicals glo.v) ills bactetia 10 101 used f0< X•ray photog<aphy fl00<escence ca~~s cane'-", but rnn cancer cclls C.lll'SeS 10-10 ------------------------------ 10 II 1()20 gamma rays 10 tted by racf:.ooct,ve, matCf1a s uses aoo effoos rl'i f0< X-rays used for stet lrz.og med,c equ:pmet1t and food 13 ,o21 DANGER RADIATION 103 • I 000 1 -•0001 10 3 • I • - ,cl 1000 For more in forma Lion about the di ITcrl!n l 1, pe~ or d e tro mag nctic: n1dia Lion, see the ne xt ...pread, 7. 1 l . Related top1cs: thermal rachation 5.7; transverse waves. frequency and wavelength 6.1: radar 6 .4; light waves and se>eed of Ught 7.1; Ught spectrum 7-4; gamma rays 7.1.1 al"Kf 10.2 ; atoms and electnc charge 8 .t 159 Radio waves A Radio waves of long and rr edium wavelengths diffract (bend) round hills. tar are natural cn1itter~ of radio waves. Th~e can be detected bv radio tele. copes. Howe\·e•~ radio waves can be produced anificiallv by making a cu1Tenl o ·cillatc in a tran ·miuing aerial (antenna). In a ~imple radio system, a micmphonc controls the currenl to Lhc aerial so that the radio \\a\'~ 'pulsate'. In the radio rccci\'cr, the incoming pulsar ions control a loud~pcakcr so that it produce a copy of the original ·ound. Long and medium waves \\ill diffnlct (bend) around hill'i, so a radio can ·till 1'\.'cci\'c signals C\'cn ifa hill blocks the direct roult: from the Lran ·mitting ac,ial. Long wan: · ,\ill also <lillract round the curved ::,uriace ol the Ea11h. VHF and UHF waves hm horter wiwdength~. VHF (very high frequency) i~ u~d for ren:o radio ~md HF (ultn1 high fr"-~ucncy) for TI' bmadc.--ai.;L-.. These wa\ cs do nol diflract round hill"i. >, for good n:cl!plion, 1here nc..-ccl~ lo be a straight path between the 1ransn1illing and 1'\.."'Cci\·ing aerials. Micro,\'avcs ha\'e the ~hone t wavelength (and highest frcquencic ) of all radio\\, \'es. They are used hy n1obile phones, \ Vi-Fi, and for beaming TV, data, and tdephonl.! ignal · to and from ·utellites and aero ·s country. Like all de tromagnctic Wa\'es, micro\\ a\'c · produce a heating cffc t when ah orbed. \\'atcr ah ·orbs rn icro\\ a, l'S of one par1.kular frcquenc\. Thi principle i u cd in microw~ne oven , where the ,,a,·e penetrate deep into food and heat up the water in it. Ilowcve1~ it rhe bod, i expo ed to mi rowa\'e , they can cau e inte1nal heating of body ti sue~. Infrared radiation and light • This dish receives microwaves from a satellite. \ Vhcn a radiant heal~r or grill i ~witched on, you can dctccl t ht! infrarcd radiaLion coming from iL by Lhe heating effocl it produces in your skin. Jn fact, all objects emit some infrarcd because of the motion ot their arom or molecule ·. Most radiate a\\ idc range.: of wa,clc.:ngth ·. A an object heat up. it rndiate niorc and more infrared, and horter wa\·elengl hs. At a bout 700 ° , l he ·ho rte t wavelengl hs radiated can be det~cLed by Lhe eye, so Lhe ohjecl glows 'red hot'. Abon• about 1000 °C, the,, hole of Lhe \ isibk spectrum is co,·ercd, so thi: ohjecl is 'white hot'. hoa I-wavelength infrared i often called 'infra1~d light', even though it i in\'b.ible. However~ trictl) ~peaking, light i ju l the part ol the electromagnetic spectrum that i vi. ible to lhe eye. warm obJect A lnfrared and ultraviolet can be detected just beyond the two ends of the visible part of the spectrum. 16o RAYS A D WAVES t:curil~ alarms and lamps c.:an be M\itc.:he<l on b) motion sensors that pick up the changing pattern of infran."CI caused hy an approaching person. L night, photographs can be taken u1.iing infn1re<l. In telephone and data net works, signab are scnl along optical fibres a" pulse~ of in Ira red 1ight'. And n:motc controllers for 1Vs work bv Lrn.nsmiLting infr.in:<l pulses. Ultraviolet radiation Very hot ohjL'Cls, such as the un, cmil some of their radiation beyond the violet end of the \'isible ·pc-ctrum. This i · ultra, iolct radiation, or for shorl. It is sometimes called 'ulLra\'iolct light' e,·cn though it is invisible. The un' UV i hat111ful to li\'ing cell . I1 too much penetrate the kin, it can cause ~kin cancer~ If you have black 01· dark kin, the i ab~orbcd bcloa\: it can penetrate too fru: But,, ith pale kin, the ultra\'iolet can go deep r. V can abo damage the retina in the c,· ~ and cau c blindne~ . A~ uhnwiolet i han11ful to living cell , it is u ed in ome t)'f)<.'"S of terili7ing equipment to kill bacteria (ge1ms ). \r\'atcr can he sterilized like this. Fluorescence Soml.! ma1crials fluoresce when the) absorb ultraviolet: the) con,·crL its energy into \'isiblc light and glow. ~urity 1narkcr pens contain special ink, norn1alh in, isiblc, ,, hich nuon.!.sccs and glo,, s \\ hen V light is shone on it. The ~me idea can be usL-<l to spol fake bank notes. nder UV, parts of a fak ~ note glo,\ tl differ ~nt colourcompaa x.l with genuine note. Using a markt.:r pen makes the diITcrcncc more oh\'ious. Sunbeds use ultraviolet to cause tanning in some types of skin. X-rays X-1--a, ~ arc given off when la t-n10\'ing electron lose cncr'g\ \ 'Cl'\ quickh. For cxarnple. in an -I'a) Lube, Lhc radiaLion is emiltcd \\ hen a beam ol electron hil a metal Largct. hort-\,-a,·clength -rav arc extrcmch penetrating. A de,, c n1etal like lead can rcduc.:c thdr scr~ngth. but not ·wp then1. Long-wa,c1cngth X-1--a, m-c le penetrating. For cxan1p1c, the, can p~ through fie ·h but 11ot bone, M> bonl: · ,, ill sho\\ up 011 an X-ra~ photog1--aph. In enginl:cting, X-1--a, can be u l:d to take photograph that rc,·cal naw inside metal · - f o.- example fault~ welds in pi pc joinl . Airport c urity \ tcm al o u~ them to detecl an, weapon hidden in luggage. All X-rays m1! dangerous bcc.:au.,e they damage li,ing cells deep in the bcx.l~ and can cau!'ic cancer 01· mutation.~ (gen •tic changl.!'). Howc\'cr, concentrated bl.""c.1ms of X-rays can be usccl to llc!lll cancer b, destm\ ing abnmmal cells. Gamma rays Gamma rays come from radioactive material~. They a~ produced when l he nuclei of un~tabl ' atom~ br "ak up or lo energy. Thev tend to have shor1c1· \\'a,dength~ than X-,-a)~ because the cncrg~ changes that produce them arc greater. Ho,\·c,·cr, there i no dit lercncc between X-ru)s and gan1ma lcl)S of the same \\'U\dcngth. Like X-,-ays, gamrna ray · can hL' u ·cd in che treacmcrll ol ca11ce1; and for la king X-ra~ -t~ pc photographs. As Lhc) kill harmful bacLeria, the~ are also u ·cd Lor ~tedlizing food and medical equipment. For questions. see the p,evrous spl'eacJ, 7.10. A An X-ray photograph. 0 Ionizing radiations Ultraviolet. X-rays, and gamma rays cause ionization • they strip electroos from atoms in their path. The atoms are left with an electric charge, and are then knO'Nn as ions Ionization is harmful because it can kill or damage living cells, or make them grow abnormally as cancers. Related top1cs: 1nfrared and thermal radiation 5,7; d1ffract1on 6 .2; light spectrum 7-4: optical fibres 7,5 and 7.12: radloact1vtty, gamma rays, and lontzat1on 10.2 161 Telephone, radio, and TV arc all fonns of tclccommuni aLion - ways or tran milling inf01macion over long di ·tanccs. The information ma) be ound , pi tu1 ~. or computer dma. The di'"1gram below left ho,\ a implc telt:phone ) tern. An encoder (the n1iauphone) tut11 the incoming info1"T11ation ( peech) into a lonn which can be tran mined (electtical ·ignal ). The ignal · pa,;s along the tran"mi sion path (wire ·) 10 a decoder ( Lhc earphone). Thi" turns tht! signals back into usL·ful information (speech). Other telecommunicatjon ~· temli u. e diflerent type or signal and u-,.in!-.mi. sion path. Thi! !-.ignal!-. ma) he change~ in \·oltage, chang~ in l he inLen~it) of a beam of light, or changes in the ·trcngth or [requency of ra(Ho waves. They may be tran ·mittc<l using \\ in: ·, optical fibrl: , or radio wan: ~. )p~) 1crophone ·- s 0 00 s 4 voltage 3 level 2 1 • es n cable voltage level sampled binary code s19r et infOfmatJoo ----.& erxoder 0 1-----......Ji~ information decoder ...,__ _,. 1 4 5 2 1 4 00000110010101000 1 0 i----+-- A Like all telecommunications systems, a simple telephone system sends signals from a coder to a decoder. A HO'N an analogue signal is converted into digital pulses. Real systems use hundreds of levels and a much faster sampling ,ate. E Analogue and digital transmission The sound waves entering a microphone make the voltage aero s il vary a · sho,, n in the graph above right. A continuow, vatiation li"-c this i~ called an analogue signal. The table how ~ho\\ it can be con,·c11cd into digital ignal - ignal t'!pre ented bv nun1be1 . The o iig:inal ignal is sampled eleclronically n1any time per econd. In effecl, the hei g ht of the graph i~ mea~ured re~atedly, and the measurement · changed into b inary codes (numbt!~ using only 0's and l 's). These a~ tran~miHcd a" a sc1;cs of pu]scs and turned back into an analogue signal al the rl:cciving end. 1 162 Advantages of digital transmi ion ignal lo e p<)\\Cr a they travel along. Thi i caJled attenuation. They are al o po ih by noise (electtical interforencc). To re tore their power and quality, digi lal pul can be 'deaned up' and amplified at diffen-nt stages by regenerators. Analogue signal-.; can also be amplified. but the noise is amp]ificd a~ well, so the s ig nals arc or lower quality when the\ r-.:a ch their de tination. RAYS A D WAV S From contactless to calls UHF radio wa~es _______________________ _m crowavcs RFrO satclhte phone 81uetooth and \Vi-F1 mobile phone (4G) i 4 M Hz 1600 MHz 2400 MHz 2600 MHz .A Con tactless card payments use RFID technology. Typical frequencies There is no commonly agreed boundary between UHF radio waves and microwaves. Some telecommunicat1ons engineers use the term 'microwaves' for both. \Vi1-cless , . tem · d on't ha \'e a wi re or cable to connec t the ·ende r a nd ~ ccin:r. Tht! follo wing use HF radio ,va\ ·cs o r mic m wun ~~ to earn the ~ig nals. RFID ( Radio Frequc nc~ Ide ntificatio n ) b used in ho ps a nd libn u·ic~ for iden1jf, ing which goods arc being solcl o r Lakcn. A Lag o r ticke r o n lhL' p rodu c• conta in · a lin~ chip. A '1·ead cr' ·ends o ut radi o wave~, cau ing •hl! chip Lo emit da ta s ig nals. Co nLactlc s~ debit a nd credit can.ls ,, o rk in this \\'a\'. Satellite phones wo rk in art!a~ 100 remote fo r o rdin a n m o bile pho nt!~. om c communicate, ia ·a tdlitc in gco tatio nm"") orbiL~ (.see spread l 1.4), o ther · \'ia a ne two rk of sa1dliLc!-i in lo w orbits aro und the Ear l h. E B1uetooth u ·es 111dio Wtl\'es 10 link fixed and m obile devices o,·er ho rt dista ncl:s l ) pi tall) up LO a bout 10 mcLrcs, less if wa lls a ~ present. \Vi-Fi \\ o r k.~ in a !-.imila r \\ U) to Bluetooth. l\1obile phones (cell pho ne ·) arc linked b) a ne two rk of ma ·ts. The\' u c microwa \'cs "ith wa ve length!-. of a le\\ centime tres , so o nh need a s ho re aerial (anlc nna) in idc th em . Ho \\ CVc r~ the s ig nals arc \\ Cakcncd b.Y \\ a ll~. Optical fibres Ca ble TV. high-s peed broadba nd , a nd Ld ~pho m: nct\\ o rk, use optical fibres lo r tra ns missio n. Thes e lo ng, thin ~trands o f glass can""\ di gital sig na ls in the fo rm o l pulse ~ o f lig hl (or infra rc<l ). A L the tr.1nsmi1ting e nd, ch.-c trical s ig na ls a n~ e ncoded into light by an LED ( light-emitting di ode) 01- a 1aser diode. At the rccci, ing end , Lhc s ig na ls a rc decoded b) a photodiode whic:h turn~ Lhe m back into electri cal igna l ·. Optical fi br e cables arc thinn l!r a nd lighte r th a n d l!CLric: cables. The, tan ) m ore signals \\ i Lh less a llc nua tio n o,·cr lo ng dista nces. The) an;! n o t affocted b) intcrfere nce and can no t h" 'tapped '. ®0 0 What 1s the difference betv.reen a d1g1tal signal and an analogue signal? TI e d agram on the nght shows part of a telephone system. a What does the laser diode do? ana oguc to d1g11al conver er oot1ca fibre b What does the photodiode do? c What does the regenerator do? o Oto- : ode d Give two advantages of sending d1g1tal signals rather than 0 analogue ones. e G,ve tV'IO advantages of using an optical fibre Im rather than a cable with wires in it. Grve an example of the use of Rf ID. OptJcal f1bres d 91ta _..,...,. to ana oguc Related topics: sound waves 6.3; optical fibres 7.5: magnetic stotage 9-4; LEDs 8.11 convertet la~·· d1oc:, ,cgcncra or ~ - - - Further questions b \\'hat do we call lhi · effect? [ I] c State why light change · direction when it cnte1 ~ a gla pri n1. [ I] 4 The figur.. how an ob.i •ct OB of height 2 cm in front of a converging lens. The principal foci of the lens an~ labelled F and F'. An image of 08 will be formed Lo the right of the lens. 1 The diagram shows a Iight ~ignal travelling through an optical fibn! made of glass. p glass fibre State Jwo changes that happen to the light when it passes from air i nlo the glass (ibrc al B . [2] b Explain why Lhc light follo,,s thl: path shown after hilting the wall of the fibre at P. (2J 2 obicct • ,, ,,,, ,, I I Copy the figure and draw two n\\ · fron1 thi: top of the object B \\ hich pass through the lens anc.l go to the image. (21 b D11t\\ the image rorme<l. Label this image I and n1casurc its size. [ I] a "" "I ",,,, ,, ",,,,,, ,, ,,,,,, 5 I mirr0< In the diagram abo, can object (a smalJ bulb) hcU> been placed in front of a plane m il-ror. roc19e a Copy the diagram. Mark in the po ilion of The diagra1n ho,, · a con,crging lens forming the image. rI 1 a real in1agc of an illuminated objccl. E b On your diag,-om. draw a single n1\ fmm tat' hvo thing · that happen to the image the objccl that reflects from the mirror and when the object is mo\'ed towards F'. (21 goes inlo the C\c. Include a c.lottecl ]ine to E 6 ·how where, to the C) e, the ra\ appca, - Lo F1s 30 mm from come lrom. J centre of lens c An ohiect i 10 cm away from a plane n1in'01: HO\\ far is the o~ject from its image. [ 11 0 1s 20 mrn from d If the objt:cL is mo\·cd I cm closer to the centre of lens and mirror, how far is il a\\'a) from its image 15 mm high then? [ I] The <liagrJm ~ho\\ · an object O placed in 3 a Cop) Lhe diagram and dra\\ the path of the front ol a con\'ex (cotl\'crging) lens and thl: ra\ ol vdlow light a it pa ·c through and pas age oi two ra,s fron1 the lop of Lhe object come out ol the gla pri m. [21 through the lcn . a Copy and complete the diagram (u ing the dimensions gi\'1,m) lo show where the image is rorm<..-d. (21 glass prism b talc two prope11ics of the image. [2] r3 <O OUP; this may be reproduced for class use solely fo, the purchaser·s Institute c Thin lenses can be dil·e1~in~ or cmn ·erging. \\'hich of rhcsc words desciibes i a con\C\ len~ ii a conca\l: len~? [2] d \i\' hich t\ pc ol lens b u~cd to correct i ~hort- ightcdnc s ii long-~ightcdnc ? [21 E The spL-cd of light is 3 x I0s m/s. akulate the trequcnc, of ,cllow light ol ,,an.:lcngth 6 IQ-7 Ill. [21 10 01 IOI 10 I 10 I II)" A I 1 g..invn rays 7 opucal f1br~ a In the diagran1, nbo,c" monochromatic nl\' of light cntc1·s an optical fib1·c . \ \That docs 111011oc:/1r0111atic nu.•an? [ 11 b \Vh, doesn't Lht: light 1.:scapc lrorn the ~ide ol the optical rib, ,? I 1I c Optical fibre arc u L'<i in tdccomn1uni ations. Gh·c one other u~ .. or optical fibn:s (apa11 fron1 ck-corathc lamps). [ 1l d The signals sent along optical fibres an~ di~iwl. \\' hal doc chi mean? [21 c Ghl: tu·o ad, antagc of u-.,ing digital ignal tor communication rather than analog ue ones. [2] f Gh·c one cxan1plc of the us• of radio ln:qucnc, identification (RrID ) tcchnologv. [ 11 8 A I a, of light, j n ai,~ trikes one klc of a 1 xtangular gla s block. The refracti\'e inde, of the gla~s i 1.5. a Ora\\ a diagram to sho,, th • dir~tion the I'!\) will take in the glass if the angle of in · idcnce is 0 '. [21 b Ora\\ a cJiagi~n, Lo show the appro...:imattdin:ction the t'a\ will take in the gla if Lhl." The diagram shows thl." main r"\!g ion, of the elect1omagnctic ~pccttl.11n. Th1.: numbc1 . show the f n .- qucncie of the" a\l: mca ut~d in hert, (Hz). a am ' l h .. 1'\!gions i A [ tl ii B . [ tl b i \\'rite down, in words, the equation conn1.: ting wa,·t: speed, \\a\'clcngth, an<l \\ ave lrcqucnc,. [ 1) E ii Calculate the (rcquenc, ol the radiation \\ith a \\U\"'l ·ngth of 0.001 m oo-l m), giY ·n thtlt all clcct1·on1agnctic wa,·cs tra, cl at a speed or 00 000 000 m /s (3 l O m /s) in space. [ 2] iii tale to\\ hid, pa11 of the electromagnetic pt:cu,.un the radiation in pan ii belong . [ 1I c E,plain how and whv n1i row~ncs can cause damage to 01· c,·cn kill lh·ing c •lls. [2) E 11 The 1gurc how a square block of glas JKL~1 with a 11\) of light incident on ~idc JK at an angle of incidence of 60 '. The r ·fracti,·c indc'i: ol th1.: glass is 1.50. angle of incidence i 45 • and calculate the angle of r ,fraction. 4l c H the p • ..cl of light in air i" 1 I( 10 n1/s, calculate the :-.pccd of light in the glass. [21 r 9 Light and gan1ma rm.~ at'\! both c,amplcs ol ckctromagnctic 1·adiation. a , amc thn:c other types of clcc11·omagnctic radiation. [31 b late t,,o diffcf"l."nce between light and ga rnma ray~. (21 M a Calculate the anglt: of I l.'fr.iction of the 1"tt)~ (21 b Cakulat~ the Cl ilical an1?k lor a ra, of .... light in thi g.la . (21 c Explain'" h, the 11\\ sho,"11 cannot emerge rron1 side KL but \\ill cm •1-ge from sid • LM. [31 12 a less than the same as rad iation. [I] ii In a \'acuum the speed of ultraviolet radiation i _ _ _ the pccd o( light. greater than Copv the entencc bclo,, and u c one of the th1~c phra e abo,·' to con1plct, each cntenc '. Each phra~c ma~ b, u ,c1 once, mon: than once, or not at all. i The \\'an~lcngth of radio \\'ll\'c~ is _ _ _ the wa\ elcngth o( ultr-J\ iolct [l] ill The fn.~ucm:.1 of ultraviolet radiation is _ _ _ the frequency of in frarcd [I] n1d iation. b amc the par1 of the ckcLromagnctic ~se the list below when you revise for your IGCSE examination. The spread number, in brackets, tells you where to fmd more information. speclrum that is used to: i send infom,ation to and from satellites [ Il ii kill harmful bacteria in lood. [I] Revision checklist Core Level □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ 166 The charactctisti . (~ ·aturcs) of light. (7.1) The n1eaning or angle of incidence, angle of reflection, and normal. (7.2) A law ol reflection: the angle of incidence and rcnection ar • equal. (7.2) The image in a plane min·or, it po ition and how it is formed. (7.2) The image in a plane min·or i \'irtual. (7.2) Dc111on. trating the refraction of light; the meaning ol angle of t~fraction. (7.4) Ho,, a light l'"a\ pa, c~ through a parallclided bloc"- of gla or pla tic. (7.4) Di pet ion: how a pli m fom1 a I)(.'Ctrum. (7.4) The colount ot the ,bible spL'ctrun1 in order oi wa,clength. (7.4) Total inten,al ,~0cction: what it me .. n and how it can be u ed. (7.5) Thl: 1neaning of critical angle. (7.5) Ho,, a con,·''< l ·lb locusc a beam of light. (7.7) The principal focus and local length of a lcn . (7. 7) Ora,, ing rj~ diagram to ho,, how and where a con\\!\ lcn fornh a real image. (7.7 and 7.8) Electromagnetic w .. , •t.-:,: the main feature~ o( the elcctrornagnetic pectrum. (7. J0) Ho,, clL'ctron,agnetic \\'an: all tra,·el at the ame pecd in a ,-acuun1. (7.10) The charnctc1istic · and propt:rtics of - radio \\'a\c-,, n1icro,,m L' - infrarcd n.1, s - uh1-a,iolct ray ' ... X-rc.1\"s, gamma rays. ( 7. 10 and 7. 1 l ) □ The u e of electromagnetic wa\'e : - domc~tic, indu trial, n1cdical (7.10 and 7.1 J) - in con1munication sy-tcms. (7.10, 7.11, 7.12) □ The harn1rul eftcct or clcctron1agnctic wa\'c . (7. I 1) □ ing clcctron1agnctic ,,a, e in - communications (radio, TV, satL'llitc, telephone) - remote controllcn, - n1edicine - ~ccurit~ systems. (7. I 0 and 7 .11) □ Micro,.._a,e and -ra, : afct, b~u, . (7.11) Extended Level A for Core Level. plu the following: □ □ □ □ □ □ □ □ □ □ □ □ □ □ The meaning of monochromatic. (7.1) Ora\\ ing accurate diagram to find ,,here a plan· min'Or fon11 an image. (7.2 and 7.3) Dclining rcfracthc indc, in te1m of light pc 'd. (7.4) Optical fibre andthciru t.~. (7.Sand7.12) The equation linking 1 ·fracth e indc-..:, angle of incidence, and angle of retraction (Snell' la,,) (7.6) Calculating the critical angle u ing the 1 ,fracti\·' index. (7.6) Ora\\ ing rav diagram to ho,.._ how a conve~ lcn can form a real in1ag •. (7.8) Ora,, ing rav diagram to ho\\ how a con,·ex len can form a ,irtual image. (7. ) sing a convc, lens~ a magni~ ing gla . (7.8) Ilo\\ lcn c arc u cd to con-eel hortightcdne s and long-sightedness. (7. 9) The ~pccd of elcctron1agnctic \\aH: (the pecd or light). (7. I and 7 . 10) The difforence bet,, ccn analogue and digital ~ignals. (7. 12) The ad\'antage ot u ing digital ignal (7. 12) sing radio wave~. micro\\ aves, and optical fibre in con11nunication ) tcm (TV, atcllit~. mobile phones, broadband, bluetooth). (7 .12) The citv of Bogota, Colombia, ... al night. Like other cities, it i so bright that it can even be ccn fron1 space. Modern industrial societies relv . heavily on the U5C or electricity - not onlv for lighting, as ho,vn here, but nlso for running factor) machiner\, info1·n1ation and con1n1unications ~ y lcn1 , and healing. Tvpically, 1 clectricit~ accounts rorahout one ixth of an indu ·trialized country' energy u c. chapt~r 8 167 Electric charge, or'e1ectricily', can come from battcrie and genera lo• . But on1e matelia) becon1e charged when lhe) ari? rubbed. Their charge b ometime called electros tatic charge or' tatic clectdcity'. It cau pa1 k and crackle when vou take oil a pullo\·c1; and it\ ou ~lidc out of a ar ~ eat and louch the <loo•~ it may even gh·e you a hock. Negative and positive charges Pol)thene and Per pe" (acrylic re in) can be c harged h)· rubbing lhem \\ ith a d1·y, wool1cn cloth. A This person has been charged up. Her hairs all carry the same type of charge, so they repel \\'hen two cha rged polythene rods are brought dose together, as shown below, the) repel (tn to pu h each other apan). The an1e thing happen~ with two c harged Per:-.pex t~od ·. However, a c ha rged polythene rod and a charged Pet pex rod al/ract each ot her: Experin1ent~ like thi ugge t that there are two dilferent and oppo ·ite types of electric charge. The e are called po itive ( ) harge and negative ( ) charge: Like c.:harge~ n .·pcl; unlikl' charges attract. The clo~c•· the chat'gL~. the g, calt"I' the fot cc bet wccn them. each other. Atom Where charges come from ---- 1 I I I I '--v--' nudeus· 4t proton neutron En.~~·rhing is made ol tiny panidcs calll'<l aLoms. These have clecrric cha1-gt: · inside them. A ~implc model or the atom is hown on the Jell. There is a ccnlra l nucle us n1adc up of protons and ne utrons. Orbiting the nucleus arc much lighter elcc.:tron ·: Electron~ ha\'e a negali\"l! ( ) chargl!. Proton · have an equal po ~itivc ( .-) chac-gc. \!eutron~ ha\ l! no charge. onnally, aton1 · have equal numbct of ek uon~ an<l proton , ·o the 1u! I (o,·c1nll) charge on a material is zero. Howc\'cr, when two material · at\! rubbed together~ electron ma) be tran ·fcrred 1'0111 one to the ot he1: One material ends up with mo~ electrons Lhan normal and 1hc other with le . o one has a net negative c harge, while the other i left with a neL positi\'e charge. Rubbing mat~rials together docs noL 11u1ke dccLric charg.:. lL just ~epamtes charges that are ah\!ad) there. I 168 ECTRICITY po .. on!. electrons transit'fred transferred b';rubbng by rubb:ng ro t. trons th nor net negat,ve cha g few re trons th n norrn I t posttrve ,harge A. When polythene is rubbed With a woollen doth, the polythene pulls electrons from the wool. A When Perspex is rubbed with a woollen cloth, the wool pulls electrons from the Perspex. Conductors and insulators Conductors \\'hen o me material · gajn charge-, the\ lo ·e it almo t imnlcdiateh. Thi , i b ~cau~e ,Jec lt·ons flow throug h then1 or the t11To tmding material until the balance ol ncgath e and po iti\'c c hat-gc- i ' rc ·to red. Conductor at~ maLcrial · Lhat let electro n~ pa ·' thro ug h them. ·t l'tal · arc Lhc be t elec trical conduc to r . Some o l their electro n arc o loo eh hd<l Lo their a eo n,~ that they can pa s frcel) bet\\ ecn the m. The ' e free electrons al o n1akc metal good thcn11a l conduc to r . 0 Good Poor metals espec,alty: salver copper aluminium water human body earth carbon ~1o ·t no n -metal conduc t charge- poorlv o r no t at all , altho ug h carbo n i an exce ption . In ulator: arc n1atc 1ial ' that hardlv conduct at all . The ir cle tro n arc tig hll) held to ato m and a1~ no t free to rno ve - altho ugh they can be tran tcn'Cd bv rubbing. In ulato1 an~ ea \' to charge bv nibbing bccau ·e any electro ns thaL gel tr-an ·fen·L'<l Lend to stay where they arc. 0 Semiconductors stl,coo germanium Semiconductors* The ear 'in-between' matcdab. The) a t"C poor condu clOI"' when cold, but rnuc h better conduc to r \\ hen wan11. Insulators plastics COllduc or e.g: (copper) 1nsu ator (PVC) A The 'electnoty' in a cable is a flow of electrons. Most cables have copper conducting wires with PVC plastic around them as insulation. ® 1 Say whether the folloW1ng attract or repel: a two negative charges c a negative charge and a positive charge b two posi tive oharges. 2 lr an atom. what kind of charge 1s carted by a protons b elections c neuttoos? 0 What makes copper a better electrical conductor than polythene? Related toPics: themiat conducUon 5-5; atoms 10. 1 PVC polythene Perspex glass rubber dry air 4 Why is 1t easy to charge polythene by rubbing. but not copper? 5 Name one non-metal that 1s a good conductor. When someone pulls a plastic comb through their hair, the comb becomes negatively charged. a \.Yh,ch eods up w,th more electrons than normal. the comb or the hair? b Why does the hair become positively charged? 0 0 + + + + + Attraction of uncharged objects + attractDon Th~ diagram on the )eh ~ho,, ,.., hat happen it a po iti\'cly harged rod b broug ht near a :-,mall picc' of '11uminium foil. Elc tron~ in the foil arc pulled to\\ ;u·ds the rod, whi c h le~n· _.s the houom ol the foil with a net positi\'c charge . A, a 1·e~ult. thl.' top of the loil i~ at1n1ctcd lo 1hc rod. \\ hik the bollom i~ repdh.:d . Howcn:r, the auraction i~ -..lrongcr becau-..c Lhe attracting charge, are do~cr than lht.• t~pdling one..,. mor~ lectrons than E- ~uoru. ,an normal A charged oh_icct will allract an uncharged object clo!--e lo it. Fm· e,amplc. cling [ilm ~tic"-~ to ) Our hand because il becomes c harg ed \\'hen pulled ofl the r o ll. repuls.oo charged obJect attracts an uncharged one. .& A ► An aircraft and Earthing 1l enoug h c harge build.-, up on omcLhing. ~lcctron~ may be pulled thr ug h Lhc air and cau e p~u-k., - \\ hich an be <langc, ou,. To p1~, enl charge building up, objc t~ c3n he earthed: the, can be conrn.:c t ·d to lh'-' g round b, a conducting matc,;al ~ that th · unwanted charge now: a\\'a\. 1ts tanker must be earthed during refuelling. other\vise charge might build up as the fuel 'rubs' along the pipe. One spark could be enough to ignite the fuel vapour. D etecting charge + + + ++l=ed metal-- - -cap -insulator Induced charges* Ch3rgc tha1 'appear' on an un ch, rged object bc.~ au~c or a c h~rgcd objfw"Cl ncarb, ar > cnll'-''CI induced charges. 1n the diagram ~Jo\\, a n1 -'tal sphcn: is hcing c hill·gcd h) induction. The ~phcre ends up\\ i1h an 011po.,ite charge to that on the rod, ,.., hi h ncn:r actually Lou hc!-1 Lht' ~phl!re. cha,gt'd rod detected using a leaf electroscope as above. If a charged obJect is placed near tnduc -o the cap, charges are induced c.harg,..-. the electroscope. l hose in the gold leaf and metal plate repel. so the leaf oses. Q+ +:+:+ ..+~ +++ Electrostauc charge can be in fl..wer , ~uoos m1 sph ele<trons 'ilov.n o replace man ~ missing ele-ctrons norma! _ insulated stand 1 ECTRICITY E Unit of charge waste gas (deaned) The I unil of charge i th ' coulomb (C). It i equal to th .. c ha rge on a hout 6 billio n billio n ch.~ tr·ons. For m or " on thi., see ~prcad .4. One coulo mb is a rdati vel) ]a rge qua ncit) o f cha ~e. a nd it is of1en more convenient to 1ncas un: cha rge in microcoulombs: J m icro oul om b (Jt C) - J o-6 l charged ash attrac ed to p5ates"-, (one mi1lio nth ot a coulo mb) The c harge on a 1·ubb ,et polyt he ne rod i • typically, onl~ about O.oo- ,,c. . .._ 0 Using electrostatic charge* In the following "xa mples, the charge com e:-. from a n d ctricit) ~uppl) ra ther tha n fro m rubbing. Electro tatic precipitators a1"l: fitted to the c hi m nc) ~ o f ·on,c power tatio n · and tac tork . They t'cducc po llutio n b~ re moving ti1n bit · of a h from the wa tc ga c . In idc the ha n1ber o f a precipitator ( cc right), the h i charged by wi re ·, and the n a tt racted to the metal pla tes by a n oppo. itc c harge. \Vhe n s ha ken fro m the plati:s, lhc ash collect~ in the l ra\ at the bottom . o. o' waste gas and ash ♦ • .0 .o, - - o.· • .o. <> .6 + o. o. t o ~ l Photocopiers work m,ing the principle s hown in the diagra ms below. Laser printe rs use the same idea except tha t, at s tage 2, a computcrcorurollc<l lascr can the pla te trip b~ ~trip Lo cn:alc the required image. 1 A An electrostatic precipitator uses charge to remove bits of ash from the waste gases produced by a factory or poNer station. 4 2 5 H1 , , ,. Inside the photocopier, a lightsensitive plate (or drum) is given a negative charge. An image of the onginal document is projected onto the plate. The bright areas lose their charge but the dark areas keep it. Powdered ink (called toner) is attracted to the charged (dartc) areas. A blan sheet of paper is pressed against the plate and picks up powdered ink. , The paper is heated so that the powdered ink melts and sticks to it. The result is a copy of the original document. ® Name an instrument that can be used to detect electric charge. What is the SI unit of charge? 3 In the diagram on the right a negatively charged rod has been brought close to a piece of aluminium foil. a Which end of the foil has an excess of electrons? b Why is the foil pulled t01Nards the rod? 4* Give an example of where a build-up of electrostatic charge can be dangerous. How can the problem be solved? 5* Give two examples of the practical application of electrostatic charge. 1 8 () - - -- A I + + + +I foil B Relat ed topics: SI untts 1.2 ; charge and current 8-4; earth wires 8 .13 171 0 Atom and charge essentials Electnc charge can be positive(+) or negative(- ). Like charges repel. Unlike charges attract. Charges come from atoms. In an atom, the charged particles are electrons(- ) and protons(+). Nor,mally, an atom has equal amounts of - and + charge, so it is uncharged. However, if an atom ga· s or loses electrons, it is left with a net (overall) negatrve or positive charge. Most matenals are made up of groups of atoms, called mo5ecules. A charged object will cause a redistribution of the -t and charges -.. uncharged objects nearby Concentrations of + or - charge which occur because of this are called induced charges. An electric current is a flow of charge. When a metal conducts, there is a flOIN of erectrons. E The girl on the right ha~ gi\'en hcr...clf an clcclr;c charge by touching the dome ol a Van de GraalT gencralo1: The doml: can teach over 100 000 \olr , although thb i reduced\\ hen he touch~ it. Ho\\'evc1; the ClllTent that no\\'~ into her body (0.000 02 ampen::,, or le~:-.) is for too small co he dangcrou~. The for e ol repul!)ion between the charge~ on 1hc girl'~ head and haini i..; strong cn()ugh Lo make her hairs sLand up. Jl electric charges fed a Fol'cc.:, tlu.•n, ~cienLific.:all) ~peaking, the) ar~ in an electric field. o l here i an electric 1ield around l he dome and the girl. Electric field patterns I n diag,._ m , lines ,dLh ::u-row on Lhcm arc used to l'cpn.-scnt ckctiic field . Ther~ arc omc.: c,amplc::. or field pattern below. In each ea c, the atTO\\S how the di," tion in,, hich the lorcc on a po,ilin? ( ) harge \\'OU ld act. A:-. like charges repel, the Iield 1in=-~ alway:-, point awav from posiliYc ( ) charge and toward., negaci,·e (- ) ch~irge. The for c clue lo Lhe field is a , ·c lor. \ll • Elcctrcc field close to a • Electric f efd between two • Electnc field between negatively charged sphere. opposite, point charges. two parallel pfates with The field around a Van de opposite charges on them. Graaff dome ,s similar to this. 172 ECTRICITY Curves, points, and ions* \ Vhen a conducto r j c harged up, the c harge · rep •I each o ther, ·o the~· c ollect on the outside. The c ha rges are mo. t concentrated near the s harpl"~l curve. T hb is ,, here the electric ficlc.l is stronges l and thi: field Ii ncs c loses t Logcthc1: -- ------..__;_ very strong - - £ clectnc f1ekl charge lect~ s away from aornzes a r this p<Xnt ~ A The electric f eld is strongest where the charges are most concentrated and the field lines are closest together. A At a sharp point, the electric f eld may be strong enough to ,on,ze the air so that it will conduct charge away. Tf a hm~p s pike is put on th ' do me of a Van de Graaff g •ncra to 1; any c harge on the dome immediatd~ leak, awa, from che point. At the point, the metal is ,cry shaq,ly curved. Her<..", the charge is so concl!ntraLcc.l that the elec tric field is stro ng enoug h Lo ioni ✓l" lhc air ( cc abo\'c). Io nizcc.l air conc.lucts, o the donu· lo c · iL, c harge throug h the air. Io ns an: clec lricall~ charged atoms (or groups of atoms). Ato ms bccon1c ion~ ii the~ lo ·c (or gain ) electron ·. A trcam o l ion is a flo w of c harge, ' O it i ano ther example o t a c urrent. Mo ·t oft he m olecule. in air are un charged , but no t a 11, a · hown o n the righ t. Fla mes, a ir mo,·emcnts, and natun1I radiation from ~pac' or rocks c an all rcmc)\ 'C clcc1ron~ fro m molecules in air so 1ha1 ion~ arc fo rmed . Althoug h these soon recombine with an~ free electrons around , m o re a1~ being fo rntcd all the Lin1e. \ \'ith no io n · in it, air i~ a gooc.l cJectdcal in ·ulato r. But,, ith io n pt\.: ·cnt, it ha c harge · that arc frL'e to m ove. ~o the air be omc a conduc to1: 00 / 00 ~ o:xrQ• n mo ceule natrogl n mo L--Cule (2 atoms) (2 c:ltOITI)J A Air is mainly a mixture of nitrogen and oxygen molecules. The charged ones are called ions. ln a thunclerston11, the concentra1io ns of diffon:nt io ns m ay be so great that a H'T) high cun'-!nt ma) now thro ugh the a ir; causing a flash of lightning. ® 1 I he diagram on t e right shows electric field lines round a c:hargcd metal sphere (In air). E) Copy the diagram. Ora1-v in the d rcction of the electric field on each held line. 0, If a positive c:harge were placed at X, an which direction would it move? G If a negative charge v.rere placed at X, in 1,,-'Jh1ch d1rect1on would 1t move? d* If a sharp spike were placed on top of the sphere, wha t would happen to the charge on the sphere? x. Related topi cs: vectors 2 .1; atoms and molecules 5.1; cha rges and conductors 8 .1: induced charges 8.2; ionaiing radiation 10.2. 173 Charge essentials 0 Electric charge can be positive(+) or negative(-). Like charges repel, unlike charges attract. Charges come from atoms. In atoms, the charged particles are protons (+) and electrons ( ). An electric cell (commonly called a hattery) an make dectron , mo\·e, but onh if Lhere is a conductor connt!cling its l\\O Le1minals. Then, chemical reacLions in~ide the cdl push electron~ from the negaLi\'e ( ) terminal round to the posith·c ( ) terminal. The cell bclo\\ is being used to light a lamp. As ck lrons flow through the lanlp, the) make a filament (thin wire) heat up so that it glo\,s. The conducLing path through the latnp. wire~. ·wirch. and balh!1~ b called a circuit. There mu t be a complete circuit for the electron to tlow. Turning the witch OFF break ahe circuit and stop ahc flow. Electrons can move through some mate rials, ea lied conductors Copper is the most commonly used conductOf'. The unit of charge 1s the coulomb (C) '-Mleo si.v1tch ,s OH (open), gap $tops elect,on flow The above circuit can he drawn u ing circuit symbols: Some circui t symbols + ~~ s ng eccll .& Ammeter _/_ 0 To measure a current. you need to choose a meter with a suitable range on its scale. This ammeter cannot measure currents above 1 A. Also to measure. SiJ'f, 0.1 A accuratet,,, it would be better to use a meter with a lower range. When connKting up a meter, the red(+) terminal should be on the same side of the circuit as the + terminal of the battery. 174 >W \JI connec wre ng 0 ➔' r c·e, 0 ,1• p Measuring current A now of charge i • called an electric current. The higher the cu11ent, lhe grL"atcr rh,._. flo\\ of charge. The I unit of cmTent b the an1pere ( ). About 6 billion billion electmn!'t flo\dng round a ircuit e\'ery . econd would gi\'e a cun-ent of I A. Howe\'cr, the ampere is not defined in thb wa\' (sec next page). Current of about an ampere or o can be mea ured bv connecting an amn1eter into the circuit. For ~mallcr un-cnts, a n1i1liammeler b used. The unit in th is ca~c i~ the milliampere (mA). 1000 mA = I A ECTRICITY ----+ Some typical current values un-ent in a ma ll torch la mp urrcnt in a car headlight la mp un-c nt in a n e lectdc kc ule element 0 .2 A (200 mA) ! t 4A 10 Putting amn1e ten. (or milliamme ten,) into a jr u it ha almo t reading reading 2A 2A no e lfect o n the c ur r ent. As fa r as the circuit i concer·nccl , th1.: m e ten:. acr j usl like pieces ol connecting wire. E-electron The c irc uiL o n Lhe rig hL h a ~ Lwo a mme ter~ in it. Any clc Iro n s lea\ ·ing flow the bau ery mu ·t fl o \\ th rough bo th , o both gi\'e the ~am e readin g: The curn:nt i--. the same ;__,t all poinh in a ~implc circuit. E 0 Definitions In 2019, some SI units were Chafge and current There i · a link between charge a 11d current: 11 charge fl ow at thi rate... l coulomb per ccond 2 coulom b per ~ccond Lhen the CUJT~nt i l a mpcn: 2 a mpere The 1ink can al o be c;\prc ed as an equa tion: CLIIH.'ll l ! chaq!l.' u Lillll.' I ...a nd oon. For example, if a cha rge o f 6 coulomb · (C) i~ d cli\'crcd in 3 sccon<l , the c un\! nt i s 2 A Current direction redefined to improve precision. The couromb (C) and the ampere (A) are now linked to the charge on the proton, which is defined as exactly 1.602 11s 634 x , 0- 19 c The coulomb and the ampere are linked like this: 1 C 1s the charge passing when a current of 1 A flows for l s. omc circuit diagra m~ ha\ e arrowheads ma rked on the m. The e ·ho\\ the con,·entional current direction: the din.-cLion fro1ll to - round the circuit. Electro n~ actuall) now the o ther way. Being negalively charged , I hey a l\! r~ ~lll!cl b\' ncgatin! c harge, M> are ptL'ihcd out o r I he negative terminal o l the battef). electron + - Oow ) The conventiona l current direction i equi\'ale nt to the direction o f tra n~fer o f positive c harge. It defined hefort! the e l1.:ctron was disco\ cn~d a nd cicnti t reali1ed tha t po itive c harge did not flow Lhrough \\ ires. Ho we \ ·c r, it i ·n't \\ ro ng'. A-l a th e m a ti cally, a ln1n ·fer o l po itive c ha r ge i the a mc a~ a tra n ·fer o l nega tive charge in the oppo it ' di, ..ction. \H\S ® 1 Conv:)rt these currents into amperes: a SOO mA b 2500 mA 2 Convert these currents into m1lhamperes: a 2.0 A b 0 .1 A 3 a Draw the c1rcu1t on the right using circuit symbols. 0 On your diagram, mark in and label the conventional current d1rect1on and the direction of electron flow. c I he current read ng on one of the ammeters is shown. What 1s the reading on the other one? d Which lamp(s) wdl go out if the sw,tch contacts are moved apart? Give a reason for your ans...ver. What charge 1s delivered 1f a a current of 10 A flovJS for S seconds b a current of 250 mA flows for 40 seconds? COfW(?fl t1onal current d rectlOO read1111J O SA 0 ammeter Related top1cs: SI un,ts 1..2; electrons, charge, coulombs and conductors 8 .1-8.2 175 0 Circuit essentials A cell can make electrons flow round a circuit. The flow of electrons is called a current. Electrons carry a negative (-)charge. As Ii e charges repel. electrons are pushed out of the negative (-) terminal of the cell. = l to cell electrons tran!tf('r enciqy to lamp e-JectrOO!t lose Potential Charge is measured in coulombs (C). Energy and work essentials Energy 1s measured in joules (J). eleclronsl return energy: energy radiated P.d. (voltage) across a cell 0 Energy can be transferred from one store to another. but the total quantity always stays the same. A cell normally ha a \'oltage marked on it. The higher the voltage, the more \\Ork i~ done in pushing out each cou1omb. f n other words, the more energy per coulon1b is Lran~lerrcd bv the electrons to Lhe lamp. The scientilic name for \'oltagc is potential difference (p.d.). It can be mcasu1cd by connl-cting a voltmeter aero ·· the Ll'nn inab. The Sl unit ot p.d. i l he volt (V). E p.d. (\/), charge (0), and ,,ork done (U') arc lin~cd by Lhi l'(IUation: Work is also measured in joules. Work is done whenever energy is transferred: work done= energy transferred 0 For example, if the p.d. aero s the cell i 1.5 V: 1.5 J of \\'Ork is done in pushing oul I C of charge. 3 J of work is done in pu hing out 2 C of charge... and so on. The p.d aero a cell i high~t when it i n't connected in a circuit. Thi maximum p.d. i called the electromotive force (e.m.f.) ot the cell. \r\'hcn the cell i ·upplying a current, the p.d. acr~oss it drop. because the cell heats up and energ~ i~ \\~L,tcd. For example, a ar baUCT) labelled 12 V mighr onlv produce 9 V \\ hen being u~ed to Lurn a ~tarter motor. Cells in series To produce a higher p.d., sc,·cral cells can be onnectc<l in series (in line) as shown bdow. The word 'batten· rcal1) mt.:an · a collection of joined cell ~, although it i comn1onl) used for a single cell a \\ell. A Voltmeter and symbol. (For information about range and connection, see note under ammeter in previous spread.) --1~--~~ battery made up ex se~ral cells (symbol) ECTRICITY I P.d.s around a circuit - --od = 3 v - - 3 p.,le5 of Mef'J'I 9'vt'n (O each coulomb l=--- l no enefgy wasted 2 ptjes ol energy supp&ed b-/ each coubnb I pufe of e<lt'f9'/ sup~ by eath coulomb , ad,n a 2 V read nQ 1 V E In the circ uit aboYc, the electron no\\ thro ugh two lamps. Some cne1"g) i tra~te n ·l.!d to the fit~ l la mp and the 1~ t to the second. (If the connecting \\'11\."S arc thick enough not to heat up, no energ) is w:.1.stcd in the " ~re~.) Like the battery, each lamp has a p.cl. aero. s it: If a lamp (or <>thcr componl!nt) ha~ a p.cl. of 1 n>lt ac ross i t, th l!n I joule of work i.-; do ne in pu~hi ng each coulomb o l c harge 1hrough it. A~ a res ult, I joule o f e nergy i~ trans fcn~ <l LO it. The ccond diagra m ho,, the a me circuit with \'o ltn1ctcr connected aero s diflcren t section (the \'Oltmete r d o not aAec t how the circuit \\ o rks). The reading illu lra te a princ iple which applie in an) circ uit : Moving round a circuit. from one batlc1)' tcnninal to the other, the ... um of the p.d.~ a1.:ro-.;-.; the components is equal lo 1hc p.d. ,1cro~" lhe battery. ® 1 In what unit is each of tl ese measured? a p.d. b e.m.f c charge d current e energy 2 lri the circuit on the right. the two lamps are of different sizes and brightne~es. a What type of meter is meter X? b What type of meter is meter Y? c What is the reading on meter Y? ~ How rnuch energy 1s transferred to each coulorr b of charge as it is pushed frorn the battery? 0 How rnuch work is done on each coulomb in pushing ,t through lamp A? 0 How rl uch cl arge passes through lamp A evety second? 0 Definitions The electromotive force (e.m.f.) of a cell (or other source) is the work done per unit of charge by the cell in driving charge round a complete circuit [Including the cell Itself). The potential difference (p.d.) across a component is the work done per unit of charge in driving charge through the component. read ng A B Current 1s measured 1n arnperes (A) using an ammeter. If 1 ampere flows for 1 second. the charge passing is 1 coulo, b. Related top1cs: SI un,ts 1..2 ; energy 41- 4.2; electrons and charge 8 .1-8.2; charge and cunenl 8-4; ceU arrangements 8.9 1T/ 0 Circuit essentials A battery pushes electrons round a circuit. The flovv of electrons is called a current. Current is measured in amperes (A). °' Potential difference (p.d.). voltage. is measured in volts M . The greater the p.d. across a battery, the mOfe energy each electron is given. The greater the p.d. across a lamp or other component. the more energy each electron transfers to it as it passes through. To niake a cun"ent llow in a conductor, there must he a polential c.liffcrence (\'ohage) aero · il. oppcr connecting wire is a good concluclor and a ctn,·ent pas...;c~ through it casih. Howc\·cr, a similar piece of nichrome wir~ is nol so good and lcs~ <.:urrcnl llows for the ·amc p.d. The nkhromc ,, in..· ha more resistance than the copper. Re i lance i calculated u ing the equation below. The J unit of re i tance i the ohn1 (il). (The symhol n i l he Greek letter onzega .) 11..·,btanc1..· (U) - p.d. aero~~ c.:onductor (V) cur n.:nt through <.:onductor (A) For example, iF a p.d. of 6 Vi~ needed to n1ake a current or 3 A llo,, in a wire: r-esi ·tancc 6 V/3 A 2 0. \ ith a lower re ·istance, a lower p.d. would be nttdcd to gi\'c 1he same curicnt. E,en copper connecting wire has ~orne re i Lance. Howe, c1~ it i · noa mal I,· o lo\\ that on Iv a \'erv ~mall p.d. i needed to make a cun-ent no,\ in it, and thi can be neglected in calculation . Some factors affecting resistance ---~-----~---- long, thin. ntchrome Wife long. ihin, copper w ire c:::==· long, thrck. copper Wife The re~i tance of a conductor depend on everal Iactor : • • • Length Doubling the length of a\\ ire clouhlc~ it~ rc~istancc. Cross-sectional area Halving the 'end on' area of a,, ire doubles it · n: isLancc. o a thin wirl! has more rcsi~tance than a thick one. A:latcrial A nichrome wile ha mote re i Lance than a copper wile ol the ame ize. • Temperature For metal conductors, re. i lance in rca -es with temperalun!. For semiconduclor • it decrease · with tcmpcra1ure. Resistance and heating effect short. thic . copper wire There is a heating effect ,,ht>nt'\t'r a cuTTI!nL Oow~ in a re!sislance . Thi'i principle is u~d in hl"Jling demcnL-.;, and al"o in lighl bulbs wiLh filamcnL'i. The heacing effect oc.:curs because electrons collide\\ ith aLoms as the) pa · Lhtough a conductor: 'l'he electron lo • cncrg,. The atom gain cnerg_\ and vibrate la te1: fa ter vibral ion mean a hight'r temperature. A The filament of this lamp 1s made of very thin tungsten wire. Tungsten has a high melting point. ISym~~ lement I Heating elements are normally made of nichrome. ECTRICITY Resistance components Resis tor ar " pecia11y made to provid" re i tance. Tn iniplc circuit~. they reduce the current. Jn more complicated cir uits, u ch as those in radio~. TV ·, ancl co mpuLcrs, they keep currents and p.d .~ al the lc\'cl~ needed for other components (pa11s) to work proper!,. f---i- Rl: i ,to1 can ha\c value ranging To n1 a few ohn1 lo ·c\·eral million o hm . For mca uring higher re i tance , the c unit arc u clul: l kilohm (k 0 ) = I 000 0 I mego hm (MO) batte,y I 000 000 0 .ic1mp Lik" all re. h,tance , re h,101 heat up wh~n a cun- nt now in the m. Howc\·cr, if th1.: c un- "nl is ~mall , the heating effect is ~light. Variable resistors (rheostats) an: u~c<l ror \'al"\ ing c un·ent. The one on the right i · controlling the brightne ~ of a lamp. In hi-Ci cquipn,cru , ro HH'\ (circ ular) \atinblc.: re ·i tot · a rc u ·cd as \"o)umc controb . s•ide contro1 Thermistors have a high re i lance when cold but a muc h lo wer resistance when hot. The~ cont ain semiconduc tor materials. ome electrical thcrmomcten; u se a thcrmi~tor to detect temperature c hange. Lig ht-dependent resi tors (WR ) ha\·c a hig h re ·istancc in the dark but a lo\\ re i tanc~ in the light. The) can be u ·cd in electronic circ uit \\ h ich \\ itc h light on and o il auto maticalh. f .& Moving the slide control of the vanable resistor to the right increases the length of resistance Wire in the circuit. This reduces the current and dims the lamp. Diodes ha\·c an e~tt~mcl) high re btancc in one directio n but a lo w re ·i lance in the othc1: In ctlcct, they allow cutTcnt to flow in one dire tio n onh. The\' ar ~ u 1.x. l in electro nic cir uit . resistor Symbol ® vanab3e res1st0< -c:::J-- 1 When a kettle is plugged in to tt,e 230 V mains. the current m its element 1s 1OA. a \"Jhat is the resistance of ,ts element? b Why does the element need to have ,es,stance7 2 In t e diagram at the top of this page, a variable resistor ,s controlling the brightness of a lamp. What happens if the shde control 1s moved to tt e left? Give a reason for your answet. thermistor cod of restStance Wire hght•depe'ldent resistor diode ~ -c:::J-- 3 Which of the components in the photographs above has each of tl ese properties? a A I igh resis tance ,n the dark bu t a low resistance in the light. b A resistance that falls sharply when the temperature rises. G Avery low resistance in one direction. bu t an extremely high resistance in the other. Related top1cs: SI un,ts 1.2; temperature, vibrating atoms, and thermomet ers 5-2; conductors and semlconductors 8 .1; current, cireuits and symbols 8.4, Potential difference 8.~ d iOdes. LORs, and l tlefmtstors 8.1t ; reststor cot.our code page 321 179 Resistance equation 0 V I, R equations Then: ·istance cqutttion can be w,;uen u ·ing )"lllbols: R resistance potential diffe,ence current Untts: resrstance: ohm (0 ) potential difference (p.d.): volt M current: ampere (A) where R - rcsi tance, V ::.... p.d. (voltage), and I current \I I ( otc the diflercnec bct\\Ccn the V for volt.) S) mbol V for p.d. and the S) rnbol The abo\·c equation can be r-carrangcc.l in hvo ways: \I R I and IR \I The e arc u efu) if the p.d. aero it, i to be calculated. E.wmzple A t 2 a kno\\'n re i ta nee, or the current in n n .•~istor ha~ a p.d. of 6 V ac, o,, it. \ Vhat is the cun 'nt in the resistor? In thi ea ·c : V \' I R 6 V, R = 12 n, and / 6 = 0.5 12 i · Lo be lound. So: (omitting unit for implicicy) - o the current b 0 .5 A. A This triangle gives the V. I. and R equations To find the equation for I. cover up the I. How current varies with p.d. for a metal conductor ...and so on. battery (or low \'Oltage supply) @ The circuit bclo\\ leh can be u,ed to in\e tigate ho\\ the crnTent in a conductor depend on the p.d. aero it. The ondu tor in thi ea e i a coiled-up length of nichrome wire, kept at a . teady temperature by immcl"!)ing it in a large amount of water. The p.d. across the ni hrome can he \·a dcd b} ac.lju~ting 1hc variable rc~iMor. T\'pical result~ arc shown in the table below. The c~pcriment i · al ·o one mt:thod of mcasuting rc · i ranee. ____ ~--~ ____ E The re ult~ an al o be hown in the forn1 of a graph, a below. p.d. cunent p.d. current ommeter 5.0 H 30V 0.6A s.on s.on 4.0V 0.8A 5.0H sov 1.0A s.on 0.4A voltmeter stJrrer---water to keep nichrome at constant •emperature 18o ~ resistance 2 3 pd/V 4 5 ECTRICITY E Ohm's law Jn • • • the C" P •ti mcnt o n the oppo ite page, the , ~ ·uhs have these fea tun.:s: A graph o f un·cnl agains t p.d . is a st raigh l Ii nc l hrough l he origi n. If the p.d . d ouble , the cun"Cnt douhlcs, ...a nd so on. p .d. -=" curre nt a lways has the same value (5 n in lhis case). Ma the ma ticall), the ·c can be umn1cd up a follow ·: The t:UJn,..n t is proport iona l to th'-'• p.d. This is known as Ohm's law, a fter GL-orgc Ohm , the 19 th centur, st:icnli ~l \\ho fir~t in\'cstigatcd the electrical properties o f\\ ires. Meta l conduc to ~ obey Ohm's law, pro\'idecl their tempera ture d ocs not cha nge. Put another wa~ . a me tal conduc tor has a cons tant resistance, p ro vided its temperature is con~tant. Thi~ i · nol alway the ca~e with othe r t) pe o f conduc tor. Current-p.d. graphs Here arc two m o re cxamplcs of cun1:nl- p.d. graphs. In both, the resista nce , -a,ies depending on the p.d. In the case of the diode, the negative par1 of the gr..1ph is lor ~ a<lings obtained" hen the p .d . is rcve, 1.:d (i.e." hen the diode i com1cc.: ted into the k t circuit the oppo itc ,, a) round). ■ ■■ 0 2 4 6 8 10 12 p.d.l V A Tungsten filament As the current increases, the temperature rases and the resistance goes up. So the current is not proportional to the p.d. ® -0.6 0 +0. 6 p d./V reve«se forward Semiconductor diode The current is not proportional to the p.d. And if the p.d. is reversed, the current is atmost zero. In effect, the diode ' blocks' current in the reverse d rection. 1 A resastor has a steady resistance of 8 0 . a If the current m the resistor is 2 A, what is the p.d. across 1t? b What p.d. as needed to produce a current of 4 A? c If the p.d. falls to 6 V. what is the current? The graph Imes A and 8 on the nght are for two different conductors. Which conductor has the higher resistance? 3 Using the left-hand graph above, calculate the res,stance of the tungsten filament when its temperature is a 1 SOO C b 3000 C. In the right-hand graph above, does the diode have its highest resastance in de forward direction or the reverse? Explain your answer. 0 0 0 pd Relat ed top1cs: conductors and semlconductors 8 .1: current 8-4; potential difference 8 .5; diodes 8.6 and 8 .11. 181 0 The effects of length and area Resistance essentials lo make a current flow in a conductor. there must be a p.d. (voltage) across it. The resistance of the conductor is calculated like this: resistance - A{_ _......,._ _ _ _ _ _ _ _ (~ same copper cross-secuona I a!<?a 8 - - - - - - - - - - - - - - -~ p.d current 8 has 2 x le gth of A 8 has 2 x resistance of A Units: resistance: ohms (U) The copper wir-cs abon! have the ~me c ro~:-.--sectional an:a and lcmpt.!1-a1ure. Bul B is twice a.~ long as A. As a result, it ha._. lu·ice the n:sistancc of A. If B wcr~ rlzrc!e Limes as long as A, il would have Lhrce 1i111e.!-. the re ·isrance. and so on. Rc~ults like this can be ~um1nc<l up as follow~: p.d.: volts M current: amperes (A) Even copper connecting wires have some resistance, although this is usually very small. Resistors and heating etements are designed to have resistance. The resistance of a wire depends on its length and cross-sectional area. It also depends on the material and its temperature (although for metals, the change of resistance with temperature is small). @ Provided other t actor::, do not change: T 1~ B ·i ~lance lcngrh (the~\ n1bol rnean · 'dirccll~ p1 opor1ional to') --------------------------I copper I C (_ _ _ _ _ _ _ _ _ _ _ _ __(,) C has 2 x cross-sectional area of B 1 C has 2 x rcstStancc of B The copper wit e above ha\'c the ~ame lcngrh and te1npcratu1c. But C ha rwice l he cro - ee l ional area of B. A., a re uh, it ha lwll the re~i tance or B. If Chad three times the cro - ectional area of B. it would have one rl,ird or the n:s i~tance, and so o n . Re ·ults like this can be summed up as follow~: E Provided other f acto1 · do not change: I r~istance urea mean~ cro:-;s- ect1ona I area') area The above propo1tionalitic · arc Lruc for orher t, pc~ of \\ire, although Lh~ re j tanc~ \\ ill diflc1: For example. niclwome ha muc h more r~i-,tance (' • I • than copper of the ~ame length , cro~~- e tional area, and temperature. The •-~!',uhs can be combin~d as follows : For an) gh ·en condu ting material at con!')tant temperalm'-!: h.·ngt h 182 E ECTRICJTY E Proportionality problems Diameter and area \\!hen there a rc n1a1hcmatical pro blems l o so lve, equation~ arc muc h morL" usduJ than proportionalitil: . r orlunatdy, the pro portio na lity linkjng re i tancc (R ), leng th (/). and ar --a (A ) can be converted into an equation like thi R = ,, I A CD a,eaA (1, - Greek letter ' rho') X - R diameter of another, as above, then it has four times the cros~sectional area. That follc,."15 from the equation for the area of a circle: 2 A - itr • Doubling the diameter doubles the radius. So. replacing r in the equation \\lllh 2, gives: A I This i useful when comparing different wires , A and B, made from the same marcrial. As p is the same for each \\in,: (al a particular temper.Hu re): n-..,i-,1ann.· \ · arc..'a" l\.',btann: 8 k•ngl h \ new area an.·a 11 - n(2r)2 k·ngt h 8 length of A t1nc.l rwit.:i.: the diamcll•r, wh,it is ib rcsistam;c? (A,,umc that both win.· s an.· al the same h .•mpcr,llur-c.) · \\ire B has l\\ ice the diameter of A, it ha four timt: the cro~ cctional area ( cc the bo~ above right). The 1~ is ta nee o( wit"e B i to be tound: call it R 8 • A - no mc~tu~ment arc gin:n, use lcttc-1 · to repn.--scnt thes e as wd] , as in the diagrdm on the rig ht. area AC Rearrang ing and c.:ancclling g h·es: R 0 ®0 0 - 2,t---1 Constantan Manganin Nichrome Tungsten 49 X 10 S 44 10 8 100 10 8 S!:> x 10 8 Table 1 n. Related top1cs: resistance and resist ors 8.6-8 .7 reel A 'fypical resistivity values/ n m 6 Wire X has a resistance of 18 n. Wire Y is made of the same material and is at the same temperature. If Y is the same length as X. but 3 times the d,ametet, what is its resistance? Wires A and B are made of the same material and are at the sam1: tempera ture. The chart on the right gives some information abou t them. a If you were to use part of wire A to make an 18 n resistor, wha t length would you need? ~ I e<--------~J> (ornitting unit~ for simplicity) 2t o, the re~istance of" ire B is 6 11U •- x - t l H a1~a, = A , then area 8 = 4A Al o, t\:si ·ta nee\ - I2 n and 1~ i tancc 8 - R 8 ubstiluting the abo,e \'a lues in chc pre\ iou · equation g i\'e~: ·A 4 r.r2 - 4A. diameter2 ~ H length,\ = x, the n lcng th 11 = 2x .r - Similarly three times the diameter gives nine times the area. and so on. So: E.wm1ple \ Vire A has a rc~btanc.:c of 12 n. It wire Bis twice the: J2 area 4A If one wire has tv1ice the \\here ,, i • a con ta nt for the material al a particular tempcratun:. ,, is called the re i tivity ot the n1atcrial (Table I ). Rcan-ang ing the abo\'e <.'Quation gi\·c ·: P- 0 b What is the resistance of wire B? c What length of wire 8 would you need to make a 20 Sl resistor? wire B length 1000 mm 2500mm area 2.0 mm2 0 .5 mm 2 resistance 2s n 0 Circuit essentials Potential difference (J).d.), or voltage, 1s measured m volts M . The greater the p.d. aross a lamp or other component, the greater the current fl~ng in it. Current is measured in amperes (A). Lamps, resistors, and other components have resistance to a flow of current. Resistance is measured m ohms (H). The lamp abo,~ have to get their power from the san1c upply. There arc t,,o ba ·ic method~o connccling kunps, rc~i to1 , or other component~ togcthc1: The circuit~ below demon trate the diUcrencc bct\\ccn then1. Lamps in series and parallel -----t~---~..,___- -----~---~1--- battety battcry amps n pa al el ,1•nps in ser ·•, These lamps are connected in series. • lhe lamps share the p.d. {voltage) from the battery, so each glows dimly. • If one lamp Is removed, the other goes out because the cIrcuIt 1s bro 'en. These lamps are connected ,n parallel. • Each gets the full p.d. from the battery because each Is connected directly to It. So each glows brightly. • If one lamp Is removed. the other keeps working because It 1s still part of an unbroken circuit. Circuits and switches H two or more lamp ha\'c to be powered bv one baue1 . , a in a car lighting , tcn1, the~ are normall) connected in parallel. Each lamp get l he full batter) p.d. Al~o. each can b" M,itchcd on and ofi indep "ndently: l I ► These diagrams show two different ways of drawing the same circu t for independently switched lamps. I I I ..L ECTRICITY Basic circuit rules p.d. There ar" ·omc basic rules for all eric.s and parallel circuit . They are illustn1tcd h), the examples helow. The particular cu1Ten t \'alues depend on the r'l!si~tancc~ and p.<l.s. However, the equation on thl! y;ght llln-ay.~ appl ies to e1·e,) rc~ isLor. M =airrent x resistance (A) (!l) 0 1 18V 3 sv- - - - - 3U 6U 2A n 9A 9A 2A 6 6V n 2V 3 ,; SV When resistors or other components are in series: • the current 1n each of the components 1s the same (E) • the total p.d. (voltage) aaoss all the componeots 1s the sum of the p.d.s across each of them. T When resistors or other componeots are 1n parallel: • the p.d. (voltage) aaoss each of the component is the same the total curreot ,n the main OrCUlt IS the sum of the 'i." currents 1n the branches. m. q}Cell arrangements - - - - 1 S v- - - - - - - - 4 SV- - - 1.SV lSV 1.SV 1.SV 1.5 V 1.SV f These cells are connected in series. The total p.d. (voltage) across them is the sum of the individual p.d.s. Here, a mistake has occurred One of the cells is the wrong way round, so it cancels out one of the others. The p.d. across parallel cells is only the same as from one cell. But together, the cells can deliver a h gher current. ® X 1 When one of the lamps on a string of hghts brea s, the others go out as v1o,ell. What does this tell you about the way the lamps are connected? 2 Grve tt,vo advantages of connecting lamps to a battery an parallel. 3 Redraw either oft e circuits on the left so that 1t has a single switch whach 0 turns both lamps on and off together. This question is about the orcuit on the right: O The readings on two of the ammeters are labelled. What are the readings on ammeters X and Y7 0, If the p.d. across the battery 1s 6 V, ,.,\/hat 1s the p.d. across each of the lamps? (Note: you can neglect the p.d. across an arnmeter.) -r- Related top1cs: current and circuits 8-4; potential difference (voltage) 8 .s; resistance 8.6-8.7 : 6v I ....L... Combined resistance of resistors in series If lW<> (or more) rc~islors arc connectl!d in ~c1;cs, Lhl!\' gi,·c a higher rc!->islancc than any ol the ~sisLOr'> by itself. The effect is Lhc snnlc as joining ·c,·cc'ill length of resistance\\ ire 10 form a longer leng th. These resistors u If n..:sistors R I and R 2 arc in se1·ies, their combined rc~istancc R is g i\'en by thi · equation: u are equ \'a cnt to this ,es1stol' 9U ,~11itance: 3 n + 6 n = 9 n There is an example on the leh. Foa tlu-cc or more re equation can be extended b, addin g R ... and o on. to1 ~. the above Combined resistance of resistors in parallel Tf two (or more) re i tor arc co nnected in parallel, thev g ive a loH·er resistancl.! than any ol the resi lor · by it ·elf. The effec t i the snme a. These ,es stors ~c J-3•• usin g a thic k piect! of rcsi~lance wire inslcad of a chin one. Then~is a \\ icier concluctjng path chan before. E U Lwo 1~sist01 R 1 and R 2 arc in parallel, their combined rcsi ·tancc R is gin~n by thi equation ( Lherc i a prool at Lhc bo ttom of the page): 6U are equrva ent to th s ,esrstor I R R. R, •1,+i For three or more re:-,istor~. the equation can be exlended bv adding 1/R 3 , ••• and ~o on. R1 A R1 If Lhe abo,·c equation for two ,~si~tors is ~an-angecl, it becom : R R 1 R, rl'-.. i~ ta nn.·~ 111 u It i pi ie<l (.·ombinl'<.l 1(.'-.i-.tarK'l' l n word : n .·~i-..t~rnc.:1..•~ add1..'<.I - 3 -i For c"amplc, if 3 0 and 6 lU Ommmg un ts f0t sunp~city. 1 I _ l + 1 r~1stan<e - 3 2 o l 1 =2 So: resastance 9 n n ~sistors are in parallel: 6 combined re is1ancc 2 tl X 6 3 2 n Jotc: Lhi~ method of calculation works onh for two resi~ton. in par"c1llcl. f E Proving the parallel resistor equation In the c,rcu,t on the left, R1 has the full battery p.d. of E across at So does R2. As current = ~.d. resistance : /I i= .f. and R1 I2 =l. R 2 But I = 11 + 12 If resist or R is equivalent to R: and R2 in parallel. it must take the same current J from the battery: ,_-Rf 186 Therefore: i - %+ J 2 E ECTRICITY E Solving circuit problems To solve problems about c:i,·cuiL'i, ) O U need to know the btL~ic circuir 11.1k~ o n the prcviou pr-cad. You a] o need to kno,, the link between p.d . (, oltagc), cun·enl, and•~ i tance . Thi i gi\cn o n the right. Example I Calcu lah.' the p.d ..... ae ro ,.., thl' 3 U n_...,i--tor and th1..• 6 S? ll',btor in th"-• circui t on 1hc right. The fir~t s tage is to calculate the lo tal resistance in the c ircuit, and then use thi · info rmation to find the c urrent: to lal res i~cancc s o: cun·ent / - 3 (V) ({ l) (A) In symbols: V - IR ---~~---~:.,_____ 18V n r6n -9 n .d. l V n.: i tance 9H 2A '---t~.::::.1--{_-:_-_-_-_7t-- Knowing that the 3 n 1 ' i tor ha~ a cun-cnt o l 2 A in it, you can calcuhllc the p.d. across it: p.d . - curre nt p.d. - cuffl!flt x resistanceO 6U 3U re i la nce . 2 A • 3 n - 6 V The p .d . ac ross the 6 n t'!sistor can be ,, orkcd out in 1hc same wa~. Ho,,c\'er, ii can also be deduced from the fact that the p.d.s ac ross the two rc~istors must add up to 18 V, the p.d. ac ross the bane,~. B~ either method, the p.d. across the 6 n re istor- is 12 V. £m m ple 2 Ca kulak· the cun't·nts / , 11, and 12 in the cin..: uit o n the right. n resisto r has the full bauery p.d. o f 18 V a cross it. I V I = p.d. 6A 1 The 3 rc~i!'\tance --•---1:-18V o: 3n Using the same met hod: 12 3U 3A The c urrent / i Lhe to t.._,l of the cu.,-enc in the t\\ O branc hes. 6U ® 1 In circuit A on the right: "T" a What does the ammeter read? : 12v 0, \l\lhat is the p.d. across each of the resistors? -L 2 In cIrcu1t Bon the right: A a What does the ammeter read when the switch is open (OFF)? "T" 0, \"vhat 1s the current in each of the 4 O resistors when 1 I 12 V the switch IS closed (ON)? G What does tt e ammeter read when the S\Vitch is closed? --'B ~ What 1s the combined resistance of the two resistors w en tl e switch is closed? 3 a Which resistor arrangement, C or D. on the right has the lower resistance? C 0, Check your answer by calculation. 4U 4H A ..,__ _ _ _ __. 1n 4U D IO U Related top1cs: current and c1rcu1ts 8-4; potential difference (voltage) 8 .5: resistance 8.6-8.7 [ 990 U IO U E Diodes Diodes allo\\ cun~nt to no\\ in them in one clirccLion onl). The drcuits below ·how\\ hat happens when a diode b connected into a drcu it one wa,· round and then the other: A Diode reverse bias forward bias 3V dodc + IN4001 + lamp banery _ (twoR20 dryce (2 sv 0 2 A) current {convent ona no current A When the diode is forward biased. 1t has an extremely low resistance, so a current flows In ,t and the lamp lights up. A When the diode 1s reverse biased. 1t has an extremely high resistance and the lamp does not light. In this case. the arrowhead in the symbol points the same way as the conventional (plus-to-minus) current direction. In effect. the diode blocks the current. 0 Rectification* Thi~ i~ thi: process of c hanging a.c. to d.c. lL i~ done using diodes which, doing th i · job, arc known as rectifiers. A ·impk rectifier circuit i ~ho\\ n belo\\. ·rhe diode let · the lorward parl · of the alternating Cllff('nt Lhrough bul block the backward part. So Lhe Cltt1·cnt in then,; i tor one\\ a'. only. It ha become a rather jerkv form of d.c. Circuit essentials A.c. (alternating current) flows alternatefy backwards and forwards. O.c. {direct current) flO'NS one way onfy. no\, When resistors are in senes, each has the same current in it. The resastor wtth the highest resistance has the greatest p.d. (voltage) across 1t. An osci lloscope can bt: used to shC>\\ how the cin.:uit changes the a.c. input. The bottom part of the outpul \\'a\'efoi-m is mi · ing. The cun~nt is flo\\ ing one way, in ·urge , \\ ith short pl!riod of no cun·enr between. \r\'ith extra component added to the circuit, the pul ing cur,·ent from a n!CLifier can be ·moothed out. The re ·uh b a steady d.c. output. dodc IN4001 ,- r output coo ~'( • or~to osc IO'>C OPl \ 188 ~ 6Vac put l s:l output resistor ECTRICITY E LEDs LED t a nd~ tor Light-En1itting Diode. th e n a n1e sugge t~, jf i a diode that gh t!!-1 off 1ight whe n a cun"Cnl b pm,secl th roug h it. Red, gn;!en, a nd blue LED!-. an .• u!->cd as indicator lighls on ck-ctronic equipment Arrays o f \\hitc LEDs a l\: Lhe source o l lighL in w me lO\\•cncrg_y bulbs a nd lol'Chl:s. symbol A LED and symbol Potential divider A potential divider i · an arrangeme nt that dcli\'c 1 onl~ a proportio n of the voltage h-onl . _l ba ctcr) (or o ther o urcc). Circuit A ·ho \\ the p1inciplc: 0 10 T n T I GV I I I 10 U I 6 VI I I 10 U A In P.d. and resistance In a potential d1v1der, the p.d.s across the two resistors are in prop0f"t1on to their resistances. If the resistances are R1 and R2 and these have p.d.s of V1 and V2 across them: 0-3V 3V this potential divider, the lower resistor has half the total resistance of the tv\lo resistors, so its share of the battery's voltage is also a half. ~=~ B Using a vanable resistor as above, the output voltage can be changed. H~ ,t R2 Vl can range from Oto 3 V, depending on the setting on the variable resistor. Some electronic c ircuit arc de ig nt!d to s ,,~tch o n when a voltage renc he · a ~er va lue. If the , a ria blc r"L~islo r in ci rc uit B we r e ~ placed b\' a n LOR (light<lcpcndcnt resistor), then Lhc circuit controlling a la mp could be ~\\itched o n \\hen it got dark. irnilarl~. a fire ahu-m could~ wilchecJ on b~ a potcnlial dh idcr conta ining a thermistor (tcm pcr..itua-c-dcpcndcnt 1~ i ·tor). metal glas.s (MS Reed sw;tch A reed S\.Vitch i~ ope r..ired h\ a m agne tic fidd . [n the l;!Xa mple on the r ig ht , the conLacts close if a mag n e t i~ broug ht near, then o pen a ga in if ii is mo\'ed a \\ a\ . Burglar alarm circuit often contain reed witches. ~rhc rnagncts arc attached to the n10, ·i ng parts ol "indo,, s a nd doo, ' . \'Vith a coil ro und it, a 1'\..~<l ~wilc h lx.-comc a reed rela . ~rhc cun"l.·nt in one circ uit (through thL· coil) ·wilchc · o n another cin.:uit ( through tht: contact ). coritctc ~ A A reed switch. When the magnet is moved near, the reeds become magneti2ed and attract each other. ®0 Whal does a diode do? What is the purpose of a rect,rier? Loo · at circuits X and Yon the right. In which one a does the lamp light up b does the drode have a very high resistance? 4 If. in circuit A above, the lower res1st0t wete replaced with one of S kS l. how would this affect the output voltage of the potential dividet? s• HO'N would you dose the contacts in a reed switch? 8 0 Related top1cs: current dtrectton 8-4; resistance 8 .6; relay 9.4: a.c. and d.c. 9 .9 X y In the circ.:uit on the lefL, thl-' battery supplk-s energy ,, hic h i~ tran ·fon·cd to 1hc lamp. Encrro i tran kn-cd hom the la111p b\' radiation . power .___ _ _ _\I ;:r SW ' battery suppl es 5 J of e rgy per s00>nd -------4~---~ ....,___ Power i the rate at which energy is tran~ferred (moved lrom one tore to another). The l uniL of power in the watt( \ ): po\\er lamp rece1\'3 S J of energy per second ,------''''-------, power= 5 W Circuit essentials In a c1rcu1t like the one 0 above. the charge is carried by electrons. Charge is 4..'114..'1)!\' tran~t~t-rt•d ti nu· takt•n The batten· on the left i uppl~·ing 5 joules of energy per econd, o the power it transfers is S wall . The lamp is transferring power to it~ ~un-oundings al the same rate, - watts. Appliantc · such as toaster ·, iron ·, and TV · have a power rating marked on 1hcm, either in wall or in kHowau : 1 kilowatt (k\ V) = 1000 watts ome l) pical power rating~ are shown below. Each rigurc tells you the pO\\Cr the appliance will cake if co1111ec1ed to,~ ~upp(,· oft he correct 1•0/w~e. For any other \'oltagc, the attual power \\ould be diffc, ent. measured m coulombs (C). lhe flow is called a current and is measured in amperes (A). 1 A ~ 1 C/s Energy is measured in joules (J) Potential difference (p.d.) or voltage, is measured in volts M. The greater the p.d. across a battery, the more energy per coulomb it supplies. 1 V= 1 J/C 2'100W (2 4 W) The greater the p.d. across a Electrical power equation lamp or other component. the more energy per coulomb is being transferred to it. For circuits, there is a more useful \'ersion of thc power cquat ion. Tf a battery. lamp, or olher component ha._. a p.<l. (\'ohagc) across it anc.l a cun~nt in it, the power is given b) this equation: J)O\\ L'I' + ( \\ ) sv ,1 V 1 I ln ') mbol : p p.d. CU 11'4..'ll( ( \ ') (A) \II 2A -'-4V 190 Era111plc In th~ cit cuit on th~ left, what is t hl· pow~r nl the batll..'ry and ~ach of th~ l~u,np~? ECTRICJTY For th l: balte~ : J)O\\ er = p .cJ. x c un·t:nl J2 V 2 A 24 \V For lamp A: p<}\\ er· = p .d . x cu rrc nl V x 2 A J6 \ V For lamp B: po\\ er - p .d. curre nt - 4 V 2 A - ::1 \ V Th ' lan1p aa' the o nh ite m:-, gcuing power fro m th e ba tten , o their to ta l J)O\\ l'r ( 16 \ \' · 8 \\') i the a me a th at upplied bv the ba tte n (24 \ \'). Why the electrical power equation works* 12V The equatron power p.d. current 1s a result of hO\N the volt, ampere. coulomb. joule. and watt are related. l he following example shoold exptain why. Here are two ways of describing what is happening on the right: 2A General description Scientific description Battery transfers 12 joules of energy to p.d. 12 volts each coolomb of charge 12 joules of energy from the battery current - 2 amperes 2 coulombs of charge are pushed out from the battery ~ery second So 12 x 2 joules of energy are transferred power - 24 watts from the battery every second + Calculating electrica enerqy Tf the pow "r of an applianc' i kn own, the e nergy tra nsfo~d in any g i\'cn tin1e can be calcula ted bv r can n nging the fir t equ a tio n o n the o ppo ite page like thi : l'&h:rgy tran,k·n\.·d po\\'l.'I" x tinw cakcn For e xa mple, if a J000 \ V heating clement i witc hed o n for 5 c o nd ( ): enerro tran ·fe n·ed - 1000 \ \' x - · ;i... ·ooo J. o the hea tin g cle me nt g i\'l.!S o ff 5000 J o f thi:1·m al c n e rg .). A po\\er - p .d . x cur rent, the a bo, e equa tio n can a l o be written like thi ·: cncrgy tn.uhkffcd (J) p.cJ. • cu1·rl.'Jll (V) One kilowatt hour (kWh) is the energy supplied when an appliance of power 1 kW is used for 1 hour. 1 kW is 1000 W. and 1 hour 1s 3600 s. So, if a 1 kW appliance is used for 1 hour: Lillll.' cakcn h> (A) 0 The kilowatt-hour Electrrc1ty supply companies use the kilowatt-hour (kWh) rather than the Joule as their unit of energy measurement: energy - power x time E \ ·11 - 1000 W X 3600 S - 3 600000 J Exm1111le A 12 V \~at~•· hL·atl.'r t;,,,kl..._ .., cun..:m ol 2 A. If it i, "" ilc hl.•<l on for 60 ~ccond,, how much cncrg_, b. trm1,lctrcd to thcnn;.,l energy? e nergy tram,lerred - p.d . x cunent x tin1c 12 V . 2 A All or this is lransfcrrcc.l to thermal c ncrg.), so: ncrgy tn msfen-cd to therm al ene rgy 1440 J ® J\ 60 1440 J 1 In 5 seconds, a hairdryer receives 10 000 joules of energy from the mains supply. What 1s the power transferred a in watts b in k1IO'.vatts? 2 If an electric heater takes a current of 4 A when connected to a 230 V supply, what pO\'Ver 1s being transferred? 3 If a lamp has a power of 24 W w en connected to a 12 V supply, what is the current through it? 4 Calculate the energy transferred to an 11 W lamp a in 1 second b in 1 minute. S A lamp takes a current of 3 A from a 12 V battery. a What power 1s being transferred to the lamp? b How much energy as transferred in 10 minutes? Therefore: 1 kWh 3 600 OOOJ 0 Counting the cost Electricity supply companies charge a set amoont per kWh for the energy they supply. For example, if the cost is 20p per hour (where ·p· stands or the local currency un,t): leaving a 2 kW heater on for 3 hours would require 6 kWh of energy, so the cost would be 6 x 20p. which is 120p. Related topics: SI unrts 1.2; energy 4 ,1; power 4-4; current 8.4 ; p.d. 8.5 191 0 Circuit essentials A p.d. (potential difference) is needed to make a current flow round a circuit. p.d. is measured in volts M and is more commonly called voltage. Current is measured in amperes (A). \ \'hen you plug a kettle into a main · socket, you ar~ connc ting it into a circuit, ru. hown below. The power comes from a generator in a po\\'er Lalion. The supply \·ohage de~nd on the country. For household circuit , ~ome countries tke a voltage in the range 220- 240 , others in the range I I 0- 130 V. Main cu1Tent i · alternating current (a.c.). It flow~ back\\'a.-cJ~ and rorwards, back\\ards and forwards ... 50 times per second, in soml! countrie . The mains fTequency b --o herl7. {H7). I n other countrie , the mains rn!quency is 60 H:t. A.c. is cm.ier lo generate thun onc-wa~ cJirecL current (d.c.) like that from a batten·. fusebox <:x orcu breaker box fuse g -.. a c. - ,,,su'ated \W~ ,,, cab!e neutral earth heating element (symbol) • This table lamp has an insulating body and does not need an earth wire. 192 Live (or line) ,virc Thi goes ahcrnateh ncgath e and po itive, making lhc current Uow back,,a,d~ and fo",a1'CI in the circuit. eutral (or cold) ,,vire Thi · complete · the circuit. Jn many sy ·tern ·, it is kept at 7cro \'oltage by the electdcity ~upplv company, Switch Thb i. fitted in the live wire. Jr would work equall~· well in the neutral, but" ire in the cable \\ould till be live with the witch OFF. Thb would be dangcrou if, for example, the cable wa accidcntall) cul. Fuse Thi i a thin piece o wire which O\\:rhcat~ and melt · if the cun~nt is loo high. Like the M\ iLch, it is placed in the li\'e wire, o[tcn as a ca,·tridgc. rr a fault de\'elops, and lhc current gets Loo high, the fuse 'blows' and break · the circuit befor-e the cable can o\·crhcat and catch fire. Man\' cir uit u e a circuit breaker (trip snitch) in lead ol a fu e ( ce pread 9.4 and next page). Earth (grounded) ,virc Thi i a afcty \\ire. It connect the n1ctal bod~ or the kettle to ca11h and ~top it bccmning live. For example, if lhc live \\ i1~ comes loose and touches the metal body, a current immediately now:-. to earth and blows Lhe ruse. This ml!ans Lhal thl! kettle i~ then safe to touch. ECTRICJTY Double insulation omc appliances radio~ ror c-<ampk do nor have an earth" ir1.:. Thi · i · be au e their o uter e a c i n,adc of p] .. tic rather than metal. The pla~tic ac ts a an extra layer or im,ulation aro und the wires. f or c, tra afcty, circuit ma, be fitted\\ ith a t)pc of breaker called a re idual current device (RCD ). T his con1pare the c un·ent · in the li\'e and ncuLra] \\ ires. I f rhc, a": not the same, then current must be llo\\ ing to ca11h - perhaps thro ugh omco nc to uc hing an e,po ·cd wit~. The RCD en e the diffcre nce and \\ itc hc off the tltT ~nt bcfo1 ' an, harm can be don e. P uas Plug arc a ate and in1plc \\ a\ o f conncc ti ng appliance to the main . On:r a d o7cn diffon~nl t)pc:,, or plug arc in use around the world. You earl see an example on the rig ht. few count1ic u c a three-pin plug with a fu c in idc. The lu c value i typicall) either 3 A or 13 A. This tells you the cun- "nt needed to blow th ' ru~e. It must be grelll er than the normal c urrent in the appliance, but llS d ose 10 ii a po~sible, o that the fu c will blow as ·oon ru, the c urrent get too hig h. For e -<a mple; • • Tf a kettle take · a CUtT "' nl of 10 A, the n a 13 A ru ·e is need ed. Ira TV takes a un·cn Lor 0.2 A , thi.:n a 3 A rUSC is needed. Thi.: TV ,, ould s till \\ 0 1·k "ith a J 3 A iusc. But ir a iaulL dc\'elo pcd, iL~ circuiLs n1ight overheat and c atch fire\\ itho ut the lu c blowing. .& This two-pin plug has earth connections in grooves at the edge. Electrica hazards Main d e tticit, can be dan gcro u . Here nt' omc of the ha7ard~: • Old, rn1\ cd \\iring. Broken s trands mean that a \\ire\,ill have a higher res istance at one point. \ Vhen a c urrent flows in it, Lhc heating cficct mav be enough to melt the in ulation and cau c a fire . • Long extension leads. These nia) O\·crhcat i r us •d \\ hen coiled up. The c un~ nt war~ms the" ire, but the heal has less al"\!a to escape from a tight bundle. • \\'ater in ·ockct~ o r plug~. \ Vatcr will conduc t a cun·cnt, o ff dc cLri al equipment g els \\Cl , there is a risk that someone might be electrocuted. • AccidcntaJlv c utting cable . \Vith la\\ nn1o wc1 and hcdgctrin1mc1 , a plug-in RCD can be used ro a\·oid the risk or electrocution. JI an acdck·nt happl.'ll'-, and ... oml.'Olll.' i, l.'k·u1 <><.:ull.·d, )<>ll mu~t '-\\ itd1 oll at till.· :--<><.:Kl.'l and pull out clw plug hl.•lorl.' giving :.un hdp. .& A plug-in RCD gives protectmn against the risk of electrocution. ® 1 What is a fuse. and hO\v does ,t work? 2 In a mains orcuit, why should the switch always be m the live wire rather than the neutral? 3 In mains appliances, \-\'hat Is the purpose of the earth wire? 4 Some countries use plugs with a fuse in. For each appliance on the right, deode whether its plug should be htted wi th a 3 A or a 13 A fuse. 5 Why should a 13 A fuse not be used for a TV taking a curren t of 0.2 A? 6 If an accident occurs and someone as electrocuted, what two tl mgs must you do before giving help? appliance current hairdryer 6A food mixer 2A iron 10 A lamp 0. 1 A Related topics: current and c1n:u1ts 8-4; voltage (p.d.) 8.5; resistance and heating effect 8.6 ; power 8.12; h<M a circuit breaker wori<s 9.4; generators 9.9 ; electri<:ity supply system 9.12 193 Further questions 1 a \Vhen a balloon is rublxcl in your hair, lhl: balloon bec.:omt:S negatively c.:harg~d. i. Explajn ho\\ the balloon becomes ncgali\'ch charged. 121 Lat~ what ~·ou know about the iz ~ and ii sign of the charge lelt on ~ou1· hair. f21 The negati\'dy charged balloon is brought up lo the surface or a ceiling. The balloon ·ticks to th~ c.:eiling. Explain ho\\ and wh) thb happen~. (3) 2 Read the following pa sage carefully before answering the questions. Spraying crops with i11sec1icide. . has lu:con,e 111ore effic:ie111. A po11able high ,,oftage ge1u!11.llor gfres the drops of liquid insecticide ,i snlllll positi\'e d,a,~e. Thfa makes 11,e liquid b,eak up i1110 111<1ller drop, awl causes the spra_v to become {iuer and spread out more. The plants, wlziclz are all rctiso11al1/e. co11d11ctor~, are i11 conlllcl The circuit ·how a batten connected lo a switch and three identical lamps. L 1, L2 and L.1. a Cop) the diagram and acid: an arrow to show the conventional current direction in the circuit ,,,:hen the ·witch i~ do ·cd [ IJ ii a \Oltmctcr V, to n1ca urc the \'Oltagc aero. s L1 [ 11 iii a S\\ itch, labelled , that controls Ll onl~. [I] b talc and explain what cffcct adcling anothe1· c-cll to the ballet, would have on thi: ]amps in the circuit. (2) E 4 The circuit diagram how a batten connected to fi,·c lan1p.. The currcnl in lamp~ A and B are shown. ri 3 amperes A E 8 2 amperes wi//1 J/w earth A.\ the d,·oplets of spray get near tht! pla11ls, the plants tlze111selw!s beco111e slight(, clwtged mu/ llltract tile dro/)/ets. a i Explajn \\ h) the po i li\'c charge on the droplcl make the ~pray spread OU t. 11 ii Late what charge appears on the plants as Lhe droplets con1e near LO them. fl] E b Druw a cliagram co show the ek-ct1·k fidcl pall~rn around one ot the droplels (as ·un1c it i ~phctical and that there arc no other droplet~ ncarhy). (21 c How would the field be different if the dr·oplel had a negath·c rather than posiCi\'e r [ ll charge? 3 battery switch 1 --~✓ --- C D \\'tile do,\n the current tlowing in a lamp C, b lamp E . [ 11 H ow much energy is transfc1Te<l by a battery of e.m.f. 4.5 V when l .0 C of charge passc tlH"Ough il? [ I] b How n1uch power is tran~fctTed bv a batten of e.m.f. 4.5 V when a current of I .0 A i pm,sing through it? [ ll 6 The diagram shows a circ.:uil which contains l\\'O re~islUt'S. 4U 2U --------1,1 1-1 1.2 V 194 [J] © OUP· this may be reproduced fot class use solely fo, the purchaset"s lnst1tute I alculatc a the total 1\.: i~tance of the two re i~to1 in c,ic-,, (tl) b the current flowing in the cdl. (A) c the current Oowing in the 4 n ,-esistm~ ( ) d 1hc n.~ading of th e ,·oltn1cccr, (V) e 1hc po,,cr lransfon~<l b) 1hc 4 n l1J I 1I r1l [ 1l 7 A ~n1all electric hairdrycr ha~ an outer case made ol plo~tic. The follo\\ ing infonnation is printed on the case: a 230 a.c. onl\ 50 H~ E,plain the meaning of these tcm1s: i a.c. onlv ii -o H / akulalc Lhc maximum cun-cnt \\hic.:h the generator i de~igned Lo supph. [ 2] b i Cakulalc thl' po,\CI needed\\ hen all the lamp at~ turrnxJ on al the san1e time. ii E,plain \\'ll\ this generator is suitable fm supph ing th1.: powc1· n .•quin.:d but ,,ould not be suitable i£ a1l the lamps \\ ere exchanged for I 00 \ V lamp . ( 4] c \\'rite down l\\ o rea"°n" ,, h, all the lam~ a, 'connected in parallel rather than in ~tic,. In each an,\\ !I', )OU should 1 •fer to hoth tYJ)\:!-> of circuit. [4 l Calculate l he resistance of the filament of l'ach 2 \ V lamp. [ 41 e The figurl' bdow :-ihows the cun~nt output ot the gcnl·t-ator when it i uppl •ing all 30 of the 2 \ \' lamp~. a [ l1 ·oo \ V I [11 [ l1 b The hairtlnl.'r doc:,, not ha, e an earth" in:. ln-;tead, it i double insulated. Explain whal thi. llll»an.-,. [ 2] c \\'hat current doc-, the hairdncr take? ( 21 d The hair-clr\cr is protected b, its o,, n lus1.:. \ \'hat is the PlffJX)'iC ot the fuse? 1l ii Ci,cn a choice of a 3 A or a 13 A fuse r tor the haird1'_\c1; ,, hich ,,ould ~ou M.'k"Cl, and wh,? [21 e * If the hairdryer ,,ere u ed in a countn whcr' the main~ ,oltngc ,,a~ onh 110 V, what dillc1-cnce ,,ould this make, and why? current ootput ~ (\ (\ 6V iM(r4°U6 ume1s Calculaac Lhe lrL'qttcnc, of the supply I rom the gcnerator. E ii Cop, the diagran1 and sketch another graph to ~how the approximate cun 'nt output o1 the generator \\h •n 1- lamps are 1·cmovcd fron1 th1.:i1- fittings. [41 9 A student in,csligalcs how lhc cun-cnt in a lamp ,arie \\ ith the , ·ohage (p.d.) across iL he u c~ the circuit ho\\ n bclo\\. i* r3l 8 A small generator i~ labdled a~ ha\'ing ~01 output ol 2 k\\', 230 V a.c. (al con tant ir~'(luenc, ). It i used to pt o, idc emergenc \ lighting fora large building in thee,··nt ol a bn:akdown of the mains suppl\'. Th1.: cin;uit is shown below. .___ _. V ,___...,. a Three of the con1poncnts arc lab ·lied, A, V, and B. \ \'rite clown ,, hat each one.: i-,. [ 31 b Describe ho,, I he student should catT~ our 1hc c,pcr-imcnl. [31 From her rcsulcs, the student plots this Thcr • a,~ 30 ligh1 fittings on the circuit, each ,, ith a 230 V, 28 \ \' halogen lamp. g1·aph: 195 d \ \'hat i the rcsi, tancc of the lan1p when th ~ voltag > aero ~ it is 2.0 V? f 21 e \\'hat is the resistance of the lamp when the voltage across it is 6.0 V? [ 2] f \\'hat happen to the re istancc of the lamp a.s the ,olcagc aero · it i increa cd? [ 1) 12 10 4 2 0 0.2 04 06 08 I0 current/ A c \\'hat i the cun·cnt when the \'Oltagc aero the lan1p i 2.0 V? [ 1] 10 A 1nall clccllic heat ·r take a power ol 60 \ V rrom a 12 V upph. a \ \'hat is the CUITCnt in the heater? r21 b \\'hat is the resistance of the heater? [21 (E) c How much charge (in ) passL~ through the heater in 20 seconds? [2] d How much cner"&) (in J) i tran lcrrcd by the heater in 20 ccond ? [2] T Use the list below when you revise for your IGCSE examination. The spread number, in brackets, tells you where to find more information. D The equation Jinking power. p.d. (\·ohagc), and check list Core Level D Two typ~ or electdc charge and the attraction" D □ D D □ □ □ D D □ D □ □ □ D D □ □ D and rcpul~iom. bct\\ecn them. ( . I) Charging b\ friction: adding or rcrnoving electron~. (8.1) Ekctrical conductors and insulators. (8.1) \\'h) metal~ arc good conductors, \\ hile most othc1materials are in~ulator.-.. (8.1) D '"Leet ing charge. ( .2) Cun-cnt a~ a no\\ of charge. ( .4) Cun'\.'nt in a metal i a 0o" of electron-,. (8.4) The ampcn.:. unit of curT~nt; mca ur;ng cun-cnt "ith an ammeter. (8.4) !-ting circuit diagram" and symbol" (e~cluding tht! diode). ( .4. 8.5 and page 321) ... ing s,, itchc • r~i..,to, , thcrmiston,. LOR , ~nd other component . (8.4. 8.6. and 8.9) Ho\\ the cum..-nt i~ thl' ~amc at all points round a st!rie~ circuit. (8.4 and .9) The volt, unit or p.d. and e.m.f.; measuring p.d. \dth a \Oltmctc1-: ( .5) O .. fining p.d. and c.m. f. ( . -) The ohm, unit or r~ i lance. ( .6) The equation linking re i lance, p.d .• and cmTl!nt. ( .6 and 8.7) Factor.-. aflecting the n.!,istance of a wire. ( .6) Ho\\ cun ~nt i\ !-.plit in a parallel circuit. ( .9) Ad\antagc or conn cting lamp in parallel. ( .9) Cakul:\ling the combined ri: i tancc r~ i tor in erie~. (8.10) The combined resi,tance of two r~i~tors in parallel i" le!-.!-. than that o1 either r~i,tor b, it ~c1r. (8.10) or □ □ □ D □ □ current. (8. 12) The equation linking energy, p.d., cun-cnt. and time. (8. 12) The kilowat t-hom: ( .12) The difference bct,,ccn a.c. and d .c. ( .13) Thekc) featuresofamain,circuit. ( .13) Using fuM!~ and circuit breakers. (8.13) The ha,1a1-ds o( main-. electdcit~; the importance of u ingea11hingordoublc in ulation. ( .13) Extended Level As ror 0l'C lc\'CI. plu the follO\\ ing: □ \ \'h\ charged obj ~l altract uncharg~d one . (8.2) D The coulomb, unjt of charg~. (8.2) D \ \'hat an electric fidd i . (8.3) □ Electric field is a \'Cctor; the direction of an electdc field. ( .3) □ Elcctdc fields pattcn1 around a point ch~u-gc, a charged conducting -.phcrc, 3nd bcl\, n two oppo itch •charg<..xl pamlld plat~ . (8.3) D The equation 1inking curr~nt. charge, and time. (8.4) □ Electron rtow and con,·cntional cun"Cnt. ( .4) □ ·1he rule linking th'" p.d. round a cir uil. ( .5 and .9) D □ □ D □ □ current•p.d. characteristic..,_ (gr..iphs) for a metal \\ ire al constant temperntur~. a filament as it heal up, and a diode. (8.7) The relation"hip b 'L\\ een the ~istancc, length, and cro ~-:..cctional a, "a of a \\ ire. (8. ) The tulc for cu,i-cnt in a parallel circuit. (8.9) Calcu]at ing the combined n: i-,tancc of two rc~i~to~ in parallel. (8.10) Diode~ and LED!-.. (8.1 I) The action of a potential dh ider. ( . 11) Computer model of the magnetic field in~id,. the doughnut- hapcd chan1bcr o a nuclear tu ion reactoa: Lik the Sun, fusion rL:acto1 1·eleasc energy b> ~n1ashing hydrogen aton1, together to fo1111 hcliu1n. One da,, the~ ma~, pro, idc the energy to run po\ver stations on Earth. In th rcacto1~ the 111agnctic field is u ·ed lo trap the charged particles iron1 hydrogen at a l "mpcraturc of over 100 n1illion °C. chapter 9 197 Magnetic poles If a . mall har~magnet b. dipped into iron fiJings, the riling are attract •d to iL, ends, as sho,\11 in the photograph on the oppo~ite page. The magnetic for<.:c sc~n1s co come from two poinc.s, called the poles of the mag net North PO'e The Eat1 h exert forces on the poles of a magnet. If a bar magne t i~ ~u~pcnclcd as on the left. it~,\ ings ruund unti] it lies roug h!~ north- Mluth. This effec t is u~c<l to name the two poles of a mag ner. These an: calh:d : • the north-seeking pole (or r pole tor hurt) • the south-seeking pole (or S pole tor hor1). 0 Propertiesofmagnets A magnet: • Has a magnetic field around it (see the next spread). • • Has l\vo opposite poles (N and S) which exert forces on other magnets. like poles repel; unlike poles attract Wil attract magnetic materials by inducing magnetism in them. In some materials (e.g steel) the magnetism is permanent. In others (e.g. ·ron) it is temporary. • Will exert little or no force on a non-magnetic material. If you bring the ends ol two !->imilar har mag net. togethe r, there b a force betw~n the pole · a~ shown bdow: Like pole-., 1~pel: unlike pole, atlract. The clo~~r the pole,, the greater the lmcc between them. mag nct,c po!es ~ repulson attraction Induced magnetism Matclial 'uch m, iron and ·tcel are attracted to magnN · bccau~ the, them~e-tve , becom "' magnetized,, hen then? j a magnel ncarbv. The magnet induces magnetism in them, a !->h0\\11 hclow. Tn each ca"e, the induced pole nean: t the magnet b the oppo ·ire of the pole at l he ~nd o ft h~ maanet. The allr-4ction ~l\H.>cn unlike pole:-. hole.I:,, each piece of metal Lo the magm:t. The skd a nd the iro n behave diifrrcn,ly \\ hen pulled right awa~ from the rnag net. The ·ted keep · ome ot it induced magncti m and become a permanent magnet. Ilo,,ever, the iron lo c \'irtually all of it induced magneti m . It was only a ten1porary n1agnet. magnet poles induced in ron dnd steel uon iron loses rnagnetJsm ~ eel permanently magnetized s N MAGNETS A D CURRENTS Making a magnet A piece of Mccl b >comc5 permanent I\' n1agnctized when placed near a magnet, but it~ magncti~m is usually weak. It can be magnctil'.cd more str·ongly b\' ~troking it with one end of a magnet, as on the righl. Ho,,c,·cr, the moM dTcclivc method of magncti1ing il is to place it in a long coil of wire and pas a large, direct (one-way) current in the coil. The current ha a magnetic dk-ct which magncti_1.c · the tt--cl. ~ ._.,.,de sweep \ away from steel N \ind JCed Magnetic and non-magnetic materials A n1agnetic material i - one which which can be n1agncti2cd and i attracted to magnet ·. All tronglv magnetic mat ~rial contain iron, nickel, or cobalt. For example, steel b mainly iron. trongh magnetic metals like this an! called ferromagnetics. They m·c clesc1ibcd as/wrd or· so/i depending on how well they keep their magnetism when magnetized: Hard magnetic materials ~uch as sled, and alloy~ ca1k"'<.I Akomax and Magnadur, arc difficult to magneti ✓e but <lo not readily lo.sc their magnetism. They arc used [or permanent magnets. Soft n1agnetic materials uch a iron and ~1un1ctal arc rclativch ea y to magnetize, but their magneti m i onlv te111JX)rary. Thcv arc u ed in the core~ of elcctmmagncts and tram,formt:r~ because their magnetic effect can be 'switchc<l' on or off or rc,·erscd casil). poles • Magnetizing a piece of steel by stroking it with a magnet. Ferrous and non-ferrous Iron and alloys (mixtures) containing iron are called ferrous metals (ferrum is Latin for iron). Aluminium. copper, and the other non-magnetic metals are 0 non-ferrous 'on-magnetic materials include metal · ~uch a bra s, copper, 1:inc, tin, and aluminium, a well a non-metal~. Where magnetism comes from* In an atom, tin\' elecuical particle called electron nlO\'C around a central nudctL-.. Each electron ha" a n1agnetic effect ~ it ·pin and orbil.~ the nucleu . In man) type!\ of atom, the rnagnctic effect~ or the dcclrons caned, but in omc the~ <lo not, so each aLom act · as a tiny magnet. l n an unmagneLiLcd material, the atomic magnet point in randon1 directions. But a ~ the material bccon1e magncti1cd, n1orc and more of it r\Lomic magnet · line up with each other. Together, billion~ of tiny atomic magnets act a~ one big magneL. If a magnet i • hmnmcrcd, its atomic n1agnct arc tlu-0\\11 out o( line: it lx"Comc demagnetized. Heating it to a high tcmpcratw'C ha the amc ellect. • Magnetic materials are attracted to magnets and can be made ,nto magnets. ® 1 What is meant by the N pole of a magnet? 2 Magnetic materials are sometimes described as hard or soft. a What is the difference beti.veeo the t'-NO type5? b Grve one example of each type. 3 Name three ferromag~tic metals. 4 Name three non-magnetic metals. 5 ll)e d agram on the right shows three metal bars. When different ends are brought together, it is found that A and B attract, A and C attract, but A and D repel. Decide whether each oft e bars ,s a permanent rnagnet or not. A • D bar C bor 2 bar3 R@lated top1cs: atoms and electrons 8.1; the Earth's magneUsm 9.2~electromagnets 9,4: transformers 9.10-9. 11 199 l n the photogr<lph below, iron filings ha,·e been sp1inkle<l on paper o\'er a bar magnet. The fHing~ have become tiny magnet ·. pulle<l into po i tion bv force ~ from the pok of the rnagncl. icntificall\ ~peaking, there i a magnetic field around the- magnet, and thi exert force~ on magnetic matedal. in il. Magnetic field patterns Magnetic fields can be invc~tigated u~ing a small compass. The 'needle' i ~a tinv n1agnct which j ~ free ro tu1 non it~ ~pindlc. \ hen near a magnet, the needle i turned by force between it pole and the poles of the magnet. The needle come to re t . o that the turning etlect i 7ero. dots on paper The diagran1 on the- left ho,, how a mall compa~ can be used to plot the field amund a bar magnet. tat1ing ,\ith the comprus near one end ol the magnet, the needle po ition i marked u ing two dot . Then the compa. is rno,·ed so ahat the nei.:dle lines up with the pre,ious dot... and SC> on. \Vhen the dots ar"l! joined up, the result is a n1agnctic field line. More lines can be drawn b~ star1ing wilh the compa.~ in <liffel"l!nl po ·itjon . 0 Magnet essentials A mag et has a north-seekilg (N) pote at one end and a Jn ahc diagram abcl\'C, a sdcction of field lines has been used 10 show the n1agnc1ic f icld around a bar magnet • The field line · run Crom the . pole to the pole of Lhe magnet. The field direction shown bv an an'()\\ lwad I i defint.-cl a~ the direction in which the lorcc on a , pole would act. It i the direc tion in which the end of a corn pa ~ needle \\ ould point. E • The magnetic field is tronge-,t where the field line~ are closest together. I south-seeking (S) pole at the other. When two magnets are • T brought together: like poles repel. unlike poles attract. 200 If t\\O magnets arc placed near each other; their n1agnetic fields combine to produce a ingle field. Two example are hown al the top of the next page. At the neutral point, the field from one magnel exactly cancel the field from Lhe othl!r, so the magnetic force on anything al this pe>int is :,,cro. MAGNETS A D CURRENTS ◄ Between magnets with uni' e poles facing, the combined field is almost unif°'m (even) in strength. However. between like poles, the<e is a neutral point where the combined f1eld strength is zero. point Magnetic screening Some electronic equ.pment is easiy upset by magnetic fields from nearby generators. motOC's, transformers. the Ear th. The equi)mc-nt can be screened (shielded) by endosing 1t in a layer of a soft magnetic material. such as iron nickel. This red ects the f efd so that it does not pass through the equipment. The Earth's magnetic field* The Ea11h ha a mag netic field . L o o ne i sun.· o f it cau e, altho ug h it i tho ug ht to come fro m elec ttic currenl generated in the Earth' core . The field i:-, rather like that ,iround a la r-gc, but VCf> weak, bar magne t. °' \cViLh no oLhcr magnets near it, a compass needle lines up with the Earth's mag netic fidc.l. The end of the nt.-cdlt: points no r1h. But an l pole is ah\a\ attracted to an pole. So it lollow that the Earth' n,agnctic pole mu t be in the no11h! It lie.':> under a point in Canada called magnetic north. °' Magnetic north is o, e r 1200 km away from the Earth's geographic orth Pole. This is because the Ea11h's mag netic axis is noc quire in line with its nor1h south axis ol ro tation. A The Earth behaves as if it has a large but very weak bar magnet ins de it. 0 A A compass is of no use in polar regions because the Earth's magnetic f eld lines are vertical. ® 1 In the diagrams on the right, the same compass is being usN.f in both cases. a Copy diagram A. Label the N and S ends o f the compass needle. b Copy diagram B. Mark in t he poles of the magnet to show which is N and which is S. Then draw an arrowhead oo the field hne to show 11$ direction. G In diagram B. at which posi tion. X or Y, would you expect the magnetic field to be the strooger? y north t maqn~t A 8 R@Lated topics: magnetic poles and the Earth·s magnetic effect 9.1 201 Magnet essentials 0 Like poles repel; un h e pofes attract. Magnetic field lines shOVII the direction of the force oo a N pole. Magnetic field around a wire ff an electric current is pa~se<l through a wi1·e, us ~hown below lcrt. a weak magnetic field is produced. The field has these features: • the magnetic field line · arl' drdcs (E) • the field i ~trongc..: ·t clo~c to the\\ ire increa-,ing the cull'cnl increa e the t1~ngth of the field. 1 • cu11en1 , conventional) + cur,cnt (convcn•1ona1) \ 0 A rule for field direction The direction of the magnetic field produced Current essentials In a ore t the current IS a flO\V of electrons: tiny partides which come from atoms. by a cun\:nl is g in..n by the right-hand grip rule sho\\n above right. i magine gripping the wire with your light hand ·o that you1· thumb point in the conventional current direction. Your finger then point in the mne direction a the field line . The current arrCMfS rovn on c·raut daagrams run from to - . This is the conventional Magnetic fields trom coils current direction. Electrons, be ng negat1va,, charged, flow the other way. A cun-ent produces a stronger n1agnctk ricl<l if the win: it flows in is wound into a coil. ~rhc diagrams bdo\\ ·how the magnetic field paucrn · produced by t\\O currcnt-can~ingcoi]l). One b jul)t a inglc turn o f \\h\"!. The other i a long coil "ith many turn . A long coil i called a solenoid. cod (single turn) • --5- - - . - ____, + 202 I- -) MAGNETS A D CURRENTS The mag netic field produced b~ a curn:nt-can-ying coil has thc~e foatun.-s: • the fidd i~ s imilar to that fro m a bar mag net , and there arc mag netic pole · at the end o l the coil incrca ing the cun · nt incre~c the trcng th of the field increru.ing th e nun1be r o f turns o n th .. coil incre ase the Mrcng th E • of the field . A rule for poles* To work o ut which wa\' round the pole · m~. yo u can u e ano thc1· right-hand grip rule, as sho,vn o n the rig ht. Imagine gripping the coil with \'Our ri ght hand so that , our ~ngc~ point in the con,·cnlional curn:nl <lin..-ctio n. Your thumb then po ints toward~ the~ pok or Lhc coil. * :1agncL., arc made - and dc1nagncti1ed - u ing coil~ a~ ·hown belo,,. ln video 1~corde1 and hard dti\'c , tin'\. coil 31~ used to put magnetic pattern on a di · ( e next spn.~d). The pattern to re pictur~. ~ und , and data. Making a magnet Above, a steel bar has been placed in a solenoid. When a current is passed through the solenoid, the steel becomes magnetized and makes the magnetic field much stronger than before. And when the current is switched off, the steel stays magnetized. Nearly all permanent magnets are made in this way. ......______. + 11 i- -------,, Right-hand grip rule for poles Demagnetizing a magnet Above, a magnet is slowly being pulled out of a solenoid through which an alternating current is passing. Alternating current (a.c.) f ows backwards, forwards, backwards, forwa rds... and so on. It produces a magnetic field which changes direction very rapidly and throws the atoms m the magnet out of line. ® 1 Tihe coil in d,agram A is producing a magnetic field. a Draw a diagram to show the shape of the magnetic field around the coil. 0, Give two ways m which the strength of the field could be increased. G How could the direction o f the field be reversed? 2 Redraw d1agam 8 to show which way the compass needles point \tJien a current flows in the wire. (Assume that the black end of eadl compa~ neecle 1s a N po~. the conven tional current directlOn is awirf from you, into the paper, and that t e only magnetic field is that due to the current.) A B 0 ©oe ;@ Wire (end v1evv) R~lated topics: current 1n a circuit 8.4; alternating current 8.12; magnetic poles 9.1; magnetic fields 9 .2;magnetic storage 9.4 203 ball£!')' ~ I .. I ' COi .' core nlikc an ordinary magncL, an electromagnet can be s,,icc:hcd on and oil. In a sjmplc clcct1·omag11ct, a coil, con ·i ·ting of ·c\'cral hundn.-d turn o in ulatcd copper wire. i ~ wound round a core, u uallv ot iron or ~1umetal. \¥hen a CUtTent flow in the coil, it produce a magnetic field. This magncti7.e the core, creating n magnetic field about n thou and time · tmngcr than the coil by Hsd I. \ Vith an iron or· Mumctal core, the magnelism is onl) temporary. and is lo~L a~ !\OOn as Lhc c:u,,-cnL in the coil is S\\ itched olf. kcl would not be suitable as a core because it would become pcrmancnll) magnclizcd. E The ·u-ength of the magnetic field i · incre-a cd b): • A simpfe efectromagnet • • increa ing the cun·cnt increu ·ing the num her of turns in the coil. Reversing the cu1Tent n:\·crse · Lhc dirccLion of the n1agnl:lic field. The follo\\ing all rnakc UM~ of elc t1omagnct . The magnetic relay 0 A magnetic rela) i a wilch operated b, an electromagnet. \Vith a relay. a . mall witch with thin wire can be u ed to turn on the cun ""nt in a much more powerful circuit - lore~ample, one ,dth a large electric moto1· in it: iron armawre Magnetic essentials A hard magnetic material (for example, steeO is one which, when magnetized, does not readily lose its magnetism. pov,'t'r si.,pplf for motor 5 A soft magnetic material (for example, iron) quickly loses its magnetism when t e magnetizing field is removed. e-Jectro- magne1 contacts C outputmcu:t nput ClfCUlt \Vhcn the S\\ itch in Lhc input circuit i · dosed, a current flows in the clcctromagncl. Thi · pulls Lhl' iron an,,atun: to,,.:ard it, \\hich do~~ the contact a re uh, a cuti'ent tlo\\ in the 1l"1ot01: The rela) abo\ L' is of the 'normally open' l) pL': when the input ·witch j 01v, the output drcuil i al o OFF. A 'normally clo ~cd' •~la) work 1hc oppo ite \\:.\\: when the input witch is on, the output circuit i o,. In practice. mo t re)ay~ are made o rhat thev can be connected eitherwa). • With a relay. a small switch can be used to turn on a powerful starter motor. c0tl switch (norma o~n) Normally open relay (symbol) 204 coi switch (norma'.,y closed) Normally closed relay (symbol) MAGNETS A D CURRENTS The circuit breaker reset b\Jtton A circuit breaker i an automatic witch whic h cut~ off the c un- •nt in a circuit if this rises abo\'e a spc ified value. It has the s ame efTe ta~ a fuse but, unlike a fuse, can be n.!SL'l (turned o, again ) afLCr it has tripped ( turned OFF). no,, · o In the t) pc hown on the 1ig ht, the ctu,~nt in t,, contac t and also in an clccu n1agnct. If the cun'Cnt get too hi gh, the pull ol the clcctron1agnct b !Comes tro ng enoug h to 1 --h:asc the iron catch , o the contact~ open and s to p the cun\!nt. Pn:ssing the reset button doses the contacts again. Magnetic storage* omc re ording. tudios UM-" magnetic ta pe on n!cls or in cw scltcs for n.-cortling sound,. The tape consists of a long, thin pla.\tic strip, c oak-<l with a layer of iron oxjdc or ·in1ilar matcJial.1\lagncticaUy, iron oxide i · bct\\L~n ·o lt and hard. Once rnagncti_1.ed it keeps it n1agncti m , but i • •~lath cl) ea ) to demagnetize, ready tor another recording. The diagram belo,, ho,, a implc ,. t 'm fort • o n.ling M>und on tape. The hard d1i,·c in a comput "r also ~,on.:~ data a~ a pattern of , ·ar~ing m agncti~m. In both cxnn1pl !'S, an de tronmg ncl crcat~ the varying magnetic field needed for re on.ling. Latc1~ a playback head can read the pattern to gi,\! a nrrying cun1:nt. curierH electr~ magnet A Circuit breaker current vaned by sound electromagnet in record:.ng head tape magnetized varying magnetrSm along tape A Recording on magnetk tape The incoming sound waves are used to vary the current in a tiny electromagnet in the recording head. As the tape moves past the head, a track of varying magnetism 1s created along the tape. ® 1 An electromagnet has a core. a What ,s the purpose of the core? b Why 1s iron a better material for the core than steel? G Write down two ways of increasing the strength of the magnetic field from an electromagnet. 2 In the diagram on tl e opposi te page. an electric motor is controlled by a S\'Vltch connected to a relay. a What is the advan tage of using a relay. rather than a sw-.tch m the motor circui t itself? b Why does tl e motor star t when switch 5 1s closed? A Computer hard drive The rec0<cf:ng head is at the end of the arm. It contalfls a tiny electromagnet v-A1ich is used to create tracks of var;;ng magnetJsm on a spinning d,sc. The disc is made of aluminium°' glass. and is coated with a layer of magnetic material similar to that on a tape. 3 The diagram at the top of the page shO'.vs a cucuit breaker. a What is the purpose of the circuit breaker? C, How do you think the perforr:nance of the circuit breaker would be affected 1f the coil of t he electromagnet had more turns? 4* Sounds can be recorded on tape. a Why is an electromagnet needed for this? b Why must the coating on the tape be between soft and hard magnetically? Related topics: using circuit breakers 8 .13; magneUc materials 9 .1; fields from coils 9.3 205 0 Magnet essentials The N and S poles of one magnet exert forces on those of another: like poles repel, unlike poles attract The magnetic field around a magnet ea n be rep,esented by field liles. These show the direction ·n which the f°'ce on an N pole would act. In the c,pctimcnt hown below. a length ot copp('r\, ire ha been placed in a magnetic field. Copp ~r i. non-magnetic, so it is feel no lorce trom lhc n,agncl. Howc\·cr, with a cun-ent pa sing thr-ough it, there i~ a force on the \\ire. The force arises becm.L~c the current produces its O\\TI magnetic field "hich acLs on Lhe poles of the n1agncL Jn this case, the forte on the win: i..,.. upward ( ·ce bo:,. ~IO\\ left). ll would be do\\ n,\artl · if either the magnetic field or Lhc cun-cnl \\'ere 1"C'\'C1 e<l. \\'hichl'ver wa~ the cxpctimenr b done, the\\ ire mo\'I..: ac,o~~ the field. It i 11ot attracted to either pole. The force is increased if: • the curri;:nl is incrctL,cd • a stronger magnet is used • the length o[ win: in the field is incn:a ed. umb Of fOfce TH rust leh hand .A Fleming's left-hand rule Field and force Fleming's Left-hand rule In the above e~pe1iment, the direction of lhe lorce cnn be predicted u~ing Fleming's left-hand rule, as illus1rated above right. ff you hold Lhe thumb and fin.L rwo fingers of your lcfr hand al right angle"-, and poinc the fingers as sho,, n, Lhe thumb gi,·es the din:ction of the force. I n applying Lhe rule, it b important lo remember how the fidd and current direct,on out of paper By itself, the current in a straig1t wire produces a circular magnetic field pattern. However, when the wire is between the poles of a magnet. the combfled field 1s as abole. In situations like this. the field lines tend to strai~ten So, m this case. the wire gets pushed upv.,ards. urrent directions an: defined: • The fidd direction is from the [ pole of a magneL to the pole. • The cul1'cnt direction i · frorn rhc po ·iti\'c h -) Lc1n1inal of a batter~ ruund to the negati\'e ( ). Thi i called the com·(.•11aoual cu1Tenl dil . .<.'lion. Flcming's lelt-hand rule only applies if the cul7'ent and field direction are at 1;ght angle~. If thcv arc at some other angle, there is still a force, but irs direction i~ n1ore difficult to predicl. If the current and field arc in the ~cmw di.-~ction, there is ,w force. If a hi:nm ol chargl.'d pm tidt...•.., hlll.: h a ... d1...·<.: ln>ns) pa... sc.., through a magnl.'l ic fidd, there is a force on i l, j u ... l as lor a cu1-re11L i 11 a wire: 'l"l.' sprca<l I 0 .2. MAGNETS A D CURRENTS The moving-coil loudspeaker Mo t loud~pcake1 arc of Lhc n1oving-coil tvp ~ hown on the ,;ght. The cylindrical magne t produces a ~tro ng radia l (\po ke.like') magnc1ic fi eld a t right ang le~ to the \\ ire in the coil. The coil is free to mon .• backward s and fo rwa rd-; and i~ attac hed to a ·tiff paper or pla~ tic cone. The loucbpcakl'r b. connected lo an a m plifier which giv~ · out altcrnali ng c u1Tcnt. Thi now backward~. tor ward , backwar~... a nd o on, cau ing a torce on the coil which i • al~ bnckward , fo rward ·, backward .... Ao.., a result, 1hc cont.! \ ·ibra tcs and gi\·es out ~ou nd wa\·cs. The sound you hc."ar depends on ho\\ the a mplifier ma k<..--s the cun ~ nt ahcrna le. Turning effect on a coil The coil below lies between the poles of a m agnet. The cun-cnt no ws in o p po itc di rect io n~ alo ng the two ·idL~ of the coil. o, acco rdi ng to Fle1n ing' lefl-ha nd rule, one ide i • pu ·hed up a nd the o ther ide b pu hcd dowu. In other \\ ord , th c1 ' i a turning c ilect on the coil. \ Vith m or' ttl171S on the coil, the turn ing cllect i incrca~t-xl. A Moving-coil loudspeaker The me ter in the pho tograph us<..>s the abo\ ·c principle. It~ po inLCr is a ttac hed lo a <.:oil in Lhc field o f a mag nc l. The hig he r the cun·enL in Lhc mctct~ Lhe lu r the r the <.:oil turn!) again ·t the !)pri ng · ho lding it, and the fur the r the po imcr mo ,e!, aJo ng the ·cale. A Moving-coil meter ® 1 Tihere is a force on the wire in the diagram on the right. a Grve two \\ays in which the force could be increased. C, Use Flerning's left-hand rule to \IVOrk out the direction of the force. c Grve two 'Aay5 in which the direction of the force could be reversed. Explain why the cone of a loudspeaker vibrates when alternating current passes through its coll. 3 The d agram above shows a current-<anying cod in a magnetic field. What difference would ,t make if a there v--ere more turns of wire in the cotl b the direction of the current were reversed? I 0 R@lated topics: sound waves 6 .3 ; cur,ent 1n a circuit 8-4 ; magnetic fields 9.~ field around a wtre 9-3; rorce on particle beam 10.2 207 Turning effect on a coil 0 If a coil is calT) ing a cun-cnt in a magm.:tic fiel<l, as un the left. lhe forces on it produce a tur~ning cl feet. Many electric motors use this principle. A simple d.c. motor magnet- - - - - - - When a current flO'Ns in this coil, there is an upNard force on one side and a downward force on the other. The direction of each force is giviln by Fleming·s left-hand rule, explained on the previous spread. The action of the commutator 0 coll---- commutator- - - (split ong) battery bru~es The diagram above how a implc electric motot: It nm on direct current (d.c.), the 'one-way' current that llows from a batten. When the coil is neartj vertical, the forces cannot turn it much further... ' ...but when the coi I overshoots the vertical, the commutator changes the direction of the current in it. so the forces change direction and keep the coil turning. E The coil is made of insulated copper\\ in~. It i.i,; fn.-c to rotate bt:t\\\!l'n the poles of the magnet. The commutator. or spli1-dng, i~ fixed to thl' coil an<l roLatc ,, ith it. it acLion is c~plainl'<l below and in the <liagrrnn~ on the lch. The brushes arc two contact ,, hich I ub again t the comnu1tator and keep the coil connected to the batter;. The, arc lk ualh n1ade of carbon. \ \lhen the coil is hori.1.ontal. the lorct!s are f urthc-.st apa,;_ and ha\\! th •ir maximum turning l!ffcct (k"\e1c1gc) on the coil. \ ViLh no change lo lhe fon.:cs, Lhe coi l woul<l eventually come to rest in Lhc ,e1tica1 posiLion. H owt.'\\.'.1~ a~ Lhe coil o\'cr ·hoot · the h .·11ical, the cominutator change the <lir'l."Ction of the cun-cnt in it. So the forces change <lin~ction and pw,h the coil further round until it i again \·e rtical. .. and~ on. In this wa,·, the coil keep rotating clock\,isc, hulfa turn at a time. Tf eitherthe batteryo1· thepo)e~of the magncl were the other way round, th • coil would rotute antido k\\ise. The turning elfect on the coil can b"' incre ed by: • increa~i ng the CUtTt!nt • w-,ing a stronger magnet • incr'\!a~ing the number of turn" on the coi] • • inc1'\!a ing the area of Lhc coil. (A longer coil mean higher forces bccau ·c there j a greater length ol wire in Lhc magnetic field;.._, \\ ider coil gi\'e the orce~ more leverage.) MAGNETS A D CURRENTS Practical motors* The implc m o to r o n the o pposite page produce · a low turning e f~•ct a nd is jc,·k) in acti o n, cspc.--cially at low s peeds. Prac tical motm·s g iv1.: a much better perfo rma nce ror these reasons: • c\'era l coils arl! us ed , ea c h set a l a differe nt ang le and each wi t h its O\\ n pa ir o f coIn mutator eg mc nts (piece ·). as s hown o n the righL. The re uh is a grea ter tu111ing eflecLand 1nooth cr n mning. • The coil conta in hund red of tu r n o f "ire and are wound on a core call~~ a n armature, w hic h conta in it-on . The a n11atu rc bccon1 ~ m agne ti zed a nd increases lhe streng th of th e magn etic field. • The pole pieces an! cun ·<--.od to cn:a tc a radial ('spoke-like') magnetic ride.I . This kL'\!ps the tu111ing cfTcl:t at a mtLximum for most o f the coil's m la tio n. In M> me m olo1' , the field is pt'ovidcd by a n electro mag net ra ther than a perm anent n1agnct. One ad\'antagc i that th " mot or can be run f'rom an a lternating cun · nt (a.c.) ·:upph. A~ th • cu n-ent flo w · backward · and forwards in lhc coil, the field from the elc trom agncl chnnges din..--c ti on 10 m atch iL, so the turning effc L is alwa_). Lhc same wa) and th e motor m ta li.:.s n01mall): The m a in~ motor~ in drills anc..l food mixer~ wo rk like this. cuf\ed pole p:icce armature • Practical motors have curved pole pieces, and several coils wound on an iron armature. 0 Brushless motors Many electric motor~ don't have brushes. F0< example, those used in electric and h~rid cars work in a d1ffereot way. An electronic unit feeds current to a set of fixed coils in such a way that a rotating magnetic field is aeated. This polls on a set of magnets so that they spin round. ◄ In this electric drill, the motor is in the centre. Note the commutator segments at the right hand end, and the electromagnet. ®0 Which part(s) of an electric motor O connect the power supply to the split-ring and coil b changes the current direction every half-turn? 2 On the right, there is an end view of the coil in a simple electric motor. a Redraw the diagram to show the position oft e cod when the turning effect on it is i maximum ii zero. b Grve three ways ,n which the ma)(imum turning effect on the coil could be inaeased. G Use Fleming·s left-hand rule to \NOrk out which way the cod will turn. 3 What is the advantage of using an electromagnet in an electric motor, rather . N (:) s e - current into paper e> - current out of pape, than a permanent magnet? R@lat@d lop1cs: rurrent 8 -4; a.c. and d.c. 8.13; magnetic fields 9.2; electromagnets 9.4 ; Aemtng's left-hand rule and turning effect 9-5 A current produces a magncLic field. H O\\C\'cr, the reverse is also pos ·iblc: a magnetic ficJd can be u ·cd to produce a current. Induced e.m.f. and current in a moving wire uisulated w ire mdJCeo curren1 0 Circuit essentials For a current to flow in a circuit, the circuit must be complete, with no breaks in it. Also, there must a source of e.m.f. (voltage) to provide the energy. A battery is one such source. Ot ers include a wire movmg through a magnetic field, as explained on the right. E.m.f. stands for electromotive force. It is measured in volts. -galvanometer (centre zero) \ Vhcn a\\ ire is moved ac,-o~~ a magnetic field, as ~hO\\ n aho\·c left, a small c.n,.f. (\·oltagc.:) is genen1LL-d in 1hc \\ in:. The.: effect is called electromagnetic inductio n . cicrnifically ·peaking, an e.m.f. i~ induced in the wire. If the wi 1\: fonn~ part of a complete.: circuit. the e.m.f. make, a cunent flow. Thi can be detected b) a meter called a galvanome ter, which i ~l"n iti\'c to \ ' "r\ sn1all cull'ent . The one ho,, n in the diagram i a cen tre-7ero type. lt pointer mo\'e to the le~ or right of the .1.e1·0, d.:pending on 1hc cun·.:nl direction. The induced e.m.f. (and ctuTent) can be jncrea~ed by: • mo\ing the wire foster • using a ~trcmgcr magnt!l • increasing the length of\\ ire in the magnetic field - for example, by looping the wirL" through the fid<l ~C\'craJ limes. a ·ho\\ n abo\'L" right. The aboH~ re,ult are ummed up bv Faraday's law of electromagnetic induction. In implined form, this can be . tnted a follow. : Magnet essentials TI e Nand S poles of one magnet exert forces on those of another. like poles repel, unlike poles attract. The magnetic field around a magnet can be represented by field lines. These show the direction in which the force on an N pote would act. 210 Thi.! c.n1.f. induc~xl in a conductor b proportional to the rate at which m~gnctic field lines arc cut b) the conduc1or. In applying thb law. remcmbc1 that field linl: arc u ed to 1-cp1-c ,cnt the trength of a magnetic Ueld a well a~ it dire tion. The clo er together the line~, the stronger the field. Either of Lhc follo\\ ing \\ ill rc\·e~c the direction of 1he induced e.m.f. and curn:nt: • mo\ing the wire in the oppo~ill" direction • turning the magnet round o that the field direction i re\ er ed. If the win: i~ not mo\'ing, or i~ mo\ing parallel to the field line~. there is no induced e.m.f. or current. MAGNETS A D CURRENTS Induced e.m.f. and current in a coil mduced current _-'--c induced current m opposite d rectlO'l If a bar n1ag net is pus hed into a coil,~ ~ho\\11 abo,c lclt, an c.nl.l. i induced in the coil. In thi - case, it j the ma~c tic field tha t i m o,ing rather tha n the ,dre, hut thl.! 1 s uh i-i the same: fi e]d line~ ~we being cut. As the coil is pai1 or a con1plete circuit , the induced e.m.f. m a ke · a c urTl.!nt tlow. The induced c. n-1.f. (and c un'Cnl ) can be increased by: • mo, i ng the n1ag nct fasLcr • using a ·n ongcr 1nagnet • incr ca ing the number of turn on the coil (a s chi increa e the le ngth o f ,,ire cutting thro ugh th e m agne tic field). E Experiments ,,ith tht! m agnet a nd coil als o gi\'e th e fo lio\\ ing rcsuh~. H thc mag net is pulled our of the coil , as s ho,, n abO\C rig ht , the dit-c ctiun of the induced c.n1J. (and c un·ent) i 1-c, ·c1 ·t: d. If the pole of the magne t , rath er tha n th e pole, i pu hcd into the coil, Lhi , al ·o r '\'e• ·~ the c un-cnt directi o n. H the magne l is held till , no Held line. are cut, o there i no induced e. mJ. or· c urTenl. • • • The playback hea d in video t'\!co1'de1 a nd ha rd dd, e" contain tin y coils. A lin~. nu, ing e.m.f. i induced in che coil as the m agnelil'ed ca pe pas~es o,cr il and fidd line~ a rc c ut by thc coil. In this wa) , Lhc magnetized paucrns on a di c arc cha nged into elec trical ig nals whic h can be U')Cd to 1-ccrea tc the o rig inal pic tures, oun<l , o r da ta. Fo r more abo ut m agne tic r ecording, cc ~pre ad 9.3 and 9.4. .& The pick-ups under the strings of this guitar are tiny coils with magnets inside them. The steel strings become mt1gnet11ed. When they vibrate, current is induced in the coils. boosted by an amphf1er, and used to produce sound. ® 1 The wire on the right forms part of a circuit. When the wire is moved downwards. a current is induced in it. What would be the effect of a moving the wire up-vvards through the magnetic field b holding the wire still in the magnetic freld c 2 lr. a b moving the ware parallel to the magnetic field lines? the experiment at the top of the page. \\'hat would be the effect or moving the magnet faster having more turns on the coil? G turning the magnet round. so that the S pole 1s pushed into the corl Related topics: current 84 e.mJ. 8 .5 ; magnetic fletds 9.2; magnetk: recording 9 .3 and 9,4; direction or Induced current {Lenz's law) 9.8 211 Magnetic essentials 0 Induced current direction: Lenz's law Like magnetic poles repel; unlike ones attract. Magnetic field lines run from the N pole of a magnet to the S pole. In diagrams. the conventional current direction is used. This runs from the + of the supply to t e -. ind iced curr nt in opposite d 't o E lf a mag net i n10,·ed in or out of a c:oil, a c u1Tent is inducec.l in 1he c:oil. Tht.• direction ot this c urrent can be predicted u~ing Lcnz1s la\v: A current<arryiog coil produces a magnetic field The right-hand grip rule above tells you which end is the N pole. It is the end your thumb points at when your fingers point the same way as the current. An induced cu1Tcnt alwuys flo\\!-1 in a dil·c tion ,uch that it opposes the change which produccc.l it. Alx>Ye. for c~amplc, the in<luccc.l curTCnt turns the coil into a weak dcc1ron1agnct whose I\ pole oppole~ the approaching i pok• or the mag net. \\'hen the rnagnct i pulled o ut of Lhe coil, lht: inc.luccd cu11"l.·nt ahc1 · directio n and the pole~ of the coil arc t'C\c1,cd. TI1i ti1nc, the coil attract the magnet a it i pulled m,'«,. So, once again, the change i opposed. Lenz's law is an example of the kn\ o f conscn·ation of cncrgv. Energy is spent ,, he n a c urrent flows munc.l a c in:uit, ~o e nergy mu~t he ~pent Lo induce the c urrent in the fi1~t place. In the L'xan1ple above, ,ou have l o spl.'nd energy to move 1he m agnet ,.-'ga.in~l till! opposing force. Induced current direction: Fleming's right-hand rule If a ·traighl wire (in a complete circ uit ) i moving at light angle~ ro a n1agnetic field, the dire tion of the induced c u1T ent can be lound u,ing Fleming' right-hand rule, a. ~hown below: thu M b ot1on If a current<arrying wire is in a magnetic field as atxwe. the direction of the force is given by Fleming's left-hand rule. If a con ductor 1s moving through a magnetic field. or in a changing field, an e.m.f. (voltage) is induced in it. motion se ( ond finge, oouced u,rent A Fleming's right-hand rule 212 MAGNETS A D CURRENTS E On Lhe opposite page, Lherc is informa tion abou t Flc mi ng's d g ht-hand ancl lcll-hand rule ·. The two rule · app l) to <liffcr1:n l ·ituation • ,,hen a current causes motion. the /e/r-hand rule applic • when 111otion cau!,c a curreut, the right-h and rule app lic . Flern ing' tight-ha n<l l'ttle foUo,, from the lch.-hand ru le and Lent:~ law. The diagran1 on the light Hlw,tralc thi . Here, the upward n1otion ind uce a ClllT~nt in the ,, ire. Thl' induced cun ·n t i in the n1agn ' tic field, so th r~ i. a force on it \\hose di rect io n is given by the /eji-ha nd rule. The force mu ·t be d own\\ ards t OO/J/JOSe the m ol io n , so you ca n use this lact a nd Lh!! left. hand ntlc to " orlc o ut wh it h WU) the c.-u1n:n1 m uM now. Ho,, c, cr. 1he right-hand rule g i\'(~ the same rcs uh - vd thoul )OU ha,ing to n:ason ouL al l the ·teps! rorc@on induced current opposes mo·roo Eddy currents* magnenc field stops ____ d sc spmning magnet lf the alumini um di: a bo,·e i • set spinning, it ma) be m a n) seconds bd o r c frict io nal force fina ll.) hrings it to rus t. H o\\ t!\'er, if it spinning bcLwccn the poles o f a magnet, it ~top ~ a hnost in1mcdiald y. This is because Lhc di ·c is a goo<l conductor a nd cun·cnt a n: induced in il as it mo\\.: · tha ough the magnetic field. Th~e arc called eddy currents. The, pl'oducc a m agneti field ,,hich , b, Lenz' la,,, o ppo e the motion of the disc. Edd\' CUJT~nh occur where\'er piece o l ni~ta l are in a c ha nging m agne1ic fi eld - for example, in the core o f a Iran fo1ml.!r. .\lcta l d L:Lccto~ rd~ on c<ldv cu~nl.S. ~ -pica II.), a pulse of Lur r~ nl through a fla t coil prod uce a chm,g ing magnetic field. Thj · induCL'S t.x.ld~ cun "t'nt in a n) rneta l o bject u ndern eath. The cdd, cun -cnt gh e oft thciro\\n changing field \\ hich in d uel: a econd pul c in the coil. Thi h, detected clcctro nicall)~ & A metal detector creates eddy currents in metal objects and then detects the magnetic f elds produced. ®0 Look at the diagrams on the oppoS1te page, illustrating Aeming·s right-hand rule. If the directions of the magnetic f,eld and the motion were both reversed. how would this affect the direction of the induced current? On the nght, a magnet ,s being moved towards a coil. a As current is induced in the c0tl, what type of pole as formed at the left end of the coil? Grve a reason for your answer. b In which direction does the (conventronal) current flow in the meter, AB or BA? J- Alumimum is non-magnetic. Yet a freely spinning aluminium d,sc quickly stops moving if a magnet is brought close to ,t. Explain why. 0 0 Related topic's: law or conservation of e-nergy 4,2; right-hand grip rule 9 .3; Flem1ng·s left-hand rule 9.5: induced current 9,7 gcl\'c.:r ornct ·f (centre zero) 213 Electromagnetic induction If a conductor ,s moved 0 through a magnebc field so that it cuts field lines, an e.m.f. (voltage) is induced in it. In a complete circuit, the induced e.m.f. makes a current flow. Alternating current Alternating current (a.c.) flows alternately backwards and forwards. Mains current is a.c. With a.c. circuits, giving voltage and current values is complicated by the fact that these vary all the tine, as the graph on this page shovvs. To overcome the problem, a type of a\refage called a root mean square (RMS) value IS used. For example, Europe's mails voltage, 230 V. is an RMS value. It is equivalent to the steady voltage which would deliver energy at the same rate. Most of our electricity come · fmn1 huge generators in power slation!'>. There are smaller generator:-. in c,irs and on some bicycles. These generato~. or d) namos, all use clcctromagnelic.: induction. \Vhcn turned, 1hey induce an e.rn.f. (voltage) \\hich can make a curn.· nt Clow. 1\.10 ·t generators gi\'c out alternating cun·cnt (a.c.). A.c. generator · arc al o c~,llcd alternators. A simple a.c. generator The diagram bel w how a imple a.c. generator. It i prc)\iding the cun'ent Ior a sniall lamp. The coil i made of in ulatcd copper wire and i - rotated by tur-ning the shafl. Thi.! slip rings an.! fixl.!d to thl.! coil and rolale with it. The brushes are l\\O contacl~ which ruh against Lhc ~lip ring~ an<l keep the coil conneLted co Lhe outside part o[ the circuiL. The) are usually made or carbon. \ Vhen the coil is rolated, it cut magnetic field lines, so an c.m.L i generated. Thi· make~ a cun'\!nt llow. A~ the coil rotate ·, each ~ide tra\·cl upwat-d'->, do\, nwards, up\\ ~ird~, downwards ... and so on, through I he nlagnetic fidd. o the current flows backwards, forwards ... and so on. In other \\ords, it i~ a.c. The graph show~ how the cu11·cnt varie th I ough one cycle (rotation). It i · a maximum when lhc coil i · horizontal and cutting I icld line at lhe la tc t rale. It i 1ero when the coil i vertical and cutting no Acid line~. The follo\\ ing all increase the maximum e.m.f. (and the current): • increasing Lhc number of turns on the coil • increasing the area ol the coil • u~ing a ~tronger magnet • rotating the coil fo te-r. Fa-;te,- rotation also incre~tses chc frequency of the a.c. Mains generators n1usl keep a slcady frequcnc, for exan1plc, 50 Hz (cycles per !'ICC<>nc.l) in the UK. mcWm mforward ~ current 100 et E so ...~ 0 -:::, :, V -50 - 100 ' •' I I I ' coil position 214 .& Simple a.c. generator, connected to a lamp A Graph showing the generator's a.c. output MAGN 1S A D CURREf TS Practical generators* • A AlternatOf from a car One of the alternators (a.c. generators) ,n a large power station. It is turned by a turbine, blONn round by the force of high-pressure steam. It generates an e.m.f. of over 20 000 volts, although nlike the implc gcnermoron the oppo itc page, most a.c. gcnc1.. to, han~ a fhed "'l ol coil ~HTangcd a.round a rotating d cctron1agnct. The ,-atiou::. coils arc madi: from n1an~ hundr~d~ or tum of wir •. o cn ~a te the Mro ngc!'>l p ossihli: mngm.:ti c field . the~ a n: \\ Olmd o n s p<..>c ia lly s h a()\.-d cores conta ining iro n . l i p ring!!'. a nd hru.-..hc" m"e still usec.1 , but o nh to calT) cun-enl to Lhc ~pinning ek-ctronmgncl. A~ Lhe other coil~ a tt.· li'<cd, Lhc cun cnt ddivL'red b, the genera tor c.loc- nol han ~to thro u gh s liding no,, cont.. et ·• ( lie.ling contacl~ can o,erhcat H the cun-cnt i , i.:r~ high.) Di n.."C't CUJT"'nt (d .c.) i 'on~-\\,, ' cu n-"nt like tha t fro m a batter,. O.c. gcncr"'J.tor.-. arc ,imilar in constn1c ti o n to d .c. mo to r.-., with a fixed n1agncl, r o tat i ng co il, hn1!-1hC!-1, and a commula trn· to rcvc1. e the conn'-' tio ns lo the ouL~ic.lc c ircuit i.:, l:t) ha lf-tun,. \ \'hen the coil i~ ro tated, a h e rna ting c un"l.'nt i~gcnermt.xL Ho\\ cve1: the ac tion or the commutacor mean.'> that thL· c uti'-.' nl in the oul:)ic.k· d1~uit aJ\, a, · flo\\ ~ the a mc wa\ - in 0Lhc1 \\ot cb. il i d .c. ar nL-cd <l.c. [o r rcc harg i11g the batten · a nc.l running o ther c ir uits. In pctro] and c.licsd car'>, the eng ine turn a genct .. tor. H o\\~\cr, an i u c<l. rather tha n a d .c. gcncra tot~ becau c it can dcl h ~r m ore u1n:nt. A d\!\·icc called a rectifier c h a ng ~ it a.c. o utput to d .c. altc111ato1 consumers get thetr supply at a much lower voltage than this. 0 Moving-coll microphone LJke generators. some miaophones use the pnnople of electromagnetic induction. In a moving-coil microphone. incoming sound waves strike a thin metal plate called a diaphragm and ma e 1t vibrate. lhe vibrating diaphragm moves a tiny coil backwards and forwards in a magnetic held As a result, a smafl alter nat1ng current 1s induced in the COIi. \Nhen amplif,ed (made larger). the current can be used to drive a loudspeake,. ® ~ rhe diagram on the right shOYIS lhe end view of the coil ma simple generator. lhe cod IS being rotated It is cor nected through brushes and slip ring, to an outside lircu1t. a Whal type of current 1s generated m the coil, a.c. or d.<:.? Explain why ,t 1s this type of current being generated. b Give three ways in which the current could be increased. c The current varies as t e cod rotates. What 1s the position of the coil when the current is a maximum? Why 1s the current a maximum in this oos1t1on? d What is the posation of the coil when the current is zero7 Why 1s the current zero m this pos1t1on? 2• Give three differences between the simple a.c. generator on the opposite page and most practical a.c. generators. Re lated top1cs: e.m.f. 8 .5 ; rect ers 8.11: matns a.c. 8 .13; electromagnets 9-4, d.c. motors 9 .6 ; electromagnetic Induction 9.7 215 A 111o l'i11g magnetic fidcJ c an induce an e .m.f. (,·olcagc) in a conductor~ 0 Electromagnetic induction a~ o n 1he kft. Adra11gi11~ mag neric lidd can h ave th e ·.ame dfec t. Mutual induction col - iron I core i- I ,I galvanometer (centre zero) If a magnet is pushed in or out of a coil, the coil cuts through magnetic fteld lines, so an e.m.f. (voltage) is induced in it. This is an example of electromagnetic induction. If the coil is in a complete circuit, the induced voltage makes a current flO\AI. 1J~h oattery galvanometer (centre zero) the electro magnet abo\'l' i~ '\\ icc hccJ o n, an e .m.f. is induced in the other coil. but onl~ fo r a fraclio n o f a l.'Cond. The cf1ec t j equivalent Lo pu hing a magnet LO\\ ard-; the coil, Cl) fa c. \\'ith a tcady curn.'nt in the electro magnet, no e.m .f. i induced becau e the magnetic field i no t c hanging. A the eleclt'Omugnet i s witc hed off, an e. m.f. L induced in the opposite din~ tion. The cffc cl i · cqui\·alcnt to pulling a m ~1g ncl a\\a~ fro m th e coil \ 'Cl} fast. The induced e.m.f. al switch.on or switc h.off is incn:ascd if: • the con: of Lhc clcctromag ncL gOt:'s r;g hl throug h the !'ICCond coil • the number of I urns on the second coil is inc reased . \\11en coils arc rnagneric-allv linked, a abo\'c, !,O that a c hanging c uncnt in one c~u,~ an induced e.m.f. in the other, 1hi i alJed 1nutual induction. I .A. Using mutual induction. 40 000 volts (or more) for spark plugs is produced from a 12 volt supply. The high voltage is induced in a coil by s'Nitching an electromagnet on and off electronically. 216 A In an induction hob, each 'plate· contains a coil that gives off a strong, alternating m<1gnetic f,eld. This generates a high current in the metal base of the saucepan, which heats up as a result. MAGNETS A D CURRENTS A simple transformer secondary (output) primary (tnput) co I. SOO turns coil 1000 turns • Symbol for a transformer - a c input 1 v 2 V voltage ~ a c output voltage D.c. and a.c. Direct current (d.c.) fl~ one way only. Alternating current (a c.) flows alternately backwards and ro,wards. core iron or Mumeta A.c. \'Ohage can be incn:a~ed or dccr·ascd u ·ing a tran former. imp1 • Imm.former is shown in the diagram abo\·c. It work~ by mutual induction. f \V~n altt:rnating current llo\\ in the primary (input) coil, it ~L'ts up an alte111ating magnetic field in the core and, the1~rorc, in the secondary (output) coil. Thi changing field indu c an alten1ating voltage in the o utput coil. Pr vick'CI all the neld lin pa · through both coil , and the coil~ \\ a.~t" no energy lx."Carn, .. of heating efJ !et~ . th" followin g c..'(ltta lio n a pplies: outpul \"oltage input \oltag1.: In ~)mbols: turn, on output coil -- turn, on input t·oil \I ' \' ' 0 - whet , ., mc..--ans ~ ondat) and p m "an~ primary For the tran io1~mcr above, './, P - 1000/500 - 2. The tran rorn1cr ha a turn ratio of 2. The amc ratio link~ the \'Oltages: V J \IP 24/ 12 2. Put in \\ Ords, the output coil has twi ce the numhcr of turns of the input coil, so the output \'ohagc i~ twice Lhc input voltage. = A transfo.-mer <loc no t give ) OU ·o mcLhing for nothing. If it int:rea \'oltagc , it reduce currcnl. Thi i cxplaint:d in the nt.:Xl prcad. C!, 0 P.d. e.m.f. and voltage P.d. (potential difference) ,s the scientific name for vol tage. The p.d. produced i.-vithin a battery or other source is called the e.m.f. (electromotive force). For convenience. engineers often use t e word voltage rather than p.d. or e.m.f. especially when dealing W1th a.c. Voltages in a.c. orcuits are common~ called a.c. voltages. although, strict~ speaking, an 'alternating current voltage' doesn't m e much sense! ® ~ In the experiment on the right, what happens when a the switch is closed (turned ON) b the swi tch Is left in the closed (ON) pos,t1on c the swi tch is then opened (turned OFF)? In the experiment on t e nght, what would be the effect of a extending the iron core so that It goes through both cods b replacing the battery and switch by an a.c. supply? 3 A transformer has a turns ratio (N/Ni) of 1/4. Its input coil ,s connected to a 12 volt a.c. supply. Assuming there are no energy or held line losses: a What is the output voltage? b What turns ratio would be required for an output voltage of 36 volts? 0 ~d v,•non · ,~r (centre zero) Related topics: p.d. a rxt e.m.f. 8.5; magne t tc field lines 9 .2; electromagnets 94 electromagne tic i nduction 9.7; d.c. and a.c. 9.9 217 Step-up and step-down transtormers Depending on it~ Lum~ ratio, a trans fo amer can inc rea c or dec rea ~e an a .c. volt ~1ge. Step-up transformers hin ·e m o re turn on the o utput o il tha n on Lhe input c o il, so the iroucpul \·ohag e is m o tl." than the input vohage . The Lransformt!r in Lhe d iagram helo\\ is a seep-up tn1nsfonner. Large stepup tr-ansforrnc~ arc used in power Mations to increase the \Oltag c to the level · needed for overhead power lines. The next spread explain · why. S1cp-do,vn transfom1crs have lewcr turns o n the oulpur coil than o n the inpul coil. so the o utput \·oltage i. le than the input \'Oltage. In battery c hargers, compute~. and other electronic equipment, they reduce the \'oltagc or chc a.c. mains tu the muc h lo\\ t!r levels nce<l~d for othe r c ircuits. • A transformer connec ted to loca I power lines Both L~pc of tran~fo nncr work on a.c., but nut on d.c. Unlc · there i~ a chan~ing cun-e1H in rhc input coil, no \'oltagc is induced in 1hc o utput coil. Connecting a tran lorn1er 10 a d.c. upph c an dan1age ic. A hi g h c un-ent Oow. in the input coil, which can make it O\'erhea t. Power through a transformer If no energy i - wa ·ted in a tran -Fonner, the po wer (energy per econd) deli\'cred h) the output c oif \\ill be the same a~ lhe power ~upplicd co Lhe input coil. So: Power essentials Energy as measured in joules (J). input \ohage x input crn-renl Power is measured in output \ohag~ • output cun-~nt watts (Vv). An appliance With a power output of 1000 W delivers energy at the rate of 1000 joures per second. In cwcuits, power can be calrulated using this equation: power = voltage (watts) (volts) ~ (V) l n symbols: \ ' ,!,, A ~voltage x cu1Tc1H i the an1c on bo th idc~ o f a tran former, it follow that a tran former,, hi ch i11crea e , the vohagc will reduce the c urre nt in the ame pro po rtion , a nd vice \'ersa . The fig tffe. in th e diagram belo w illustt·ate this. x current 500 turns (amperes) 1000 turns (A) a c mput 1 V 24 voltage v a c output voha9e current 2 A powet output power input a Vi, lp • 12V >C 2A =24W 218 core iron or Mumctal a Vs Is • 24 V >C 1 A =24W MAGNETS A D CURRENTS Practical transformers* 111put co The diagram on the ,;ght how two wa ~ - of an-angi ng th • coil a nd cor " in a pract ical lran."fom, ·r. Both method~ an.! dc:-iigncd to trap the magnetic field in the con: so that all the Field lines from one coil pa. s thro ugh Lhc other. All trrur lorml't - wa ·te o me cnerro bccau ·cot heating e ffect in the core a nd coil . Here a rc two o l the cau ~c : • The coil arc n o t pcd cct electrical conduc to1 a nd heal up bccam,c of their resbtance. To keep the resi tancc lo\\, lhick copper wire is used \\ hen ~possible. • The core is itself a conductor, so the cha ng ing magne tic ricld induces cun-cn r.s in it. Thc~c circulaling edd currents h a\'C a hea ting effec t. To reduce the m , the core i · la,nina tL'<I (layered): it is rna dc lro m thin, in ulated heel o l iron or Mumc ta l, ra thl'r tha n a olid block. Large, wc ll-dc~ig ned 1ra ns lo rmc n, can have e fficiencies a'-; high as 99rr. In othc,· wor·ds, thei r useful pO\\'er output is 99<r of the ir powe r inpul. Solving problems lam111 ated core iron or Mumetal output co,I \','Otmd over anou1cotl A Practical transformers input coil: output coil: 100 turns 2000 t urns £ra,11p/e ,\~~um ing that th • tran~fonncr on the righ1 ha, an "•rtid1.mcy of I O(Yo, c.: nlculall.! a chc supply voltt1gl.! b 't h l! curn:nt in ahc input co il. ( I I a Thb i o h cd u ing the tran ~(o n n c r equation: V~ - N = - ' 10V whcrc V 1 i the upply \ 'Oh agc to be calculated. I OV ubslituting \'a lucs: uppl) vol aagc Re ar ranged , this g ive : E b Thi j \\here 100 a.c. suppty ~upply ,·oltagc lamp: PoW, 2000 40 W 200 o l\'cd u ing the power equa tion: \.\1, i ~a lread~ kno\\n Lo ubstiluting values: ® ; Rearra nged, lhis gi\'es: bc 40 \V. 200 V inpul c urrent - 40 \ V inpul cu1Tcnt ~ 0.2 A 1 How does a step-up transformer differ from a step-down transformer? 2 [xplain each of the following : a a transformer Wlll not work on d.c. b • the core of a transformer needs to be laminated G 1f a transformer increases voltage. ll reduces current. 3 In the carcuit on the right. a transformer connected to the 230 V a.c. mains is providing power for a low-voltage heater. Using the information in the diagram. and assuming that the efhc,ency is 100%, calculate a tt e voltage across the heater @) the power supplied by the mains G the power delivered to the heater Q tt e current in the heater. ,.._, L>-----. current. 0 1 A heater R@lated top1cs: resistance 8.6: pm..•er calculations 8.11: eddy currents 9 .8; d.c. and a.c. 9.9; power transmission 9 .12 219 400 ooov 33 ooov po,,·,er st~t,or generat ion schoos transformer substat10n transformc, (step-up) tran Stnission (step-down) farms 11000V 33000V transformer substa on transf°'mer substation transf°'mer slibstat10n A A typical mains $upply system. Actual voltages may differ, depending on the country. Power essentials 0 An appliance With a power output of 1000 watts W'I) delivers energy at the rate of 1000 joules per se<ond. In circuits power - voltage x current (watts) (volts) W'I) (V) (amperes) (A) 0 Transformer essentials Transformers are used to increase or decrease a.c. voltages. If a transformer is 100% efficient, its pov.-er output and input are equal. So rf it increases voltage, it reduces current in the same proportion so that 'voltage x current' stays the same. 220 (ste-p-doi,vn) (step-down) {step-down) d istribu ti on Po\\er for the a.c. main L generated in power tation , 1rw,.,,11i11ed (sent} through long-di tance cable , and then distributed to con umer . Typic-alh, a large po,,er lation might contain four generator , each producing a cun-ent ol 20 000 ampere~ at a voltage of 33 000 \Olts. The current from each generator i fed to a huge step-up tran. lonner which transfon-. power to O\ 't>rhead cublc!-i at a greatly increased \·ohagc (27- 000 Vor400 000 V in the K). The n:ason for doing Lhi~ is explained on the nc~t page. The cables fcL-<l power to a nation\\ ide supply network cal led a grid. sing the gri<l, po,\c1· station ' in aavas ,, here the de1nand i lo\\ can be u ed to upph a1 'a where the den1and i high. Al ~o power tation can be ited awa\ from heavih populated area . Power from the grid is <lbtributed by a ~crie~ of substations. These contain step-clown t1-c1nsfomlcrs \\ hic h n:duce the \'C>hage in stages to the le\'cl needed b) consumers. Depending on the country, this might bl.' between 110 V and 230 V for home consume1 , although indu ·11 . nornK,11) u c a higher ,·oltagc. Transmission issues A.c. or d.c.? Alternating curnmt (a .. ) is used for the mains. On a large scale, it can be generated more efficient I~ lhan 'one•\\ a)' <lin.-ct cun~nt (<l.c.). Ho\,c,·cr, the main advantage: of a.c. b that \'oltagc ' can be ~teppL-<l up or down u ing tran,ton11c1 . Tran~lo11nc1 ' will not \\'01 k with d.c. MAGNETS A power input ,.._, - 2000W \ voltage Calculating power loss When current flo\NS in a cable reStStanGe -2 0 - 200V I current ■ power loss p(M<er input • 2000W ,.._, ■ 1O A (because 2000 W i. 200 V x 1O A) CUrrent2 X resistance ;: 1cj X 2 ;;: 200 W \ voltage cable reStStanGe =2 U • 2000V D CURRENTS cabfe, the resistance causes a drop in vol tage along the cabfe and a loss of power. power loss - voltag~ drop x current But: voltage drop - current x resistance So: po'Ner loss - current x resistance x current 2 - current x resistance In symbols: P current ■ 1 A (because 2000 W power loss c ■ fR 2000 V x 1 A) currcnt2 x resistance = 12 x 2 c 2W High or low voltage? Tran n1i ion cables an: good conductot '. but they still h,n e ig nfficant re ·i~tance - e~pec ially when they are hundred of kilome tres long. Thi!-. m~an:-. 1ha1 tmc~ b wasted because of Lhe ◄ These calculations show the power losses an a cable when the same amount of power is sent at two different voltages (for simpl1oty, some units have been omitted). healing cffccl of thc c urrcnl. The c alcu la Lions abo\ l! dcmon~Lrate \\ h, le · power i • los Lfrom a cable ii pOWl:r i tram,millL-<l through it at high voltage. B~ u ing a tran former to incrca-;e the , ohagl!, the cun·cnt is reduced. '-)0 thinnc1~lighte1; and cheaper cable can be u~ed . Overhead or underground?• There an: two \\ ays of running highvoltage tran mis ion cable a ero countr\'. The, can be u pcnded overhead from tal1 1o wc1 called p\ lon~. or l hcv can be put undcrga und. Jn countt;cs whe1·c power ha to be transmitted \Cl) lo ng c.li~tanccs , O\'crhcacl c able~ an! more common bcc au~l! lhcy a1-c c hcaf>'!r. The, arc t.'~ier to in~u]alc bcc:a u c , on:r most of their length, lhc air acts a an ins ulator. Al o, cosll~ digging operations an: m oidcd. Howcn.·t~ pylons and overhead cabk -;poil the en, iaonment. The, a1c o lten nor allowed in den clv populated area o r in area of o ut landing natural beaut,. o underground cable (calJcd land tin~) arc u ed in tea d. ® 1 In a mains supply system, hO'N are voltage changes made? 2 Explain each of the tollowmg. a Ac. rather than d.c. is used for transmitting mains pOW"er. b The voltage ,s stepped up before po'lt<er from a generator 1s fed to overhead transmiss10n cables. 3• Give an example of where underground transmiss,oo cables might be used instead of overhead ooes, despite the extra cost. Related topks: power stat ions 4.5- 4.6 ; resistance 8.6-8:;. 9.10-9.11 4 • Pyions and overhead cabfes are not usually permitted tn areas hke this. The second paragraph oo the opposete page describes the output of the four generators in a typical, large power station. Calculate the poi.ver station's total polh-er output in MW. ( 1 MW - 1 000 000 W) The diagram at the top of this page co~ares power losses from a cable at two different voltages. Calculate the pO'Ner loss 1f the same pO',,\ler 1s sent at 20 000 V. ( ) 4 kW of power is fed to a transmiss100 cable of resistance 5 H. Calculate the pov.,er loss in the cable 1f the pO\\let is transmitted at a 200 V b 200 000 V. 0 mafn-s electr1dty 8.13; generators 9 .9 ; transformers 221 E Further auestions f 1 An electron1agnct is made by winding" ire around an iron core. _:_ \ springy contacts TL---@)----/-- -,- soh rro'l cod v..re coil 1 • pwt s --I xplain, in detail, how do ing ~\i..·itch S cause the motor M to ·tart. [41 4 The diagram shows a long \\ire placed bet wccn Lhe poles or a n1agnet. When currcn t I nows in the wire, a force act · on thl' wire cau ing it to mo\'c. The diab11·am shows an clcctromagnel connct:te<l Lo a circuit. SLale two \\a\' ' of making Lhe strength of the ekcLron1agnet weaker. l2J b Explain \dl\ the core i made of iron insh.-ad of le ,J. [ ll 2 A, B, C and D arc malJ block:, of different maL ·rial . The lablc belO\\ how "hat happens wh ~n two ol the b1ocks ar~ placc.--d neat· one anothc1·. Arrangement of blocks ~~ ~ - -l!] [fil [] Effect ~-------- attraction attraction - - - ~ - -~ - - K) - ~ - -no ~ effect [ID @] glettC no effect maceri.al a non-magnet,c material se one or the phrase-. in the abcwe boxe · to describe the magnetic pmpcny of each block. Each phrase may be used once, mon: thar\ oncl' or not al all. a Block A is b Block B i c Block C b _ _ _ _ _ __ d Block D is _ _ _ _ __ ------- [41 3 The figun..' below shows a circuit, wh ich induc.le · an electrical rela,, used to switch on a motor M. U e F1cming' left-hand rule to find the dir~tion or lhe force on Lhe \\ke. Copy Lhe diagram and show l he di r~ction or the foa-cc on )Our copy wath an arrow lahdlt:<l F. [ I] b tale whaL happens to the [orce on lhl' \\ ire \\hl'n i Lhc izc of the curt"Cn t in the wit "' b i ncrca c..'CI, [ 1l ii a \\ eaker magnct is used, [ ll iii the di1·ecLion of the cun~nl is r·c,·c1"S<..-d. [ I] c Nan1c one practical de, ic..: which uses [I] th i · effcct. E a 5 The diagran1 below ~ho\\ a pen11anent n1agnet being movc..xl toward. a coil whose ,nd arc connected Lo a scnsiLi,c ammctc1: Alii Lhe magnel appnmches, the ammctc:rnec<lle gin.•s a small <lenection to the left. 222 e OUP: this may be reproduced f0t class use solely r« the purchase,·s lnstttute s A -------4 A l - - - - - - , d Explain whv transfo1mcrs arc usL-<l \\ hen po\\ ~r nt.·cd~ to be transn,i ttcd o, er long di tance~. [ 31 c \\'hat b thL· core of a tran~lo1 mcr u~ualh made of? [2] col a tate what )OU would e,pect the amn1cte1 to ~how if, in turn, i th, n1agnct ,,as pulled aw,1y from thl! coil ii thL' magm:L "as rcn!~cd so Lhat the pole\\ as mo,c<l 10,,ar<ls the coil iii the magnet "as no\\ pulled a,,a, rrom the coil at a n1uch h ighcl pecd. 4] b Give the name of the pro e!-.~ ,,hich b illustrated hy these ,,pc1imenh. [ 1l amm •tc1: Th 'I , arc l\\O ~hort iron bm~ in~idc a coil of insulated "ii •. One 001 is fh:c..'Ci and cannot mo,c and th • ot lv-1· is on th 'l!nd of a pi,otc..-<l pointe1: The diagran, sho\\~ the ammt.:tcr in LLse and mcasu,;ng a ctun:n[ or 1.5 aJllpl.'1'\.· (A). - ~ ~ - term11al pivot --+---iff .,;:i,...- - -mov ng iron bar '"....___ _ hxed iron bar cO!I of w,re _..___.7'---Spnng Man, power slat ions ha\'c to burn f ucl in order Lo gcm.·111te dc-ctricit,. Explain how the enc~\ tran-,k·1 red f rorn the burning fuel b evcntuall) can ied awa) b) an ck--cuic cu1-rcnt. b Po\\ •r stations use tnmsforme1 to incr ·a.,e thl! voltage to ,en high vnlues before u·ansmilting it to all parts of Lhc country. E,plain "11\ L'IL-ctricit, is transmillL-<l al \ L'I high \ oltagt.·s. c 8 The diagitlm ho,~ the main pa.11~ of one l\ ,~ of r I 6 a s C r11 A fX>\\CI Lation produce clccuidt,\' at 25 000 V \\ hich b incn:ascd b, a transfo1111cr to 400 000 \ ~ Th • trnnsf ormcr has 2000 tu111s on its p1imat)' coil. sc the fonnub , ultJg1.: •''-" "''P•11nan 1.ml n111nb'-'1 u l 111m, d ll r• im,t" t.: Uil to calculate the nrnnber ol turns on its econdan coil. 7 The diagram sho\\s a simple translorm 121 '1: care How n1uch clcxtlical charge will pa~~ tlwough this ~mmetcr in on • mi nut •? lnclud • in ,our answc1· the t.-quation \ ou a1 •going to u ...c. ho,, clcarh ho,, , ou get to your final ans\\cr and gi\c the unit. [3) b i Apart lrom a heating eHcct, what will be p1 duced b,• the coil of \\ i 1~ when the clcctricit\ pa~M-~ through it? r l] ii \\'hat efl\.'Cl will thi~ ha, 'on the two iron ha,~? \\'hat causes the cite t? D1-aw one or n1m\..' diagrams ii this\\ ill help \OU to explain. f4) ro llll u·e, pm·t a. you will 11eed iPlfon11a1io11 E a Ji·o111 Chapu•r 8. E 9 a \\'hen a coil rotate in a magn •ti field, an alternating \'ohag • is producc..xl. E:\ph1in how thl! voltage is produced. [21 outpu ') pnm. ·ry co 1000 turns) secondaf't coil (50 turns) The tran"lorn1c1· is a step-down transformc1·. [ 11 a \\' hat is a step-down transfom,cr? b Ho\\ can )OU tdl lrom the <ljagram that thi i a step-down t1'" n-,lonn~•? I 11 c Calculate the output ,ohag~ of thi transl on11c1: ') ') t»h-~tM ® ® (0 b The diagram A Band C ho\\ thr~e positions of a coil as it rotak clock,\ be in a magnetic field produced b, t\\ o pole~. The graph hdow sho,\s how the ,ohagc produced chang1.:s as the oil I otatcs. 223 s E E \\'hen the coil is in the position shown by diagrjm A, the output \oltage is zero and is voltage G) ---------------------® tune © marked a J on the , oltagc-time graph. talc which point on the, oltag--- tin1c graph COtTP pond to the coil po~ition . hown b\ i diagram B, ll ii diagram C. [ 1l c talc one way of increasing the size of the voltage produced b) this coil rotating in a n1agnclic field. [ JJ r Use the list below when you revise for your IGCSE examination. The spread number, in brackets, tel Is you where to find more information. R v· · n hecklist Core Level □ The lwo t\pc of 1nagnctic pole and the allraction and rcpul ion bct\\ecn them. (9.1) □ The propertic of magn 't . (9.1) D Induc 'd magneti~m. (9.1) D Magnetic and non-magnetic matc1;als. (9.1) D Hard and soft magnetic materials; the diflcn:nL magnclic properties of steel and iron. (9.1) □ Plotting the field around a magnet. (9.2) □ The field around a bar magnet, and the direction of th' field line . (9.2) D The magnetic fields around a cmTcnt-can ·ing straight wire and a solenoid (long coil). (9.3) D Electromagnets and their uses. (9.4) D How a magnetic relay \\orb. (9.4) D The force on a cu1Tent-carrying conductor in a magnetic lield; the effect ol rc\'cnting the current and 1cld dil 'Ction . (9.5) D How a moving-coil loudsp •ak •r wm-ks. (9.5) D The turning cflect on a cu1nmt-can-ying coil in a magneLic field and the factors arkcting it. (9.5) D Electromagnetic induction: how an e.m.f. is induced in a ,\ire or coil if it is in a changing magnetic field. (9.7) D The factor affecting th' ize of an induced e.m.f. (9. 7) D The conslruclion of a tran~former. (9.10) D tl!p-up and step-down trans£ormcr~. (9.10) D The cquation ]inking a lransf armer's input (pritnat}) and output (second.at)') voltage~. (9.10) □ Ho\\ tran forn1c1 an: used in the cran rni ion of n1ain pO\\Cr aero counlQ. (9. I 2) D \\'h) pow 'r i trarn.mitted at high \'Oltag '. (9.12) 224 Extended Level As for Con! Level, plus the following: D The va,-iation in magnetic licld slr~ngth around a currcnt-cat~l)'ing straight\\ ire and a olenoid. (9.3) □ How the magnetic field lrom a traiglll wire or olcnoid i aflcctcd if the cun~nt i incrca cd or it~ dir :et ion changed. (9.3) □ How to \\Ork out th • direction or the force on a currcnt-canying \\ ire in a magncLic field (Flcming's left-hand rule). (9. -) □ How a simple d.c. molor works, and the action of the com1nutator. (9.6) □ Ilow the direction of an induced cun-cnt alwa, oppo l.~ the change cnu ing it (L ·nz.' law). (9.8) □ How to \\01·k out the direction of the induced currunt "hen a wire is mo\'ed through a magnetic field. (Flcming's righl-hand rule). (9.8) □ How a implc a .c. generator works. (9.9) □ How the output ,oltagc of an a.c. g ·ncrator \'arics \\ith time, and i related to the position or the coil. (9.9) D How a transformer works. (9. JO) □ \.\1h\ a trJnsformcr use~ a.c. not d.c. (9. l 0) □ The equation linking a tran fonncr's inpul (pa imat)) and output ( ccondar\) PO\\ 'I~. (9. 11) □ ing the equation P - ! 2R to e,plain why po\\ er lossc!-> in transmi~sion cables arc lo,, er when the ,oltagc is higher. (9.12) The aurora borealis Cnorthern lights') in the night sky over Ala ka, USA. The hin1n1cring curtain of light i. produced \\ hen atomic particles streaming from the Sun hike alon1. and n1olcculc, high in the Earth' atn10 pherc. The Earth's magnetic field concentrate the incon1ing alotnic particle_ above the north and south polar rcgion.5, ·o that is ,vhcre aurorae are non11all~ seen. chapter 10 225 0 Charge essentials There are two types of electric charge: positjve (+) and negative (- ). e charges repel; unlike charges attract. ►A A simp le model of the atom 1 EYcn·1 - hing is made of atoms. Atom~ are far too small Lo be st!cn \\ i th any ordinal") micro ·cope - Lhcrc an: more than a bil1ion billion of them on the surface of thi · lull stop. Howevc1·, by ~hooting tiny ~uomic '-' particle through atom , cienti t ha\'c been able to develop models (d~cription ) of their tructurc. In advanced work. denti t u ea mathematical model ol the uton1. However, the imple model below L oflcn U!)ed to explain the ba ic ideas. - simple model of the atom. In reahty. the nucleus is far too small to be shown to 1ts correct scale. If the atom were the si2e of a concert hall, its nucleus would be smaller than a pill! -----} proton nucleus:- neutron --An atom is made up of smalli:r particle : • • • element chemkal atomic symbol lhydrogen J H number (proton number) l' 1 He 2 l.il 3 Be 4 boron B 5 carbon C 6 nitrogen N 7 oxygen 0 8 radium 88 thorium Ra Th uranium u 92 plutonium Pu 94 helium 226 90 • There is a cenlral nuc le us made up of protons and neutrons. Around ,his, e lectrons orbit al high ·pccd. The number of particles depends on the,~ pc ol atom. Proton have a po itive ( ) charge. Electron ha\'e an equal negath·c (- ) charge. orn1ally, an atom h the ame number of electron a~ protons, so i [s tota 1charge is ze1·0. Protons and neulmns are called nucleons. Each is abou t 1800 times n1orc ma~i,·e than an clcclron, so \·irtuall) all or an aton1's n1ass is in its nude us. Electron arc held in orbit b) the fore{." of auraction between oppo ·itc charg . Proton and neutron arc bound tightlv together in the nucleu by a different kind of lorce, called the s trong nuclear force. Elements and atomic number All n1aktiab are n1ade from about 100 basic ub ranee called elements . An aton1 b th" malle l 'pie c· of an element you can have. Each element hru a diflen:nf numbe1- ol p1·01ons in its atoms: ii has a clilfon:nt atomic number (sometimes called thl! proton number). There are some exampk•~ on Lhc lcf1. The atomic number also tell-; )Ou the number or electron~ in lhc aton'l. Isotopes and mass number The atom ~of any one clement a1·c not all exactly alike. omc may ha\'c more neutron than others. The e diftcrcnt \ 'Cl ion~ o( the clcnlcnt arc called i otopcs. The, have identical chemical propenies, although their atom!'> have different ma~ e . Most elen1ent are a n1i'\llll\! of t\\'O or more isotope . You can sce ome e~amples in the chart on the opposite page. ATOMS /\ND RADIOACTIVITY The to Lal numlx:r of pro co n., a nd neutro n~ in the nud cu"i i!-1 called the mass number (or nucJeon number). isotopes ha,·e the sanu! a tomic number but diflere11t ma~· num bca . For example, the ffletal li thiunl (atomic nurnbcr 3) i a mLxturc of two h.otopc.. _ "ilh n1a numbet 6 and 7. Lithium-7 i the mor-e con1mon: over 93r t of lithium a torn~ are of thi · type. On th ~d ght, you can ~c how to 1~ prcsenl a n atom of lithium-7 using a ~ym bol and numhcrs. Each dincrent type of a to m, lithium-7 fo r example, is ca)k'CI a nuclide. element mass number (nucleon number) t'\ . - atomic number (proton number) e == electron (-) isotopes 1e >99% symbol for element p ■ proton(+) n = neutron 1e <1% hydrogen [El 0 2c <1% [E] 2c >99% helium E] 2p 1n um-3 93% hth1um Electron shells* Elc-ctron orbit the nucleus a t cc11ain fhcd level · onl~. called shells. Thcl\: i a limit to how manv electron each hell can hold - for example. no mOI~ tha n 2 in the fi1 t ·hell and 8 in the ~ond . It i an a ton1'· o ute,1110 t electrons which fmm the chemical bond~ wi th o ther a to m~. !-lO ele me nts with ~imila rcl ect ron a rra ngem e nt~ hm·e ~imila r c h c mica) p roperties. ® For questions 4 and 5, you will need data from the table of elements on the opposite page. 1 An atoms contains electrons, protons, and neutrons. Which of these particles a are outside the nucleus b are uncharged c have a negative charge d are nucleons e are much lighter than the others? 2 An aluminium atom has an atomic number of 13 and a mass number of 27. How many a protons b electrons c neutrons does it have? 0 The periodic table 1s a chart of al the elements. E.lements in the same group have similar electron arrangements and similar chemical properties. 3 Chlorine 1s a mixture of two isotopes, with mass numbers 35 and 37. What 1s the difference beti.-veen the two types of atom? 4 In symbol form, nitrogen-14 can be wntten i;N How can each of the following be written? a carbon-12 b oxygen-16 c radium-226 5 Atom X has 6 electrons aod a mdss number of 12. Atom Y has 6 electrons and a mass number of 14. Atom Z has 7 neutrons and a mass number of 14. Identify the elements X, Y, and Z. Related topics: etectrtc charge 8 .1-8.2; experiment al evidence for nucleus 10.9 0 Isotope essentials Different versions of the same element are called isotopes. Their atoms have different numbers of neutrons in the nucleus. For example, lithium is a mixture of two isotopes: lithium-6 (with 3 protons and 3 neutrons in the nudeus) and lithium•7 (with 3 protons and 4 neutrons). Some mall'dals contain atoms,, ith unstable nuclei. In time, each unstable nuclcu~ dbintcgracc · (bt caks up).~ it doe~ so, it ·hoot out a tin, pa, tide and. in omc ca!,C • a bur t of\\ me energy a well. The pa11ide and wa, c 'radiate' from the nucleu • ~ the\' at , M>mtime!:> called nuclear radiation. 1ale1ial. which emit nuclear radiation are known as radioactive maLcrials. The disinlegraLion of a nudcus is called radioacth·e decay. omc of Lhc materials in nuclear powl:r staLion • arc hi g hly radioacti\'C. But nuclear r..,dialion come~ from nalural our-et.• as ,,ell. Although it i convenient to talk about 'radioacthe material ', it i rC"alh pa11icular i 01ope of an clement that are radioactive. Here an: ome c,ample : isotopes stable nude1 unstable nude,. ----- carbon-12 found in radioactive carbon-14 air, plants. animals carbon-13 potass,um-39 potassium-40 rcx:ks. plants. sea water ~ - - - - - - - - -~ - - - - - - - - ~ uramum -234 rocks uramum-235 .( uramum-238 ek>cron 0 atom 0 pOSltl\"e IOO A If an atom roses (or gains) an electron, it becomes an ion 0 Discovering radioactivity Henn Becquerel discovered radioactivity, by accident, in 1896. When he left some uranium salts ne~ to a wrapped photographic plate, he found that the plate had become •fogged'. and realized that some invisible, penetrating radiation must be coming from the uranium. 228 Ionizing radiation Ion are charged atom (or group~ of atom.). Atoms become ion. when they lose (or gain) electron·. '-=ud~r rndiation can remo\·c dcclron from atom~ in it!-. path. so ii ha~ an ionizing effccl. Other form~ of ionizing r..ldiation include uhra\'iolct and X-ray!-.. It a ga · become:, ionized, it \\ ill conduct an electric current. In living thing , ionization can dan1age or de tro" cell ( cc the next prcacl). Alpha, beta, and gamma radiation Thea"" arc three main t\'P "'S of nuclear radiation: alpha particles, beta particles, and gamma rays. Gamma ray!-! are the n10 l penetrating and alpha part ides the kast. a!-. sho\\ n bdo\\ : mv1s ble nucte~r rad1at1o«1 alpha beta gamma paper ATOMS /\ND RADIOACTIVITY type of radiation alpha particles (a) each particle 1s 2 protons 2 neutrons (1t 1s 1dent1cal to a nucleus of helium-4) relative charge compared with charge on proton ➔2 mass high, compared Y.'lth betas ----~ speed each particle 1s an electron (created when the nucleus electromagnetic waves decays) similar to X-rays ~---------~ 1 0 low ~---------~~----------~ up to 0.1 x speed of hght ionizing effect - beta particles ((i) gamma rays ("'t) --~-------- up to 0.9 x speed of hght strong penetrating effect not very penetrating: stopped by a thick sheet of paper, or by sbn, or by a few centimetres of air effects of fields deflected by magnetic and electric fields penetrating, but stopped by a very penetrating: never few millimetres of aluminium or completely stopped, though lead other metal and thick concrete will reduce intensity r deflected by magnettc and electric fields Alpha and bt!ta particle~ an: deflected h, a magnetic field (see the diagram on Lhe light). An alpha lx•anl i a flow of posiLivdy ( ) charged pa11iclc ·, ·o ic i · equivalent to an dectlic: cUt,\;llt. It is ddk-cte<l in a direction given by Flen1ing' · lch-hand rule ( cc prcad 9.5). Bcca pa11icl are mu h lighter and ha,e a nc~ativc ( ) charge, o the\ are dclle ted niore, and in the oppo itc dire tion. Being uncharged, the gamma ray · are not dcnectcd. Alpha ancl beta particle~ arc also aflectcd b\ an ck-ctric Iidd - in other- ,i..·or-ds, therL' is a force on them ii the) pa between opposite!~ charged plates. 1 Name a rad1oactrve isotope vJh1Ch occurs naturally in hving things. 2 alpha beta gamma WhJCh of these three types of rad,at,on a ,s a form of electromagnette rad at1on b carries positive charge c 1s made up or electrons d travels at the speed of hght e 1s the most ionizing very v.1ea k weak E Alpha particle arc mor,. ioni1.ing th~n beta particles. They ha\'e a grealcr charge, so exert more force on electrons. And they are slower, so spend morl! lime dost! to any clcclrons the, pass. Gamma ray arc least ionizing bcc:au ·e they ar~ uncharged. ® speed of light I I not deflected by magnetic or electric fields strong magnetic eld A How alpha. beta. and gamma rays are affected by a mdgnetic field f can penetrate a th,c: st eet of lead g ,s stopped by ; in or thick paper h has the same properties as X-rays 0 is not deflected oy an electric or magnetic field ? 3 What is the d fference between the atoms of an isotope that is radioactive and the atoms of an isotope that is not? 4 How is an ionized mateual d1fferetlt from ooe that is not ionized? Related top1~s: electromagnetic waves 7.10-7.11; X•rays 7.11; Aemtng's left-hand rule 9.5; isotopes 10 .1 229 Radiation dangers 'uclear radiation can damage or d~troy living cell" and top organ in the body working properly. ft can a]so caw e mutations (change in the genetic in ·•ructions) in cell ·, which may then grow abnormally and cuuM! cance1: .t radon gas from ground @ The greaLer Lhc inten ·ity of the ra.diacion and 1hc longer the C:\pOsurc time, the g r1:ater the d~~ T ground and b d1ngs mcd cal <ndud ng X-rays) food and drm•· cosmic rays from space nuclear test fallout nuclear power stat10rl> nudear waste other A Where background radiation comes from (average proportions) Radioacthe gru, and du tare especially danger Lb bccau e thevcan be taken into the hodv with air, food, or ddnk. Once absod)Cd, they are dil ficuh to remo\·e, and their radiation can cause damage in cell"> deep in the body. Alpha rudiation i.._ the mo~t harmful lx.->catL~ it is the mo.sc h ighl~ ioni;,jng. 1'01 rnall~, then: i muc.:h le · risk from raclioacti\c sourccsoubitle the body. u1 c in nuclear power Mation and labora101ic at~ well hicldcd, and the inten it\ of the radiation decrease ru; you mm·e awa~ fron1 the ource. Beta and gamn1a ray are potentially the mo t hannful becau e they can penetrate to internal organ ·. Alpha particle~ an: stopped bY the skin. Background radiation There i~ a small amount of r&1diation around us all tht: Lime hecau!-.e of radioacth·c materials in the en\'ironment. This is called background radiation. IL mainly con1c~ from nalurj] ·ou11.:cs such as oil, rocks, air. building m ..,ccrial , food and drink - and c\'cn ~pace. Jn ome area . • over a half of the bac kground radiation comes fron1 radioacti\'e radon ga~ (radon-222) ~eeping out of rocks - especially ·ome type!~ of grc.1nitc. In hig h risk arl.!as, houses ma) need t!Xtra undcrnoor ,·encilation lo stop the gas collcccing or, ideally, a ~calcd floor Lo stop it entering in the first place. Geiger-Muller (GM) tube This can be used Lo detect alpha, beta. and ganuna radiation. It:> t1llctu1'C i · !:thown below. The '\\indow' at the end i thin enough for alpha 1xu1icle to pa~ through. If an alpha pm1icle ente1 the tube. it ioni10 the ga in.side. Thi · ~ts off a high-voltage ·park acros~ the ga and a pulse of cun""ent in the circuit. A beta pa11icl~ or bun;I of gamma radial ion has the same efTecL ______ _____ Ge19e1-Mu .._ er tute l A This nuclear laboratory worker is about to use a GM tube and ratemeter to check for any traces of rad1oact1ve dust on her clothing Ml ( thin mica ·w,ndc,.•./ ratemeter metal tube central w,re gas (mainly argon) or sea er + 450V DC suwy ATOMS /\ND RADIOACTIVITY The Gl\1 tube can be connc-ctcd lo the following: ratemeter Thi~ g ive~ a readin g in count~ pe r se o nd. Fo1· e xa mple, if 50 alpha pa11iclcs were detected h\ rhc M tube: CH.~1~ ~eco nd, lhc: • rJ temetcr would read 50 count per ·L-cond. calcr Thi counts the total numbc r o( particle (or bur t · of gamn1a radiatio n) d etected by the tube. n a1nplifier and loudspeaker The loud~pcnke r ma ke\ a 'cl ick' \\hen each pa rticle or hu,- t of gamma radia lio n b detected . • • \\'hen the radiation fro n1 a r.ulioac ti, c source i~ m1:a ~unxl, the reading a h, ay include any bac kground radia tio n pre en c. o an a\'erage rt:ading fo r the backg ro und radia tio n a lo ne must al ·o be found and ubu-actcd fro m the to tal. Cloud chamber* Thi i u. dul for tud, ing alpha pa11icl · becau~ it n1ak~ their track~ \'i~ih1e. The chamber has cold alcohol \'npour in the nir in ide it. The alpha paT1 id es make rhe \'a pour condl.!n!-ie, so ) Oll sec a trail oft in, dro plcb \\ here each partidc pa~sc~ th roug h. Ac one time, cloud chan,bc~ \\·c1-.: widely us<.."Cl in nuclear 1't: ·enrch, but th ~~ ha\'e sin e bct:n r~pla cd by other de\'icc~. A Safety in the laboratory 0 E.xperi ments with weak. radioactive sources are sometimes carried out u, school and college laboratories. Such sources are normally sealed so that no rachoactive fragments or dust can escape. For safety, a source should be • stored rn a lead container. in a locked cabinet • picked up with tongs, not by hand • kept well away from the body, and not pointed at other people • left out of ,ts container fOI as short a time as possible. air vJ1th ~kohol vapour in ,t \Wa . ~ hP"'- -.....::..- alpha source cooling un t A Cloud chamber ® .A Tracks of alpha part1des in a cloud chamber. The colours are false and have been added to the picture. The green and yellow lines are the alpha tracks. The red line is the track of a nitrogen nucleus that has been hit by an alpha particle. 1 What, on average. as t e biggest singl~ source of bac ground radiation? 2 Radon gas seeps out of rocks uodNground. Why is it Imp01tant to stop radon collecting in houses? 3 VVh1ch is the most dangerous type of radiation a from radioactive sources outside the body b from rad1oactrve materials absorbed by the body? 4 In the experiment on the right: a What Is the count rate due to background radiation? 4J) What ,s the count rate due to the source alone? c If the source emits one type of rad1atron only, what type Is it? Give a reason for your answer. rad1oactrve source Jo lead block GM tube I □ count rate (average)... counts per second ...with the source an place ...with the source and block an place ...w,th the ~ource and block removed 28 18 2 R@lated topics: properties or alpha, beta. and gamma rad,at1on 10.2 231 r Nucleus example mass number (nucleon number): total number of nucleons (protons + neutrons) in the nucleu$ Tihesymbol system used for \ representing atoms can also be I J 2 He - - used for nuc1e, and other particles Beta particle (electron) 4 nucleons mass negligtbfe compared with a proton or a neutron \ chemical symbol fo, element \ ~f3 I relative charge 2 atomic number (proton number): also the relative charge on the nucleus compared with + l for a proton ~ or +fc I relative charge equal but opposite to that on a proton ~ If a n isotope i~ radioacti\'e, it has an unstable anungement of neutron. and pnlfons in it · nuclei. The cmis ion of an alpha or bcca particle makes the nucll!l-L._. mo ~ stable, huL ahc~ th e number~ of pro tons and neutrons in it. So it becom es the nucleus o f a different dcn1cnt. The o rig inal nudctL'i is called the parent nudcu~.Thc nudcu~ lo tmL-<l is the daughter nudeus. The daughter nuclcm, and an · emitted pa r1idc arc the dcca products. 0 Nuclear essentials Atoms of any one element all have the same number of protons in their nucleus. Elements exist in different ve~ions. called isotopes. 1For exampte, lithium is a mixture of two isotopes: lithium-6 {with 3 protons and 3 neutrons in the nudeus) and lithium-7 (with 3 protons and 4 neutrons). E Alpha decay Radimn-226 (aton1ic number 8) deca, b~ alpha emL ion. The lo~s of the alpha pa11icle lea\'e,, the nucleu with 2 proton a nd 2 neulrom, l~ . than before. So the ma:-,~ num ber drop~ to 222 a nd the a tomic number to 86. Radon ha!-. a n atomic numher of 6, so r,.ido n i~ the new clem ent fo rmed: decay 2p 2n Any one particular type of atom, for exam~e lithium-7, is called a nuclide. However the \iVOrd 'isotope' is commonly used instead of nuclide. Radioactive isotopes have unstable nude,. In time each nucleus decays (breaks up) by emitting an alpha or beta particle and, in some cases, a burst of gamma radiation as well. 232 .- Alpha particle (helium nucleus) p = ptOton rad,um-226 nucleus radon- 222 nucleus (parent nucleus} (daughter nucleus) helium-4 nucleus (alpha particle) decay products • n a m~utl The de av proce can be \\Tittcn a a nuclear equa tion: 2i~Ra ~ 2;;. Rn During a lpha deca~·: of Lhe equal io n • Lhc to p numbers bala nc;c on ho th side~ • ( 226 222 + 4) , s o the m ass number is conscn·L-<l (unc hanged) the boHo m nu,nbcrs bala nce o n both ·ides o f the equatio n ( 8 86 ,- 2), o c harge i · con c1,·cd • a nc\\ cle ment b formed, \\ ith an atomic number 2 I~ The n1ass numher j 4 le~:,, than before. than before. ATOMS AND RADIOACTIVITY E Beta decay Todinc-131 (ato mic nun1bcr 53) d ecay · by beta cmi. ion. \ \'hen thi happens, a neutron ch,mgc~ into a proton, an electron, and an uncharged, almm,L ma..._s]cs~ rclati\·c of thi.! electron called an anlincuu·ino . Thl! clcclron and antineutrino leave the nucleus al high ~pced. ~ a pro Lon ha~ replaced a neutro n in the nucleus, the atomic number rise · to 54. This me-an · that a nucku<i o t xcnon- 131 has lx..--en (ormcd: Alternative names atomic proton !ia number number mass nucleon number number 0 _. . anuneuttlllO decay ) -- --·---.. - iod oe- 131 nudeus xenon- 131 nudeus e ecuon (beta particle) ~ay products E The c.h:ca~ procc ·scan be wrillen as a nudear equation: I BI 5J ➔ Ill ,q XC 0 •I ~ ( 1 .: antineutrino) During thi t~pc ot beta decay: • • • the top numb •1· balance o n bo th ~idt.."S o f th e <.."(Juatio n ( 131 131 0 0), so the ma!-is number is con~crn:d thL' hoLtom number~ balance on bo th side~ o[ the equaLio n C- 3 54 - l 0 ), ~o c harge is con~er\'cd a new clement i ta nned , " ith an ::uo mic nurnbcr 1 n1o rc than bdo re. The ma number i unc han g:lxl. Gamma emission \Vith o ml' i o to pl: . th e cmi~ io n of an alpha o r beta paniclc fro m a nuclcu leave the proto n~ and neut ron~ in an 'c'\citcd ' a n -angcn1cn1. A~ the pro ton nnd neutrons rcan11ngc to b x;ome mo re Mable, they lo c energy. This is emitted as a burs t of gan1ma radiation. • ®0 Cam ma ~mi~~ion b! itself cauM.."S no c-hangl! in n,a ~ number o r ato mic number: Tit e following equation represents the radioactive decay of thonum-232. A, Z. and X are unknown. : Th ➔ 1 :X + ~,x a What type of rad1at1on ,s being emi tted? b What are the values of A and Z? c Use the table on page 244 to decide what new element 1s formed by the decay process. d Re\-'mte the above equation, replaong A. Z. and X wath the numbers and symbols you have found. e What are the decay products? 0 0 Beta and beta l here asa less common form of beta decay, in which the emitted beta particle is a positron This is the antiparticle of the electron, With the same mass, but opposite charge ( 1). During this type of decay. a proton changes into a neutron, a posi tron. and a neutrino. The element formed has an atomic number one less than before. To distinguish the two types of beta de<:ay, they are sometimes called beta- decay (electron emitted) and beta• decay {positron emitted). When radioactive sodium-24 decays. magnesium-24 is formed. The foUov.ing equation represents tie decay process. but the equation is incomplete: 2.1 11 Na ➔ 2tl 12Mg Assuming that only one charged particle 1s emitted: a What is the mass number of this particle? b What as the relative charge of this particle? c What type of particle 1s it? Related topics: nuclei and isot opes 10.1; alpha, beta, and gamma radlat lon 10.2: more on beta decay 10.10 Radioacth'c decay happen · spontanL'Ou~l~ (all by it ·df) and at random. There is no way of predicting when a pa11kular nucleu will di intcgralc, or in which direction a particle\\ ill be emitted. A1 o, the pt c~ b unaflected bv pre · Ul't', temperature, or chemical changt:. llowe,e1; omc type_ of nucleu are more un table than othe1 and deca~· at a fa~ter rate. Rate of decay and half-life lodinc-131 is a r.ulioacti\'c i otopc of iodine. The cha11 below illustrate the dec-av or a ~rnplc of iodjne- 131 . On average. 1 nucleu~ dbintcgrat1.: ~ C\'el") econd for every 1 000 000 nuclei pre ent. e 1 m hoo undecayed oucle1: K>dine-131 40 m lion undecayed nucfet Q 1 mil1on daughter nude1: xenon-131 S mlhon undecc:1,.ed nuclei 10 m.ll1on und<"Cayed nuclet 20m1I on undecayed nuclei I - - - - ■ I I■ I ■ I ■ I I I ■ I I I 1..------------vhme ..-----------+-----------. 8 days 16 oa~ 24 days I O I tlalf-hfe hc1lf-l1fe ha f-hfe To begin with, there are 40 million undeca,·ed nuclei. 8 day~ later, half of thc!>C ha\'e disintegrated. \Vith 1he number of undccayed nuclei now hal\'ed, the number of di~1inLcgr-L1ti.ons over the next 8 da)~ h, al"i<> halved. It haln~s again o\'cr the nc:<L <lay~... and so on. Jodinc-131 has a half-life of days. The half-lifo of a ra<lim.n:Lin.• i~olopc is 1hc time Lakcn for half the radioactive isotope half-life boron-12 0.02 seconds radon-220 52 seconds n udei prc~ent in ..u1, gi\·cn sam pll· Lo <leca,. The h .. If-lives ot ·on1c other radioactive isotope arc given on the left. It might ccn1 trangc that there hould be any hort-lived isotope till remaining. However, omc arc radioactive daughter of long-lived parent-. while others are produced artificially in nuclear reactor ·. 2~ minutes 3.8 days Activity and half-life radium-226 carbon.14 rn a radioa ·tiYc sample, the average number of disin1egn1tions J'>t!l" sc ond i~ called the activity. The I unit of acti, ity is Lhc becquerel (Bq). An acli\'ity of, say, 100 Bq means that 100 nu lei an.: d~intcgrating pcrsc ond. 5730 years plutonium-239 24 400 years uran,um-235 uranium-238 234 rs 7. i 9 4.5 X 10 years The graph at the top of the next page ho\\ ' how, on a\'cragc, the activit\' ot a ample of iodine-131 \atie with time. As lhe activity i alwav proportional to the number of undecayed nuclei, it too halve C\'ef) days. o ' half-life' hus another mt!aning as well: The half-life of a radio,1ctin: bolOf>': is the time taken for the uctivity of any gi\'cn ...,ample lo foll Lo halt its original value. ATOMS AND RADIOACTIVITY ◄ Radioactive decay of ,od,ne-131. 40 todine-131 has a half-hfe of 8 days. From any point on the curve, it always takes 8 (days) along the time axis for the activity to halve. s o-i-------+---------4-----t-----o days 8 16 24 \_..__ _ _ _...,,A..__ _ _ _...,,A...___ _ _ _ _ _,1 y i y half-Me hal •hfe half-I,fe t11ne/ To obtain a graph like the one abo\e, a Gl\1 tube i u ~d to detect the p~u1ick cn1itted b, the ample. The numbcrol count per ~cond re orded bv the ratcmetcr is adjuMed lo allow for backgro und radiation (E) (sec spread 10.3). Th .. o.djusted figure is pmpo11ional to the ac thity though not c..~ual lo iL , bccau~c not all of the cmiHed par·Li ck~ arc dctc te<l. A Rad10act1ve decay is a random process. So, ,n practice, the curve is a 'best f1t' of points which vary irregularly like this. T Stability of the nucleus E In a nucleu~. some pro portions or neuLrons to proton~ an.: mon.: stable than other .·. If the rlumbcr of r1cutron · is ploLLL-<l again~L the number o( proton for all the diflercnt isotopl: · of all the clc,nenL-;, the general (o n11 or the graph i a ho,,11 on the lig ht. It ha the e reatu1 ~ : stab 11y lne- v\ ~1 ~ C .... 0 • • table isotopes lie along the sta bility line. Isotopes above the .stabilit) line ha\'C 100 man~ ncutr·ons Lo he s1able. They deca~ b, bcLa- (electron ) emission because this n.:<lucc~ the number o f neutron~. J ·otope · belo,, the tability lint: have too le,, neuta·o n to be ·table. The, deca) b) beta+ (po itt'On ) emi ion bccau c thi increa e the number o f neutron . The hea,ie~t i ·otope (proton nun1bcn, - 3) de ay b\' alpha e n1i ion . • • 20 40 60 80 proton number ® To answer questions 1 and 2, you will need information from the table of half-lives on the opposite page. 1 If samples of stront,um-90 and radium-226 both had the same activity today. which would have the lower activity in 10 years· time? 2 If the activity of a sample of ,odme-128 is 800 Bq, wha t would you expect the actMty to be after a 25 minutes b SO minutes c 100 minu tes? 3 The graph on the right shO\vs hov., the activity of a small radioac tive sa""ple varied with time. a Why are the points not on a smooth curve? b Estimate the half-life of the sample. Related lop1cs: nuclei an d Isotopes 10.1: GM tube 10.3 c:,a) ■ ■■■■■■ ■■■■■■ ■■■■ t me/ hours 100 Nuclear essenti als 0 \Vhcn alpha or beta particles are cmiucd b~ a n1dioaclin: isotope, the~ collicll' with surmun<ling atoms and n1akl' them mo\'e faster. In other words, the tcmpl'raturL' rise· as nut:lcar cnerg~ (potential enl'l"g) storl'd in the nuclcu~) b translormc<l into thennal cner~ (hear). Atoms of any one element all have the same number of protons in the nucleus. If this number is altered in some way. an atom of a completely different element is formed. Elements exist in d1fferent versions, caled isotopes, with different nllTlbers of neutrons in the nucleus. Radi~ isotopes have unstable nudei In time, these decay (bre up) by emitting one or more particles and, in some cases. gamma radiation as well. Jn rndioacth·e deca\', the ene1'g\ released per atom b around a 111illion times gn:alcr thun thal from a chemical change such a!') burning. However~ the raw of de(."ay i~ U"iuall, \'t!I') slow. Much frL,tc1· de<.11~ can hapf>'!n if nuclei an: rnaclc more unstable by bombarding Lhem "ith neutrons. \Vhcncn:r a parLiclc pcnctratL'S and changl'S a nudcu ·, this is called a nuclear reaction. E Fission atural w·anium i ' a dcnM-' radioacth·t• mclal con~i Ling mainl) of cwo i otop~: uranium-23 (o\'er 99' c) and uraniLm1-235 (le s than 1lJ~). The diagram below show!', whal can happt.:n if a neulron oike and penell«le., a nucleus o1 uranium-235. The nudeu~ becomes highly un~table nnd split:,, inlo Lwo lighter nuclei, shooling out two or rh~c neutrons as it docs M">. The splilting prcx:ess is called fission, ancl the fragment:,, an: thm,\ n apart as cnl'JID i r~lca.,l'cl. lf Lhe t:miucd neutron.~ go on Lo ~pliL other nuclei ... an<l so on, Lhe t~-sult i ' a chain reaction, and a huge and rapid t\!leasc of energy. I ► A chain reaction. A neutron causes a uranium•235 nucleus lo split, producing more neutrons, v.ih,ch cause more nuclei to split ... and so on. - • shield peor\fe from direct • • Concrete. steel. and lead shielding reduce radiation, and radioactive materials are kept in sealed contailers to prevent gas. dust. or liquid escaping. .......... ............ --. stray r utron / neutrons ..,. ........_ I-" nuclear radiation keep people's time of exposure to radiation as short as possible prevent radioactive materials from getting into the body. ~ .. . ./ Nuclear pO\Ver stations have safety procedures to c/'••/ • . . . .. _ -✓ c ·~ ___C c✓ .~ .........__ ~ " -• ........_ ~ - • --·- " -• '--.. E For a chain reaction to be maintained, the uraniun1-235 h.._, · to be abo\'~ a , othcr,d~e too man\- neutron~ cM:ape. In the At t aton1ic bon1hs, an un ontrolled chain reaction was stm1ed b\' bringing two lump~ of pure uninium-235 together-so that the c1·itical mas was exceeded. In pt-cscnt•<la~ nuclear weapons, plutonium-239 is used for ris:,,ion. ce11ain critical ma Fission in a nuclear reactor In a nuclear reactor in a nuclear power cation, a controlled chain reaction takes place and thermal energy (heat) i~ relca~d at a ~te~d) rate. The energv is u.~ed 10 mukc st1.'am for the turbine , ~ - in a con,·entional power ~tat ion. In man\' r\..'acton., the nudcar fuel is ur,mium dioxide, Lhc natunil ur~nium being emiched \\ ith cxtrJ w--aniurn-235. The fud i~ in M:aled cans (or tu~~). ATOMS AND RADIOACTIVITY Maintaining the reaction • To mainLain the chain reaction in a n:actor, I he ncut rons have to he slowed do\\ n, otherwise man) oft hem g el control rods ah ·orlx.id by tl ~ uraniuni-238. To low them, a material called a moderator i~ needed. Graph_itc i u cd in omc rcactot , water in other . The rate o( the reaction i · controllL'<I b~ rai ing o r lowcting control rods. These contain boron or cadmium, n1atcrials "hic h ab~orb neutrons. not Nuclear waste* After a fuel can ha"i been in a reac tor fo1- thn.!" or four) cars, it must be re moved and •~placed. The an1ount of uraniuni-235 in it ha fallen and the n ion product at' building up. l\.1an, of the c product arc thcn1~cl\'e radioacthc, and tar too tiang~rou · to be rclea ·cd into th~ en, iro nment. The\ indude tht: [ollo\, i ng isotope~. 11one of which occur natw~ll). trontium-90 and iodine- I 31 , which an: e,L"iil~ ab orbed b) the bod,. trontium becomes concen1raw<.I in the bonL-s; iodine in the thyroid gland. Pluto nium-239, which i p1oouc<.id when uranitnn-23 i bo rnban.Jcd hy neutro n . It i it ell a nuclear fuel and b u 'din nuclear weapo ns. It i al ·o highl) to:\ic. Ba ·athcd in a dus t, the ma llL-st a mo unt can kill. • • Spent tuel can · arc taken to a r--cprocc • ing plant \\ her--c unu&'<I tucl and plutonium are 1~mo,·cd. Tht: remaining waste, now a liquid, is scaled off and stored wiLh thick shielding around it. Some of the isotO('X>-s hmc long half-li\'cs, so safo Mo rage \\'ill be needed for thousands of year~. The problem of Anding acceptabl" it~ for long-term stor-age ha~ till not be "n soh·cd. Energy and mass A A pressurized water reactor (P'NR). For safety. the reactor is housed inside a sealed containment building made of steel and concrete. (£) According Lo AlbcrL Ein tcin ( 1905), enea-g) ilSelt has ma~·. I f an o bject gains cnerID, iLs ma~s increases; if it lose~ energy, iL~ ma. s <lcc~a."i.Cs. The mtL,"i chang~ 111 (kg) is linkt..-d lo the energy chang~ E (joules) by this equation: I • £:: (where c i the pc "d o f lig ht , 3 x I 0~ m/s) The\ aluc of c 2 is so hig h that cncrgv 1:,111incd or losL b) c\'cry<lay o bjccL"i has E a negligible effect on their mass. Howc,cr; in nuclear reactio ns, the encrg\ c hange · per aton1 m "much largcc and produce detectable ma. change ·. Fo r c"an1plc, when the fi ion produc t ol uranium-235 arc lowed down in a nudearreactoa~ their to tal ma~s i ' ioLmd to be reduced b~ abo ut O.l ct. ® 1 The high temperatures deep underground are caused by the decay of radioactive isotopes in the rocks. \'\thy does rad oactive decay cause a rise in temperature? What is meant by a fission b a chain reac tion? 0 0 Give one exarr pie of a a controlled chain reaction b dn uncontrolled chain reaction. 4*a Where does plutonium-239 come from? b Why 1s plutonium-239 so dangeroos? 5 In a typical fission process, uranium-235 absorbs a neutron. creating a nucleus which splits to fOfm barium-141, krypton-92, and three neutrons. neutron uranium-235 nucleus banum-1 4 1 nucleus krypton-92 nucleus mass/kQ 1,674 X 10 17 390.250 233.964 152.628 X X X 10 27 27 10 27 10 E) The reaction can be represented by this equation: A B C B inU r/l ➔ ~ Ba -Kr + 3on Copy the equation. replacmg A, B. C. D. and Z Wlth the correct numbers. (:) From the data in the above table, how could you tell tha t energy is released by the reaction? R@lated top1cs: energy 4 .1; power staUons 4 .5- 4,6; radlal aon dangers 10.2- 10.3: radloacttve decay 10.4- 10.s : half-life 10.s : fissiOn reactton 10.7 A The steel flasks on this train contain waste from a nuclear reactor 0 Nuclear essentials The nucleus of an atom is made up of protons and (in most cases) neutrons. Each element has a different number of protons in the nucleus of its atom. The lightest element, hydrogen has just one. E l n I he nucleus of an atom, the proton~ and neutrons arc hdd tightl~ rogcthc...·r b~ a force called, simply, the strong nuclear force. Howe\'cr. in omc nuclei, thcv are more tightly held than in othe1 . To get nuclei to release energy, the trick i to n1ake the proton and neutron regroup into more tightl~· held an-angement than beto,·e. Pr-uton~ and neutron. in 'middleweight' nuclei lend to be the mo ·1 tight!) held, ·o plitting very hem .· nuclei releases energy: thal happt!m, in nuclear fission. Howcn.!r, energy can also ~ rclca.-.;c<l by [using (joining) \'Cf'Y light nudci together to make hca\ icr one . This i · called nuclear fusion. H i~ the process that powc1 the ta1 . One day, it n1ay d1ive p<)\\Cr tation on E •.uth. I 1 hyd rogen-2 hydrogeo-3 Elements exist in different version5, called isotopes. These have different numbers of neutrons in the nudeus. fusio n 0 Hydrogen Hydrogen 1s the most plentiful efement in the Universe. The Sun is 75% hydrogen. There is also lots of hydrogen on Earth, though most has combined With oxygen to form water (H20). Most hydrogen is hydrogen-1 . Hydrogen-2 (also called deuterium) and hydrogen-3 (tntium) ate much rarer forms. l + energy r,eu tron E The diagram alxn e shows the fusion of two hydrogen nuclei to form hdiun1. Fu~ion i"i di fficuh to achic\'c be ausc the nuclei arc charged, and repel each othc1: To beat the ,~pul ·ion and join up, they must travel \'c~ fa l - which mean · that the...- gas mu~t be n1uch hotter than ;._tn) temperature~ no1111alh achic\cd on Eaa th. Building a fusion reactor cienti and enginee1 are tryjng to de ign tu ion reactor lor u~ a an energy ::,ource on Em1h. But there are huge problen1 to O\'ercon1e. Hydrogen mu t he heated to at least 40 million degrees Cclsiu ·, and kept hot and compressed, othcn,~sc fusion stops. No ordinal) container can hold a supcrhot gas like this, so ~cicntists ar~ <le\'doping 1~actors that tr<.1p the nuclei in a magnetic.: fidd. t Fu ion react01 will have huge advantage over toda,' fi ion reactm . They ,\ill produce n1ore energy per kilogram of fuel. Their hydrogen fuel can he e , tracLe<l from st'a water: Their main waste prcx.lu ·t. helium, b, not mdioactin:. And the~ ha,·c huih-in safely: if the syslcm faib, fusion Mop~. A This magnetic containment vessel, called a tokamak, 1s being used to investigate fusion Fusion in the Sun The un is a star. Like most other star ·, ii get~ it encit-1)' from the fusion of hydrogen into helium. Deep in its core, the hl'al ourpul and hug~ gr-a\itational pull keep the lndrogen hot and comprc ~ ·cd enough to maintain fusion. It has enough hvdro!!en leh lo keep jt shining lor another 6 billion ycm ~. ATOMS AND RADIOACTIVITY IF usion in the Sun's core The Sun is 73% hydrogen and 25% helium. Energy is released as hydrogen is converted into helium. • • hefium nucl~ + other particles hydrogen nude, Four hydrogen nuclei fuse together for each helium nucleus formed. This is a multi-stage process which also involves the creation of two neutrons from two protons. I n the un, f u~ion happc:ns at •only' 15 million <lcg rc:cs Celsius. But the un u ·c di(lcrcnt fu ·io n reaction fro1n those being tiied on Earth. If the un were calcd down to the i1c or a nuclear 1 · ac to 1~ it power output would be loo low lo be u cful. Fission and fusion compared Here i~ at) pical fi ·ion reaction n:actm-: or the type that happen in a nuclear A ncu1ron hiL~ a uranium-235 nudeu~. ,,hich ~plits to ro1m two lighter nudei and L,,o nL'utrons. The c:ncrg) rdca.~cc.l per atom is about millio n titncs g~atcr than that per atoin from a c hemical reaction such a bur,iing. In the fus ion procc s on the oppo~itc page, two rare f onns o f h\'drogcn nuclei c ollide and combine to form a helium nucleus: -,.. H 1H I 1 - > 4H 2 e or'\ A Present day nuclear power stations all use fission in their reactors. Fusion is for the future. Althoug h the energy t~lca cd per fu · io n b le · than lCY t o f thac fro m a fi ion reac t ion, fu~i on (a in the example abo\'c) i a much better energy ourcc if the procc s ' S arc compai·ed per kilo~ra111 o f niatctial. ®0 0 0 Splitting very heaV'/ nuclei to form lighter ones. Joining very light nuclei to form heavier ones. a Which of the above statements describes wha t happens during nuclear fusion? b What process does the other statement describe? What advantages will p0\1\/er stations wi th fusion reactcxs have over today's nuclear power stations? Why have fusion reactors have been so difficult to develop? 0 Nuclear reactions are taking place in the Sun's core. a What substance does the Sun use as ,ts nuclear fuel? b What 1s the name of the process that supplies the Sun wi th its energy? c What substance is made by this pmcess? s• Comparing burning, nuclear fusion, and nuclear fission, which of those processes yields a the most energy per kg off uel b the least energy per kg of fuel? Related topics: gravity 2.9; power stations 4,5; energy resourc~ 4 .7- 4 .8; atoms 10. 1; nuclear flss1on and energy 10.6 239 Nuclear essentials Elements exist in different versions. called isotopes. For example, lithium is a mixture of two isotopes: lithium-6 (with 3 protons and 3 neutrons in the nucleus of its atoms) and lithium-7 (with 3 protons and 4 neutrons). Radioactive isotopes have unstable nuclei. In time each nucleus decays (brea s up) by emitting an alpha or beta particle and, in some gases. a burst of gamma radiation as well. In a radioactive sample, the number of nuclei decaying per second is called the activity. Radioacti\'c isotopes m't: called radioisotopes (or radionuclides). omc arc prcxluccd a1 Li ficiall) in a nuclear reactor\\ hen nuclei absorb neutron · or gamma radiarion. for example. all narural cobalt i cobalt-59, ,, hich is stable. II cobalt-59 ab orbs a neutron. it become cohalt-60. which is radioacth·e. Here a~ some of the practical uses of radioisotopes. Tracers and treatments Radioisotope~ can be detec1~d in very small (and ~re) quantitjcs, so the~ can be u~d as tracers - their mo\'cmcnts can be tracked. E.xampk"'S include: • Checking the function or bod} organ~. Fo1 c,amplc, ro check th) 1oi<l (unction, a patient drinks a liquid containing iodine- I 23, a gamma cn1ittc1: Over the next 24 hour.-., n detector rnea~ure the acth itv of the tracer 10 find ouL how quickly it become · concentrated in the lh)roid gland. • Tn1cking a plant's upLake of fortilizcr f ron1 rools to lca\'es by adding a tracer to the ·oil \\ ate 1: • Octcctjng leaks in underground pipes b~ adding a 1racer ro the fluid in the pipe. Forte ts like tho e above, artificial radiobotopes with !-,hart half-li\'CS arl! used ~o that Lherc i~ no derectahlc radiation afll!r u few day~. Gamma rays are very peoetrat,ng. beta particles less so, and alpha particles least of all Al three types of radiation damage or destroy living eels if absorbed. gamma camera m use. The patient has been injected with a liquid containing weakly radioactive technetium. The camera above her will pick up the gamma rays from the tracer and form an X-ray-type p,c.ture of her kidneys. ►A E In a hospitul, a gan1ma camera like the one in the photograph above may be w.;cd to detect the gamma rays t'oming from a radioaclhc Lr~ccr in a patient's bod~. The c-c1mcra farms an image sim ila.r Lhat produ LIC.i b) X-rd~'S. Jn one form of radiotherapy. gamma n1diaLion is used 10 kill cancer cells. ll can pcnetrc1te the hod\ lo reach a tumour. And by using several beams coming from different di1~clions, thdr energ can be conccntr••,ted at one point. 240 ATOMS AND RADIOACTIVITY r Thickness monitoring Tn ~onic produc lio n procc C.!-. a ~l !ad\' thic kne s of n1a te ti~I ha · to b ~ m a intained . The di agr am bdo\\ sho,,s o ne wa) o f d o ing thb. beta source ◄ The moving band of tyre cord has a beta source on one side and a detector on the other. If the cord from the rollers becomes too thin, more beta radiation reaches the detector. This sends signals to the control unit, which adjusts the gap between the rollers. rollers tyre cord control unit E Gamma irradiation o mc food-proce:'i ing facto1i c Lt>C ga mma inn diation cha mbct to kill ba teria (and ma ll in~cl~) in food. The gamma ray pen ~tratc deep into the food. And \\ilh lhc bacteria killed , the food kt.-cps lo ngcr,,ithou1 m uing. Medical in~trumcru~ can be ste rili~etl using the s ame mcLhod. Coba lt-60 i u cd a the gamma t'a\ o u1 c . It ha a ha lf-life ol ju t O\'er fh·c vem a nd n1u t be r placed before it weake n too much to be cite ti\'c. Smoke detectors A mo kc dctcclo r can g ive vo u a n ~ l wa n1ing o f a fire. It i d e ·igned to trigger a , c11 lo ud ala rm whe nc\'er s m o ke pa n icle~ e nte r it. It wo rk~ like this : In the d e tecto r, there arc two mecaJ pla te · \\ith a voltage aero ·· them. Between the plate , the re i a \ 'CJ') weak o urce o [ alpha partick · (an1c ti ci um-241 , half-Jil c 432 vca1 ). Thc_c io nize the a ir: the io n ~ 111 0 \ 'C b •tw •en the pla l~~. o a mall current alway flo w . H o wcve1·, ii m oke pa rticles enter th e c ha mber, the ion~ a uach to them . Thi~ r xluccs the c urre nt and 1riggcrs the a la nn. A A smo e detector contains a very wea radioac.tive source. Testing for cracks Gamma n1y~ hm·e the s.amt: properties as s hort-wtl\'dcngth X-rJ.)~. so the) can be u l.x.l to pho togri,ph m etal~ to 1-c\·eal cracks. A cobalt--60 gamn1a o rn-cc- i compact a nd doc no t need clccuical power like a n X-ray tube. ® ~ a What are radioisotopes? b t ow are art1hc1al radioisotopes produced? c Give r,110 medical uses of rad101sotopes. E) In the thickness morntoring system shown above: a Why is a beta source used. rather than an alpha or gamma source? b What is the effect on the detector ,f the thickness of the tyre cord increases? 0 a Give rwo uses of radioactive tracers. b Why 1s ,t important to use rad1oact,ve tracers With short half-lives? In an irrad1at1on chamber, why are gamma rays rather than alpha particles used to kill bacteria in food? b Give one other use of an iuad1atioo chambet. c Give one otter use of gamma radiation. Oa R@lated top1cs: X-rays 7.11; alpha, beta, and gamma rad1at1on 10.2 10.3; radk>active decay 10-4- 10.5; half-life 11.0 5 241 electrons E Atom - an: made up or eYcn smaller particle . Fmm C.:\'PCrimcnlal C\idence collt!Cted C>\'<!r the pasl hund~d years, sdenl isl~ han! been able lo ch!\·c1op and irnpro\ c their moclds (descriptions) of atoms an<l the partides in them. Thomson's 'plum pudding' model + + A Thomson's 'plum pudding' model of the atom The electron was the first atomic pa11ick 10 be discovered. l l was identified b) J . J. Thomson in I 97. The electron has a ncgati\'c ( - ) clectlic charge,~ an atom" ith electron in it n1t1 t abo contain positi\'c ( • ) charge to make it elecllically neutral. Thom~n ugge ted that an atom n1ight be a phcre of po itin! chnrgt: with electrons dotted about im,idc it rather like rai ins in a pudding. This lxcamc knows as Lhe 'plum pudding' model. Rutherford's nuclear model beam of alpha ~r· tC'es movable Rutherford 's explanat ion detector - - - - -+ Most aJpha par•,des are uooeflected A few alpha par IC.le~ are voewm deflected slightly / undeflected ~hght I~ deflection deflection A 'e-w a pha partl(les bounce off nucleus E The ahon! expcrimenc \\~L._. carried out in 191 1 by Geiger and Mar.-,<lcn under the supervision or Ernest Rutherford. It produced results\\ hich could not be cxplainL-<l b) the plum pudding model. Thin gold foil was bmnb:udcd \vith alpha patticlc -, ,,hich arc posiLi\'cl) charged. Mo r pa~~ed traight through the gold atom . but a few were repelled o trongly that they bounced back or were denccted through large angles. Rutherford concluded that the atom mu ' l be largely emply pace, with its pm,ili\·e charge and mosl or its ma~s concenlraled in a tin\' nucleus at Lhc centre. In his model, the ,nuch lighter dcctrons orbited the nucleus 11.nhcr like the planet · around the un. ++ + ++ + Discovering particles in the nucleus* ele<trons .A Rutherford's model of he atom: electrons orbit a central nucleus, (If the nucleus were correctiy drcJWn to scale, it would be too ~mall to~-> Ruthc1ford's model said nothing about what \Va in idc the nuch:us. However, in 1919, Rutherford bon1barded nitrogen ga with fa t alpha particle and lound lhat po ili\'el\' charged pnt1icle ~ were being knocked out. Th~e were protons. In 1932, James hadwick di co\'ered that the nucleus also contained uncharged particles with a simila1~ ma"is l<> protons. He called thc~c neutrons. ATOMS /\ND RADIOACTIVITY 0 The problem of spectral lines* Light essentials Light 1s one type of electromagnetic r adiauon (electromagnetic waves). The colour seen depends on the wavelength of the light. lig ht come · fro m a toms. The pe trun1 of white lig ht is a continuo u range of colo ur from red (the lo nge~t wrn ·d c ngth ) to violet (the s ho rlc~t). Ho wever, not a ll spt.-ctrn a rc like this. Fo r example, if there is an dec t1ic disc ha rge thro ug h hydrogen, Lhc g lo \\in g gas emiLs particular \\a\dcngLh o nJ) , o the !)pc t: L11.1m i · m ade up of lines, a s ·ho\\ n belo w. A ' it tood , Ruther fo rd's model could not c,pl::,in \\h) ~pcct1-a like thi occu n~d . To o lve thi problen1, the m odel had to be modified. ◄ Part of the line spectrum of hydrogen. Each line repre~nts light of a particular wavelength. shorter...............................................wave Ieng th .................................................longer The Rutherford-Bohr model* I n l 9 13, i\cils Bo hr mcxlific<l Rutherford's model by appl~i ng th e quantum theor dcviM--<l b~ ~1a., Planck in 1900. According to this ttu:ory, cncrg) canno t be dh ided into c, er 1na llcr amo unt ·. It i o nl) cn1iucd (or a b~ rbc.:d ) in tiny 'packet ', eac h called a quantum. Bohr reasoned tha t electro n:-, in high ' r o rhits ha\·e n1ort.! energy tha n th o~ in lower o nes. o, if o nly qua ntum encrg) change a n! possible, o nly certa in el ~ctm n orbits are a llo wl'd . This modi ficcl mod el is kno\\"n a~ the Rutherford-Bohr model. sing the modd, Bohr \\11 a ble to c ,'J)lnin ,, h~ a to m e mit lig ht o f p ar1ic ular w,wdcng1h~ o nl~ (see 1he ne°'t s prea d ). He e\'en pr~di ctcd the position~ of the lin~ in the SpL'Cttum of h\drogcn. Howl'\l'r, his calcula tio n.... <lid not wo rk fo r ·ubstances with a mo1~ complicated elec tro n s tn.1 lure. To d eal ,, ith thi problem, scicntjscs ha, c d e\'clo pcd a , ave mechanics rno<lcl in \\ hich allo wed 0 1 bit ai " 1cplaced b'!. allo\\ cd energy levels. Ho,\c\·c1~ thi i ~m cnti1 "ly ma thcn1a ticJI nppronch, nnd the Rut hc1fo rd-Bohr n1odcl is till u ~d a~ a wa~ of representing atoms in picture~. ele<trons • The Rutherford-Bohr model of the atom (Wlth nuclear particles inchJded). In this model, only certain electron orbits are allowed. ® ~ What is the difference between Rutherford's model of the atom and Thomson's 'plum pudding' model? Z- What is the difference between the RutherfOt'd-Boor model of the atom and Rutherford's model? On the nght, a beam of alpha particles 1s being directed at a thin piece of gold foil. How does the Rutherford model of the atom explain why a most of the alpha particles go straight through the f0tl b some alpho particles are deflected at large angles? Why do the results of the experiment on the right suggest that the, ucleus has a positive charge? gold f01 0 0 Related topics: light waves 7.1 and 7.10; spectrum 7-4; electric charge 8.1-8.2; partk:tes 1n the ato m 10.1 243 How an atom gives off light If an electron gi'! ns energy . Boh 1 \ c,p1analion ol how an a Lon, gi\ c~ of[ lig hL wa.... like lhi!!.. If an electro n gain~ energy in omr \\'a\ - for c,amplc, becau c it~ atom collide~ \\1th anoth~r one - it ma,· jump to a higher ·nerg) lc,·cl. But the atom do ~ not Hl) in thi~ excited stale for long. on, I he •k-ctron lo. cnl'rR' bv <ln>pping back 10 a lower lc,d. A · ording lo the quanLum Lheon, the encrg, is rndiat<:d a., a pul~c of lig hL called a photon. The g reater th<: cncrg~ c han ge, the sh011er the \\c1,deng th ui the light. W~n the electron d ops back to a lower level .. As a ]inc spectrum contain~ particular wa\'clcngth.., onh. it pro, idc~ c, id<:ncc Lhar onlv c.:crtain cnerg, change~ al\.' occ.:urring wilhin the aLom - ~,nd theL~fore that onlv certain cncrg~ lcvds an~ allowed. .. a photon ~ em1t•ed • A How an atom gives off light Fundamental particles A fundamental particle i, one,, hich i.., 1wJ made up of other particle.... An atom i~ not fundamental b~causc it is made up of dc<:tron.,, proton~. anc.l neulron~. Bul arc thcM: f un<lamcnlal? Tu an!-1\\'<:I* this and other queMion...,, cicnti h c..un· out c:'\periml'nl~ \\ ith particle accelerator . The~ hoot beam~ or high-cncrro pa11ick ( uc h a · proton~) at nuclei. or mother beam , and detect the pa11ide~ enPrging lr ni the collbion.... In collidc1 t.·x~dn1cnt • new pa11ic k are crc:accd m, "n "l'g\ b con,·'"'"rt<..xl into ma..,~. HO\\C\Cr, most of thc:-;c partick~ do nol c,i. tin the atoms or ordinan matter. ► One ot the g ant detectors surrounrnng part of the Large Hadron Colhder at CERN near Geneva. Hadrons are a family of particles whrch includes protons and neutrons In the collider, beams of protons are accelerated by electromagnets round a circular path 27 km long, then made to collide head-on. 0 The Higgs particle Amapr success at CERN, in 201 2, was the discovery of the H,ggs pa rt1de. long Pfed,cted by the Standard model, thrs fundament~ partide IS required to explain i.\lhy most partides have ma~. 244 The p1~:-;en1 them~ of particle~ is alll!d the ~1andard model. According to thi~ modd, elec tron!-. ar<: fundamental particle~. Ho\\ l!\'er, ncuLrons and ptolon arc made up or other part ides calk-d quarks, a~ ,ho,, n in the chart on the ncxL page. In ordin._u, matter, lhc:rc arc l\\o L\ pc o quark, called the up quark and the do, n quark ror con\'cnicrn:c . Each proton or neutron b made up ol thrl~ quar~. The quark~ ha\'~ fraclional charl!es compared with the chri rge on an elec tron. ATOMS /\ND RADIOACTIVITY fundamental particles of ordinary matter • electron -1 proton neutron This rs made up of 2 up quarks and 1 down quark This rs made up of 2 down quarks and 1 up quark I relatrve charge up quar · (u) do.Yn qua • (d) 0 0 d ota rel tive eh ,ge + 1 tota r ative eh rge 0 l ndi, i<lua l qua rks ha,·e nc\'cr been <leLccccd. The cxh,lcnce o f quarks ha · onl) been <lc<lucctl fro m Lhc paUc tn ~en in the propc c1i~ o l 0 Lhc1· particle - tor c~a mplc, ho\\ hig h-cncrg) pa11iclc a rc ~cancrcd . Quark changes in beta decay In the lTIO~ t common torn1 o l beta dcca\ , a neutron dccav to fo n11 a pro to n. a n elcclron (th • beta particle), a nd a n antinculrino: ne ulre>n pro to n + e lectro n + antineutrino lf thi\ i') r~" l'ittc n to s ho w Lhc q ua r"-s: up qu ark do,, 11 quark up qua rk ➔ up qua1 k • e lectron + antincutrino d o,,n quark d own quark Fro m the ubon·. yo u can sec tha t this L~pe of beta de ay occurs ,,hen a <lo,, n quark changes inlo a n up qu a rk, as follo ws: d o wn qua rk (- 1/3) ➔ up qu a rk e lectro n ( t 2/.,) ( - 1) Decay essentials 0 The breal-up of an unstable nucleus is called radioactive decay. During beta decay, a beta particle is shot out. In most cases. this particle 1s an electmn (- ). However. more rarety, it a positron (-f ). an antiparticle with the same mass as an electron. bu t opposite char~. a ntinc ulrin o (0) The rclati\ c c harge, underneath the equa tio n how that there c ha nge in total charge. In o ther word , cha rge i con crYcd. j n Jn the less commo n fo nn of beta dcca), a pro to n deca~!'> to fo nn a neut ron, a po!\itn>n (th e beta pai"ticle), a nd a nculrin o. This happen-.; when an up quark in the pro to n changes into a do \\ n qu a rk. ® 1 When an electron dtops back to a 1011.re, energy an an atom. it loses energy. a What happens to this energy? b If the difference between the two energy levels was greater, how would this affect the wavelength of the light emitted? c Why do atoms emit certain wavelengths only? 2 What is meant by a fundamental particle? 3 Which of the following are thought to be fundamental particles? ele<:.trons protons neutrons quarks 4 Quarks have a fractional charge. Explain why, if a neutron ,s made up of three quarks, it is uncharged. 5 In one form of beta decay, an up quark d anges into a dcNvn quark. Explain why, in this case. the beta partDCle emitted must be a positron ar d not an electron. Related top1~s: Ught waves 7.1 and 7 .10; electric charge 8 .1-8.2; particles in the atom 10.1; beta decay 10-4- 10.5 245 - - - - Check-up on atoms and radioactivity Further questions 1 electrons a nuclei protons waves Cop~ and complcLl! the follo,\ing scnlcncl!s usinu::, words rrom the abon~ list. Each \\ord n,a~ be usl'<l once, inore than once or not at all. i Radioacli\'e ub tancc ha,·e atom ,dth u n. Lab le _ _ _ _ _ _ [11 ii Beta panidc..~ arc _ _ _ _ _ [ 1l Gamma ,·a,s arc - - - - rl l b '!amt.: anothi.:r L, pL· of ra<lioacti,i.: particle not mentioned in parl a. I l] 111 2 The , rnbol ~,Cl rcpr~nt~ one alOm or chlo1inr..:. a talc the name~ and nun1he1~ of the dilfcn.mt types ol (4U-ticle lound in one of these chlo1·ine aloms. r3l b tale , ,:herc these particles an~ lo be 1ound in thi.: atorn. 12) 3 proton number 26 mass number 59 radiation emitted beta and gamma 1 The tabk· abo, . _. ·ho,\ i nfon11alion about a radioi otopc of iron called iron-59. Calculate: i the number of neuu-ons in lhc nucleus; [ 11 ii the total number of charged paa·tidcs in a single atom or iron-59. [ 11 b lron-59 and iron-56 are bulh isotopes of jron. \ \'hat a,~ i ·otopes? l 11 c Iron-59 cn1it. t" o tvpe ol radbtion. B1icny explain ho\\ Lhe gamma radiation could be separated fron1 the hcta radiation emitted. [ 1l 4 Phosph01·us-32 is a rac.lioacti, c isotopi.:. lt can be uscc.l to pro\'c that plants absorb phosphun1s trum the soil around them. a i The stable botopc of phm,phorus ha~ a ma number of 31. Sta tc the u·uctural diftc1 "ncc between aton1. of phosphorus-31 and phosphorus-32. r21 ii* Explain,, h~ both isoto()l's of phosphon.Js hm·e idi.:nti<:al chl'm ic:al properties. [ 11 b Phosphoius-32 is a beta-emitter ,.., ith a half-life ot 14 da, . [l] i \\'hat i ~• beta panicle? a ~ OUP; .. The proton nun1bcr of phosphoru ·-32 atom i • 15. SLatt: the ne,, value ol the proton nrnnbcr and n1a nun1bcr or the atom iu. t ahcr it has cmillcd a beta particle. r21 iii E:\plain what is meant by the te1111 hall-life. [ Il C A solutjon or lht.: j ·otopc is ,,ate,~d onto the soil around the plant. Each dav for the next \\CCk, a lcar i~ rcmo,·cd from the plan and IC!-itc..-d 101· rnclioacLi\'itv. i late three ·afcL\ p1·ccautions which should be adople<l "hen <loi ng e~~dJncnt · ,.., ith phosphoru -32. [ 31 ii De ri be n-.·o n1cthocb \\ hich could be llM.xl to n1ca~Ul\! the activil) of a lc~tl. r21 5 P h~ l i. in hospital. he is injected with the rc1dioisotopc tt.-chnc-tium-99m. This isotope is absorbed b, the Lh\'roid glanc.l in her throat. A rac.liat ion c.lcteclor p]ac:e<l outside her boch and abo, L' hi.:r thnK,t detects lhe radiation. Tcchnctitm1-99n1 ha. a half-life ot 6 hour~. It en1its gan1ma radiation. a \ \'h~ is an cmiUer of alpha rac.liation unsuitable? [ ll b i Ho,\ long will it take for the acli\' lt\' of the tech netiu1n-99m to rall LO 4-, q uarler oJ its original value? 12] ii Ahcr 24 hout , ho,-.. will the activitv of the h.'Chnctium-99m compare with it original value? f21 C E\'enLual I\ the le, el or 1·adiation from the Lechnctiun1-99m will lall to less Lhan the level oJ thi.: background radiataon. State nvo naturaJI~ occun·ing ource · of backgl'ouncl radiation. f 21 6 Thi. que. tion L about an accident at the Chcrnoh~ I nuclear po,\c1· station in which 1·adioacti\'l' gas and dust \\ crl! released in Lo the atmosphere. The r.i<lioaclh~ isoloJ)L-s in the Chemob\'] fallout which caused mo t conce1,1 ,-..c,~ iodine-13 1 mid cat.:, ium-J 37. Both are beta and gan1n1a E 11 th~ may be reproduced f0t class use solely f0t the purchaser·s Institute ATOMS A D RADIOACTIVITY cmitte1~. Iodine-I 31, in rainfall, ound it~ \\ay into n1ilk hut cac-.ium-137, \dth a hall-lilc of 30 )Ca•~. mav cm.L,c more long-term p1 ohlcms. a F1·om \\ hich par·t of thr...· atom do the br...·La and gamma ra, s conu~? r 11 b E~plain what the numlx-r 131 tdls ou about the io<li ne a to 111. r21 c Itc1 the Chernob) l accident. a milk sample containing iodinc-13 l \,a._ found to ha\ • an tl ti, it, of 1600 unit., pl!1 litn:. The activily of l hL' sample wa.., mca..,urcd c, en 7 day-. and thc n.·sull~ a,~ ~ho\\ n in the table bdo\\. time/days 28 activity/units per htre 140 77 35 Draw a gr..1ph ol ac.:tivity again ... t time. 121 using the gtid bdow as a guide. ii E ... timatc the halJ-lile of iodine-131 and ~how on the graph how )OU a1Th...-d at your n n," er. f2 I 1 6oo 200 000 un tsJ: trc ----- -.,-·-0 10 20 30 40 l mrf d Y5 d Gi\ L' a reason wlw c.:aesium-137 could c.:aust• longer-te1 ·n, problem~ than iodine~l 31. 7 a 8 Thi.., question i~ about info1n1ation in a leaflet. radioactive. ii E\'.plain th1.: clan ~·.- of breathing radon ga-.intothclungs. [41 Extrac t 2 is a diagram showing how radon 200 0 i ~ame the pa11ide [ 1] ii ' l ' thl' inlormation given in the t."ql:lation abo,c to find the I total nun1hc1 of c.hatgt.~ particles in each -.odium atom [I] II number ()l nr...•utrons in the nucleu.., of a odium 24 atom . [ l) a Extrac t 1 'Radon i, a natu~1lly occun·ing radioacti,c gas. It c.:omes fr01n uranium which occu1 . in rocks and oil~.' i Explain the meaning ol the word ,100 aclMfV ii how long it will take for l ht· radioactivil_\' lrom the injcl'tion to bcl:Ollll.' undeLcctablc. 11 J c Tcchnl·tium-99111 i., a gam1na ( ")') l'mittcr and do •s not pt oduc • alpha (o) orb •ta ( ) 1 adiations. E~plain whv it is sail! to ini1..1et tcchncliun1-99m into t lw bod). [ 2] E d Radioacli\'c salt (sodium chloride) is also ust:d in n1t:dicil'll.". The radioacth c sodium (~a) in the ah dl.'C..\\,, ac.:cmding to the equation -.hown ~lo,,, to lonn n1agncsium (~1g). ,.. a _ _ _...,. ~~ Mg + X + -y nuJiation [2] E:\:plain wh, some sub,tancc.., arc radioaclhL' and ~ome an: not. r21 ii talc the (au ...e ol background radiation. 1 dl.'Gl\'~ 112 Rn ' (alpne1 + (a pha) 11 I iii Explain \\ hat ou unckt tand hy the meaning of the half-life of a rad ioact h c clement. r2 l b Tcchnctium-99m is a radioacli\l~ matt•rial ,,ith a half-life ol 6 hours. It is used lo stud\ blood flo\\ a1 ou nd Lht: bo,h. A ...ample ol tcchnt:tium-99m ha, an ~,ctivity ol 96 counts per minute when injected into a patient\ blood stieam. Estimate i its acth it) altc1 12 houa-... fII Po Bi Po ' (alpt · Pb T,\ o of the nuclei hown in thl· <liagl'am art: i otopcs oj polonium. b E~plain thl· rncaning of lhe "m d isotope. [ I ) 247 ATOMS A D RADIOACTIVITY In the diagram , radon i, shown n, -.~ Rn. In ~ ncut ral radon ~tom,\\ hat is th .. num~r or i protons ii dcclmns iii nculn)ns? f31 9 A radioocth~ isotope! or gold has the svmbot 1,;Au. c 10 Isotopes of the radioacti\'c clement uranium occur naturjll~ in small proportion in some rock . The table gh ~s information about one uranium i otope. If thi isotope is injected into the bloodstn:am of a patient, it can be u cd b, docto1 a a tracer to monitor th1.: \\a\ the patient' heart works. The i otopc cm its gamn1a radiation that b dct<.'Ct<.xl out ide the patient'~ body. a \\' h~ \\ou]d an isotope that emits alpha radiation be unsuitable as a trJccr to monitor the working of the heart? [ll b Gi\'c one non-medical u e ior a radioacti\·e tracer. l1 J nucleon (mass) number proton (atomic) number 238 - - - - 92 radiation emitted alpha particle How many neutrons an~ then! in an atom of this u1~anium isotope? [I] b From \\ hich part of the uranium atom doc the alpha particle come? [ 1] c \\'hat doc an alpha particle con bt of? (2) a Use the list below when you revise for your IGCSE examination. The spread number, in brackets, tel Is you where to find more information. Revisiion checklist Core Level □ The pa11icle-, in an atom and the charge-, on them. (10.1) □ The meaning of atomic numb •r (proton number) and mass nun1b •r (nucleon nun1ber). (10. 1) □ \\'hat isotopes an:. (I 0.1) □ \\'hat a nudide is. ( 10.1) □ Rcprc enting nuclide in , mbol form. For example: !Li (10.1) □ \ Vhat radioacthc material, arc. (10.2) □ \\That n1dioacti\'C d1.:ca, means. ( 10.2) □ How atoms h1.:con1c ions. ( 10.2) D Alpha and beta partides, thei1· prope,·ties and detection. ( 10.2) □ Gamma rays, their properties and delc-ction. ( 10.2) □ The ioni1ing and penetrating cflcct of alpha, heta, and gamnia radiation. ( 10.2) □ The dangers of nuclear radiation. ( I 0.3) D \\'hat background radiation i~. and where it comes from . ( I 0.3) □ Detecting and mea~uring nuclear radiation. (I 0.3) □ Handling and t01ing radioactive matcriab safclv. ( 10.3 and l 0.6) □ How the emis ion of an alpha or beta particle changes an atom into one of a cliffcrcn t clement. ( I 0.4) □ The random nature of radioacti, e decav. ( 10.5) □ □ □ How the rate of radioacth·c dc-cav change with time. ( l 0.5) The n1eaning of half-Iii•. ( 10.5) \ \forking out a half-life from a radioacth·c dcca, cun·e or other· data. ( I 0.5) Extended Level A.s for Co1~ Le, cl. plu the following: □ \r\'hv alpha partich.'!-i, b 'la particle , and ganima ra, shave <lHforent ionizing cffects. ( 10.2) □ Ho\, alpha and beta particks are denl!ctecl by electric and magnetic fic1ds. ( I 0.2) □ \r\'h, gamn1a r.:1,· are not deflected b, electric and magnetic field . (10.2) □ I<lcntil)•ing \\ hich t" pc of radiation arc con1ing from a radioacth·,. source. ( 10.2 and 10.3) □ Allowing for background radi::uion wh~n dealing with data about radioactin: deca, . ( 10.3 and l 0.5) □ sing svmbol equations to rt.:prcscnt Lhe changes that happen during alpha dcca) and beta dccav. (JOA) □ Ho\, th • tability of a nuclcu is aft\.-ctcd b ' radioacth· • d ~ay. ( 10.5) □ \ Vhat happens during nuclear fission. ( I 0.6 and I 0.7) □ \\'hat happen during nuclear fusion. ( I 0. 7) □ The practical application ol alpha, beta, and gan1ma en1i sions. ( 10.8) □ II ow the , cattcring of alpha pa11iclc b, metal foil proddcs C\idcnce (or a nucleus in an atom. ( I 0. 9) Glo,v ing gru ·u rround · a black holeattheh artoftheMe ·i ,87 galaxy. 55 n1illion 1ight car fron1 Earth. The black hol is huge - about th size of our olai- y tern - hut is ~O far a\vay that a nehvork of eight radio teh.: cope · around the \\'Orld \Vas needed to detect and create thi ~ in1age. The ' hado,v' area is cau cd by the gravitational bcndjng and capture of light. It i about th1-ee times hu-ge1than the black hole it elf, ,vhich i i nvi ible. 249 Diameters Sun 0 Earth 1 390000 km 12 800 km Moon 3500 km Distances (average) Earth to Sun 149 600 000 km Earth to Moon 384 000 km T eSun The un is a hug~. glowing ball of ga c alled a sLar. 11 is c:-.tr~mcly hot , \\ ith a tl;!mf)\!raturc of 6000 ° on the surface rising to 15 million " m its ccntr~. Its energy is n:lca~cd by nuclear rcacLions in it con:, and il radiates mo!-.t1) in the infr-'1recl, ,i.sihlc, and uhm\·ioll!L reg ions of the dec trumag netic s pec trum. The Earth: day. night, and seasons Eanh turn, sl()wh on iL, a xi, once a day. Half of l he Earth is in sun light. and half in ·ha<low (jn tlarknc~ ·). As each place move from unlight into shado,,, it passes from cJa, time into nig ht. ru the Earth rotates. Florida moves from sunl ght into sh d<:rN So rt passes from dayt me. sunlight I 1s JullC Because of the Earth's tilt, Florida has a longer da;1une. Solar heating energy from Sun The Earth is heated by energy transferred from the Sun. Zones A and 8 receive equal amounts of energy per second. But zone A has a larger surface area. so the e er(JJ is more spread out. This is one reason why zone A is colder than zone B. ► Many parts of the wortd get four seasons: spring, summer, autumn, and winter. However in equatorial regions other seasons apply. .. than ntght The Ea11h n10,·c round lhc un in a nea.r:-circulal' path. The path b called an orbit. Each orbit lake ju t over 365 da~ , or o ne , ·ear. The Eaa1h' a-..:b i tilted hv 23. - 0 a. ho\\TI in the diag ran1 .. Because of thi., most ~ gions ge1 varying hou~ of daylight through the year a nd \'arying climalic condition .... In other ,, or<ls, thl') have different season~. \Vhen iL is sum mcr. the1"'c are two rea sons for the higher temperatures. Firs l, because o f the tilt, the uI ac:e i · moI\." • ·quaI·c on' 10 the un , so the un·~ radiatio n i le ·~ prca<l o ut, a c~plaine<l in the panel o n the kh. 1.-cond, . then~ arc nlore hour o l unli~hl. THE EARTH l SPACE The M,oon The Moon mo,·e · around lhe Earth in a near-circ ular orbit. Each o r·bit lttkc · about a month - 01-, more tlccuratd), 27.3 da)s. The Al oon also takes 27 .3 days lo tum once cm its axis, \\ h ich is wh) it ah, U) s keep, the same lace toward us. The Moon is mailer than the Eanh and ha a rocky, crater "d urfacc. The c rater~ were main Iv cau ed hy the impact o f laq~e n1etco1itcs o,·er a billion year~ a go. The • ·cas' are not s1.>as at all, bul faid, Oat areas of basalc 1·ock. \ Ve see lhc Moon because ii~ surface n:ncct:!-1 sunlight. Once a month, \\ hen there i~ a ' full M oon', the whole of the sunlit s ick is lacing us. A When we look at the Moon. only the sunlit part is visible. But mo ·t ol the time, we can onl) sec part of the sunlit s ide. 1' hc rest i · in ~hadow. A The phases of the Moon Half of the Moon is always in sunlight, but we see an increasing then decreasing proportion of that during the course of a month. The views above are from well north of 1he equator. For the view weO south. in Australia f0t example. rota te each image of the Moon by 180°. Orbital speed Kno,, ing Lhc radius ,. of the 1\\oon's o rbit around the Em1 h and the orbital period ( Li1nc for one orbit) T, yo u can calculate the Moons o rbital ~pec<l. · ·uming the orbit i · circulat; as in the diagram on the rig ht: , di tan c\.! travdkxl during o ne o rbit = 2rcr -.a... ] .. <li ta nee 2nr o: 01-.,Jla ~peeu1 = - - - - = time Fo r chc Moon, r . 3.84 x 1o:; km, T r i::t 27.3 da~s . 655 .2 hou~ Using these ,a]ucs in Lhc equation: 01·bital speed -= 3.68 x IO\ km/h That' abo ut the amc pccd a the ® \\ 0 1 ld' fo t t e\'cr jt:t aircraft. 1 Grve the time taken (to tl e nearest day) for a one rotation of the Earth on its axis b one rotauon of the Moon on its axis c one Otbit of the Earth abou t the Sun d one cxbit of the Moon about the Earth. 2 Expfain the following. a From the Earth, vve always see the same side of the Moon. b The Moon sometimes appears as a crescent. c Well north of the equator, there are more hours of daylight in June than in December. d Well north of the equator. aver age temperatures are higher in June than m December. 3 Using information you can find on the opposite page, calculate the average orbital speed of the Earth around the Sun in kmht Related topics: shadows 7.1; the Sun 11.5- 11.6 251 The Earlh is one of many planet. in orbit around lhe un. The un. planet ·. and other object in orbit, arc to gether kno,, n ~ the Solar ystem. The olar )Stem is so large that it b almost impossible to show the planet 'sizes and Lhcir distances trom the un on the ·ame scale diagram. That is why /U'O diagrams have been used hen: - one below and one on the next page. Planet · arc not hot enough Lo give off their own light. \Ve can onl) ·ce them becau~e the~ renect light from the un. From Ea1·th, they look like Lin) <lot · in the ni ght ·ky. \Vi t houL a tcle · ope, it i · difficult to tell wheLher you aru looking at a slar or a plancl. @ The planet~ an: kept in orbit hv the gra\'italional pull of the un. Most arc in an almo ·t circular orbit with lhe un at the centre. However, for Mcrcur) and Ma~. the <>1·bit is more of an ellip. e ('stretched out circle'). The planeL~ all travel round the un in the ·ame din:ction. They also tra\'d in approximately the same plane. Mo~t of the planels have smaller moon. in orbit around Lhcm. The table at the top of the ncxL page gi\'es some data about the plancL Here ar~ two feature~ shown by lhc data: • The further a planet i · fron\ the un, the slo,, er it tra\'cJs, and the more time it lakes lo complete an orbiL • In general, the further the planet is from the un, the lo,,er it~ average surface t1.:mperaturc. This is bccau ·c the intensity or the un's radiation weakens with distanc<.:. (Doubling the disLance means thal the energy p~r econd reaching each ~quarc metre of~\ surface is reduced to a quart<.:r.) n the next sprca<l, then: is more infonnation about the planets, and about other objects orbiting the un. The Sun contains nearly 99_9,a of th@ Solar System's mass. Its 9raV1tdt10NI pull holds the planets ,n thelf orbits. The inne r planets The5e <lre small and dense. and mamty made of rock and iron. Sc,enusts call them the terrestrral planets. 252 The o ute r p lane ts These are large, mainly gels. are thousands of m1n01 planets. Th@ largest lS only 1000 km across. and ha,e no solid surface, although trey do ra11e a solid corl;! . Sc1eot1sts call them tr~ gas giants tF0t more information about Pluto. see the next spread) THE EARTH I SPACE Uranus average distance from Sun/ million km 2870 4490 time fOJ one 0Jb1V years 0.24 0.62 1.00 1 .88 11 .86 29.46 84.01 164.8 diameter (at equator)/ krn 4880 12 100 12 800 6790 142 980 120 540 51 120 49 530 mass compared with Earth (Earth = 1) 0.06 0.82 LOO 0 .11 318 95.2 14.5 17.2 gravitational field strength at surface/ Nlkg 3.8 8.8 9.8 3.8 25 10.4 10.4 13.8 average density/ g/cm3 5.4 5.2 5.5 3.9 1.3 0.7 1.3 1.6 1JO °C 460°( 15 °C -23°C -110°( -140°( -210°( -200°( 0 0 2 79 82 27 4 • average surface temperature number of moons I • For comparison: water has a density of l .0 g/cm3 ( 1 cubic centimetre has a mass of 1 gram); iron has a density of 7. 9 g/cm 3 Thi.! uni , ju!')t onl.! of billion · ol star~. \!t an~ pluncl'i ha\·e bc--n detected around other ~tars bul the, are much too far a\\'aY to he\ iewed dirl!cth through a tcles opc. To fit the nearest star on the d iagran1 abo\·c, the page would have to be more l han u kilometre wide! I ® • lo ansVv"er the follo.ving, you w,11 need to refer to data in the table at the top of the page. 1 Which is the largest of the gas giants? 2 Which planet has the highest gravitational field strength at its surface7 3 Which planet orbits the Sun at the highest speed? 4 Ceres. a dwarf pla et, takes 4.6 years to orbi t the Sun. Between the Of bits of which two planets does Ceres lie? Give a reason for your ans\A/et'. ... .. • • In 2006, Pluto was 0 reclassified as a dwarf planet (see the next spread). 5 a Why does Mars have a IO'vVer average surface temperature than Earth? b Extreme global warming has given one of the planets a much higher surface temperature than expected. Which planet do you think this is7 Give a reason for your answer. 6 If the speed of hght is 300 000 knv'secood, use the equation time= distance/speed to work out how long it ta ·es the Sun's hght to reach us. Related topics: Sun. Earth, and Moon 11. 1; gravity and orbits 2.9, 2.14, and 11,4: formahon of the Solar System u .5 The inner planets Mercury is the c.:lo~esL plancL lo thl' un. I n tnan) wa~s, iL is a largl.:r n.'1 . ion or our O\\ n ~1oon. lL ha a cr~Hercd surJ ace and no atmo phcl'c. cnu i the brightl' ob_jcct in Lhc night k\ (apart from lhc loon). 1t is almo-.l Lhe ,amt• si1e as Lhc Eaa th, bul condition~ there ail.' very difkrcnc. The plancL b co, ercd by thid. douc.b ot -;ulturic acid, and it l aLmosphL·rc (97t, carbon dioxicll') cau.ses a severe greenhouse L'fl~cL. Do\\ n on the su1 lace, Lhc tcmpcraLun: can 1L.'ach nearly 500 C. Earth i the only pl~ ncl in the lar v~ll:nl kno\\ n to upport life. Mars i~ M>n1ctimc.s called th1..· tcd planet lx: au~ ot it urfacc colour. It has a thin atmo~phe1'\.· (n1ainl) carbon dioxide). a <lusL~ urfacc, and polar caps. Fro m the hapc ol · me or it~ ,allev . ~ienti b think that \\~Her n1a) once ha\'C flowed ther--c. l l also has volcanoes, although 11ont: arc active. The asteroids Tht: i.l -.teroid-. ha\'C dimensions r.inging lrom a fo\\ kilomt:Lrl.'~ up to J 000 km. 1\.to~t ha\c orbit between Lhosc 1 ~1an, ancl Jupiter. But 0111c (i;\ hau~ muc h more elliptical orbils that c:.ru~~ lht: path~ of olht:r plant:L... . 'i-' There i ·omt.· I...'\ ident:l" that, .._u·ound 65 n1illion ~car . ago , an i.1stL:roid about I O krn acroS-, ~Lruck the Earth. The dfL't:ls of Lhi~ ma, haH! A This asteroid, photographed caused th<: t:\.tinc tion o f thl...' dinosaurs. by lhe Galileo spacecrafl. is outer planets nearty 60 km long. Tre Jupiter b mo1~ ma, ·i\L.' than all Lht..· other plL1nel~ put togl.'thl't: lt i~ mainly ga, (it atmo~phcre b 90<', h\drogcn ) and ha~ no olid ,ua focc. The Great Red pot i a huge ~torrn chat ha~ raged tor ccnturjt:s. One of Jupill'l' n1oon , l o, ha ac ti\'e vol anoc!> on it - the lit ·t to be found be) ond th..: Ea11h. 0 .A ..lupiter's Great Red Spot is a storm so big that the Earth would fit inside it! .A Saturn's rings are millions of pieces of ice. each ,n ,ts own orbit about the planet. THE S a turn too is m a in)) gas. IL is s u rrounded b) very thin rings. These a rc not a soli<l mas ·, but million · o [ pieces of ice (mo ·tly). r a ng ing in s ize fro rn gra in to bou lder . Eac h i - a tiny 'n1oonlct' in it · own o rb it. ranus i a nother ga giant. lt i-; unu ua l in tha l it ax i o f rota tion i tilled at more than 90°. It too ha ling , but much fainter one~ tha n a tu111• . re ptune is the outermost of the gas giants. rt a lso ha~ a faint ring system. Pluto was, for ma n, yeaP.\, common I~ kn o\\ n as the outcrn1ost planet. Ho wen~r, because or its sma ll s ize an<l o ther f ac tor-s, m osl astro no mer~ no lo nger con ·i<lc,· it to be one of lhc main planet · (sec rig ht). Comets, meteors, and meteorites me t ha\'c highly elliptical 0 1bit which, in ~ me ea --. • can ta ke them out bevond Pluto and then do~ in to the un. In the ·Jicad' of a comet, ther e is an i c) lump, typi cally SC\ " ~ral kiJ omctn.:s ac1·0. s. H "a tcd by the un, pa rticles o f dust and ga'-; stream ofT it into space, fo rming a huge 'ta il' millio ns o i kilo metres lo ng. This is vis ible because it n!fll!cL'-; the sunlig hL. *A the Ea rth mo, ·c thro ugh pace, it n.1 n into tin\' grain o l ,na tetia l which hit the a tmo pherc o fo t that they burn up. Each o n ' cau c a ~trea k o f light called a n1eteor. Ra rdy, a larger c hunk of m a te ri al rcach c!-. the grou nd witho ut co mplctc1) bu r ning up. The chunk is called A T Ice in space I SPACE 0 To astronomers, 'ice' does not necessarily mean frozen water. It can also mean frozen carbon dioxide. methane, or ammonia. 0 Pluto reclassi fied In 2006, an international committee of astronomers carried out a reclassification of the planets. As a result. Pluto lost 1ts status as a planet and was reclasstf1ed as a dwarf planet. along ""'th Ceres (m the asteroid belt) and Eris (further out than Pluto). There are at least sax other dwarf planets beyond Pluto. a meteorite. • Halley's comet can be seen from Earth every 76 years. The last time was in 1986. To answer the following. you may nero to refer to Spread 11.2 and data m the table at the top of this page. 1 a List the mner planets and the outer planets in order. b Grve the MO main ways in which these are different from each other. 2 Name one dwarf planet. A large meteorite caused this i~act crater in Arizona, USA, around 50 000 years ago. The crater is 800 metres across. 3 Expain why ,t would be very difficult for astronauts to land on a Venus b Jupiter. a What 1s the d1fference bet...veen the orbit of a comet and that of most planets? b* How is the 'tail' of a comet formed? 0 Related topics: planet ary data 11.2; comet s an otblt 11-4; format1on of the Solar System 11-.5 Gravity and orbits \ Vi1h no for~c acling on il, a planet, a moon, or any other objecl, would lravel through ~pace in a straight line. To mon~ in the cun:ed path of an orbiL, there mu~t be an inward f orcc acting on it That force is provided by gra\'ity. There is gr..ivitalional aHrac.:tion hcl\\ccn all masses. The lorcc betwl!cn everyday object~ is far too weak lo detect, but with objects a~ masshe as moons and planets, the force i~ com,idcn1hlc, and conlmls their molion. Gra\·italional fon:e weaken~ with distancl:.'. Isaac . ewlon found that lhe fort.: e obeys an inverse square law: doubling chc di tance between l\\'o masses reduce~ 1he grc1\·itaticmal force between thl:.'m to a q1wr1er ... and ·o on. Comets in orbit Comers have highly clliprical orbir ·. Here is an example: .A The orbit of Halley's comet. From the positions and dates. you can see that the comet speeds up as it approaches the Sun and slows down as it moves away from it. A comet has lea. t peed when it i nu1he t from the un. That i also when the gra\'itational pull on it i ~ weake!;l. A!> the conlet nl0\'1.. : · cl er to the Sun, the force oi iravit\ incr~es. Al o, the com t pced up a it 'fall 'toward the Sun - it~ gra\ itational potential cnc11:,~· i con,·cr1cd to ki nctic enc1-g>. Satellites in orbit An, object in orbit around a more Jlla!) ~jve one i called a satellite. So the Moon i a natural atellite of the Earth. Ilowe\·e1; when people talk about ' atcllilc ·, the\' u ually mean mtilicial atcllik launched from Earth. There are hundred of artificial atellite in orbit around the Earth. ~1o l are in circular orbil~. A . atellite in a low orbit need the highest ~peed. For example, a atcllitc at a height of 300 km, ju t above the Earth' atmo phcre, n1uM travel at 29 l 00 kn1 /hour to maintain a circular orbit. At thi ~pccd. ic take~ 6 minute to orbit the Ea11h. Thi i the period of its 01-bit. A higher orbit requires a lower peed, and the pc1iod i. longer. THE EART SPACE • A satellite in a geostationaty orbit always appears in the same pos.tIon relative to the ground because the period of its orbit, 24 hours, matches the period of the Earth's rotation. To be geostationary, a satefhte must be put in a crrcular orbit Communications satellites beam radi o, TV, an<l other ~ignals from one pa11 of the arih to another. atcllitc ~ like thi arc nonuall) put into a geostationary orbit: the ir n1otion cxaclh matchc the Earth'~ro tatio n M> tha t the) appear ta tionat) n:Jati\'e to the gr ound. Ai.., a re ·uh, di ·h aedal:-, 35 900 km above the equator The required speed 1s 11 100 km/hour. on the gro und do no t ha\·c to tra k them, but c an point in a fixed direction. avigation satellites are u ·ed h) ea~ . boat , nnd planes to locnte thei r positio n. The Global Positioning ystem (GPS) has a ncl\\'ork of satellites tr-c1n~miLLing s~ nchro nizcd time si gnals. Down on Lhe gro und, a rccci\·ec· picks up ~ignal · from <liffcn:nL atcllitc , compa1 cs their arri\'al time , a nd use · the data to c alcula te it position to ,, ithin a fc\\ mctr·c-s. 1\1onitoring sate11ites, uch as wea ther a tdlitcs, contain c~m e ra or o ther d t>tcctors for sc annin g and S l.trYC) ~ ng the Earth . me are in low orbils \\hi c h pass o n ·. r rhc o rth and outh Poles. A..., Lhe Earth rotates beneath them, they can scan the \\ hok o f it s urface. Astronomical satellites, such as Lhc Hubble pace Telescope, contain l"Quipmcnt (o r obsc1,•ing <li ·tant La i · and gala~ic ·. Unlike o b!)CtYa to ries on a11h, the lig ht or 01her radiation they receive j not di r uptcd and weakened bv l he pre encc o f th.: a tn1 0 phcrc. £ Using a GPS receiver. The readings on the d1solay grve the positron. ®0 Tlhe diagram on the right shows the orbit of a comet. At which point a 1s the Sun·s gravitational pull on the comet greatest b 1s the Sun's gravitational pull on the comet least c does tt e comet have the greatest speed d does the comet have the least speed? 2 a What is a geostationary orbit? b What is the period (orbi t time) of a satellite in a geostationary orbi t? c Why are communicatioos sa tellites normally put into a geostationary orbit? 8 0 Related topics: fotce, motion, and gravity 2.7 and 2.9; ctrcular mot ion and otblls 2 .14; sending signals 7.12 257 0 Millions and billions 1 million - 1 000 000 - 10° 1 b1I lion = 1000 million - 1 000 000 000 = 109 The un i a tat. A!> tat · go, it i rather average. There arc much bigger and much brighcer tars. However all other tar . look like tiny dot to u. bccau ~c the\ arc n1uch further a\\a~. Light year Di tanc1.: between tar are o \'a~t that a!->tronomer ha\·c pc ial unit for mea uring them. For exan1ple: One light year (ly ) is the distance travelled by light in one year. The . pecd ol light L nearly 300 000 kHometre ~ per econd, light tra\'el n1ore than 9 million million kilometrt!s in one year. E~pre scd more ac uratch: 1 light ·car 9.... I 0 12 km Th~ n~rcsl slur Lo Lh.. un, Proxi111a Ce11uwri, is 4.2 light yea~ away. Jn other words, its light tak~ 4.2 yea1 to reach u. : we ~ee it ru it wm, 4.2 ~em . ago. For omparison, lig ht from the un lake~ 8 minut"-"S lo reach us. Galaxies The un is a member of a huge slar ~y!'\tem called a ga)a.~y. This contain, at le, t I 00 billion (I 0 11 ) tm , and i more than J00 000 light yean. across. BcL\\cen the scars, there is 1hinl~ spr~ad gas ancl du"-L called inter tellar n1atter. The ga. i~ mainl~· hyd1·ogen . . he gala'\:y is slow)) rotating, and is held together by gra\ ilational attraction. ur galax~ is called 1he Milk-y \\'ay. You can st.~ the edge of ic~ disc as a bright band o1 tars across the night . ky. It i ju, t one of many hill ion of galaxic!'\ in the knc>\\n niverse. Our own Sun is about halfway out from the centre of our galaxy. A The Andromeda Galaxy is 2 million light years iriNay. It is ve<y similar in structure to our own galaxy. THE A T SPACE The birth of a star d cnti ~t think tha t the un a nd the 1c t o the Solar y-,rcrn formed about 4 500 n1illion ) Cat ago in a huge, r tating cloud o i gas (n1ainlv hydrogen ) a nd du t cnlled a nebula . B' a u e o l g1, vity, the nebula s lowly collapsed inward , ro ta ting fo ·ter as il went . As more and more ma terial wa..., pulll'd in, a massin~clump ~ta rted to lo rn, al ii~ centre. And as the g ra \'ilational pote ntia l cncrg_, of the incoming material wa~ con, cr1cd into thc1mal encrg) thi · protostar lu:atccl up. Ocl:p in iclc il , the ga.-., became hottc1 and 11101 • comprc ed. E\'cntuall), the tcm pcr.1tu1·c and pre ure ,, ere high enough to tr igger nuclear fusion ,dth hvd rogen a it ~ fuel ( ·ee next page). The pro tostar had becon1e a ~lm: A The formation of the Solar System \ hen the out\, a rd pressure fron1 it radia tion bala nced the pull of g t"avit), this new lar beca me table. Around it, the re ma ining gas a nd dust formed a huge, rotating accretion disc ('accretion ' means gradual g1u \\ th b~ th i: addition o f ma terial). Hen:, gn1ins of ma teria l were s lowed b) colli ion and pulkcl inco clump · bv grJVity. The e clunl p wo uld become plancL a nd moon . The un's radiation drov~ oft mo t of the gn!-, from thl! inner pla net ·, o 1hc, were le h ~mall a nd rock~. Ho wc,·er, lunhcr o ul , when: it was cooler, rhc planc L~ n ~taine<l gas: the, bc:canle gas giants. ® 1 E:•plam what 1s meant by the terms a nebula b galaxy c M1ll.y Way d Unrverse. 2 a What 1s an accret,on disc? b Why does the material in an accretion disc start to collect m clumps? c When the Sun was a protostar, 'Nhat made the material in it heat up? 3 a What 1s the name of the process that supplies the Sun with its energy? A The Great Nebula in the constellation of Orion. Stars a,e forming in this huge doud of gas and dust. b What element does the Sun use as its nuclear fuel? 4 Proxima Centaur,, a star, as 4.2 hght years away. a What 1s meant by a hght year? 0 How far avvay 1s Proxima Centauri in km? G Today, the fastest roe ets can reach speeds of up to 50 000 km/hour. If a spacecraft travelled to Prox,ma Centauri at thas average speed, about how long would its Journey take? Related top1cs: potential and thermal energy 4.1; Solar System 11.2- 11.3; gravity 11..4 Atomic essentials Everything is made from about a hundred basic substances called elements. The smallest bit of an element is an atom. The nucleus of an atom is made up of protons and (in most cases) neutrons. Each element has a different number of protons in the nucleus. E 0 - - } nucl~us: - hydrogen atom hehumatom (2 ptotoos) (1 proton) e proton O neutron carbon atom (6 protons) Fusion power in the Sun If hy<lrogL"n nudci can be ma<lc to fuse (join ) together lo form helium nuclei. cncrro i released. But nuclei do not readily ,ioin bccau c the, are clec tricalh charged, and repel each other: To n1ake them e , the, ha ve to collide at C\'.trcn1el~· hig h speed~. In prac ti ce, r hi, mean~ maintaining a gu~ at an exln:rndy hig h tcrnpcr~ture: for e,umple, ru l - millio n ° in the un 's core. Fusion in the Sun's core The Sun 1s 73% hydrogen and 25% helium. !Energy is released as hydrogen 1s converted into helium. • • heh um nucl cus hydrogen nuclee + other l)clrttde5 Four hydrogen nuclet fuse together for each helium nucleus formed. This is a multi-stage process which also involves the creation of two neutrons from tv110 protons. Death of a star E In the un\ con!, thcm1al acti\ ity prc\·cnt~ gra\'it\ from pulling the material further inwartls. Ho\\'C\'Cr, in about 6 billio n years time, all of the hydrogen in the t or~\\ ill ha\\: been convL"rtc<l into hcl iu1n, hydrogen tu ion will cea~. and the cot~\\ ill collapse. Al Lhc an1c time, the un·~ outer layer will expand to about l 00 time i l~ present diameter and cool to a red glow. The un will then be a red giant. Eventuallv, it~ outer !aver ,\ill ch-ift into ~pace , exposing a ho1 , cxtrcmel) den:-.c core ailed ~1 white dwarf. This tin\ sta,· will use helium a~ ib, nuclear f ucl, c:c>n\'l!TLing it into carbon b) lu~io n. \ \'hen lhc helium run~ out, the ~tar\\ ill cool an<l fa<lc: for C\'Cr. THE EARTH I SPACE In about 6 billion years time. the Sun will become a red giant. Later, ,ts core will become a white dwarf, oefore it cools and fades for ever. E Supernovae ... Tn everv gala·\"y, new tat are fo m1 ing and old one are d~ing. But more mas~ive stat · have a diflcrent late from that o f our un. Eventually, the) become red supergiant.s, and blow up in a gigantic nuclear explosion called a superno,-a. This lca\·c~ a core in which maucr i~ so con1prcssc<l that electrons and p1'0ton~ react lo fotm ncut1'0n . The t~s uh is a neutron star. .. .and black holes Astronomical torches \\'he n the n10 t ma h·c tar ot all explode, the core canno t re i t the pull o r gravitv and goe on col lap~ing. The result b a black hole. ~ o th ing can escapl.! from i.t, not e ven lig ht , so it cannot be ·ecn. Howe \·er the prc~ence of a blac k ho le can be de tec ted b, it~ effcct o n ma r tcr near it or lig ht going past it. cicnti~Ls think chat th en: is a niass in: black hole at the ccnlrc o l mo~t gahu::ie . Made from stardust In ta, , lu io n reaclion c hange lighter clement into heavie r one . I low~\·cr, to n1akc \'CJ"\ hca\'\ clcn1cnt (gold and ura nium for example), the e~treme condilion tha t c rc nte a supe 1110 \ 'U a re ne'-!ded . Tha t i!-t b "'Cau se, l o make cle men t!-> heavie r tha n iro n, e nerID mus t be 511pplied f mfus ion , and is not rclca.~cc.l b.) it. The un and in ncr planet!-. con l a in \ 'Cl> hca\ y clement~. This suggc~ts that the nebula in which they fonne<l irtdudc<l ':,,care.lus t' f ru n'\ an ea rlier upcn1ova. In o ther wo rc.b, thL' un i a second-generation star. 1 What element will the Sun use as its nuclear fuel when its core runs ou t of hydrogen? 2 Describe m stages what will happen to the Sun when its core runs out of hydrogen. 3 Stars and planets contain many elements. bot the nebulae 1n v/hich they form are mainly hydrogen. Wha t process produces all the other elements? 0 Type 1 a supernovae all reach the same brightness at their peak, and can even outshine their galaxy. This makes them very useful tor estimating the galactic distances. Imagine two identical smal tore es. One is close to you and looks bright. the other is much further away and looks dim. Type 1a supernovae are like asttonomical torches. By comparing t eir apparent brightness. tt eir relative distances can be calculated. 4 What as a supernova? 0 why are some supernovae useful in estimating the distances of galaxies? 0 How are neutron stars and black holes formed? O what evidence is there tha t the nebula in whrch the Solar System formed contained remnants from an earher supernova? Related topics: atoms and elements 10.1; grav•ty 10.4 : nuclear reactors 10.6-10.7: proton-neutron conversion 10.9 261 Stars, galaxies, and 0 gravity The Sun ,s one star in a huge star system called a galaxy. This contains over 100 billion stars Stars and galaxies are shaped by gravity. There is gravitational attraction bet\veen all masses: the greater the masses and the closer they are, the stronger the f0tce. 0 The light year One hght year is the distance travelled by light in one year. It is equal to 9.S x 1012 km. Typically, neighbouring stars are a few light years apart. Electromagnetic waves These include hght and microwaves. He<e are some typical wavelengths: vis;ble spectrum from 0.000 4 mm (violet light) to 0.000 7 mm (red fight) Microwaves from 0.001 mm to 300 mm wavel ngth +-+ ► With radio telescope arrays like this. soentists have been able to detect radio waves from the most distant parts of the Universe, including microwaves which may be the remnants of rad,at.aon from the Big Bang. Then.~ are billion ol galaxie in the Unh·i.:1 e. l cighbouring gal~ xic are, t~ pically, a fow million light year · apart. 'fhc mo ·t distant gala.,il:s detccled lrom Ea11h arc more than 13 billion lighl )Cm awa) - their light has 1akcn o, er l 3 billion ( l 3 >-. 109 ) year · lo reach us. The expanding Universe \\'hen objects inovc a\\ a~ frorn Ea11h at high pee<l. the Iight wa\'c · 11 om them become 'stretched out'. Thi i knO\\ n a the DoppJcr effect. Jt mean that the \\a\'dcng1h · an: ~hilted toward · Lhl' red (longct wa\·elength) end ol the vi ible pectrrnn. Thi i called red shift , and it can be u l-<l ro cakulatc thl! ·pcl'<l. l n the 1920 , Ed,\in Hubble obser\'e<l thar lighl h·orn di ·tant gala."<ics i · red hilted, and that, in general, the red ~hih increa~e!\ "ith the di tance of the g..,lax~. This ilnplics that the mon.• <li tant gala."ic · arc receding (mo, ing awa)) from u at high pced. \ Ve are living in an expanding niverse. The Big Bang theory According 10 thb theory, the nive,:e (and time) began man\' billion. of ) cat ago\\ hen a inglc, hot' ·upcratom' cruprcd in a btu t of cncrg) called the Big Bang. All the matter in the Uni\'er e came from thi . Here al'c two piece of evidence to uppo11 the theor,: ~ the galaxie appear to be moving apart, they n,a, once ha\'c been Logcthcr in the s.ame ~pace. • Radio tele cope ha\'e pickl--d up n1icrowavc radiation of a pa11icular ln.:quency coming from e,cry <lin.--ction in space. Thi may be the hea\'H) red-, hifted r1?mnants of radiation h~om the Big Bang. h L calk·<l cosmic micro\\ravc backgrotmd radiation. or CMBR for hort. The Big Bang was not an e:-.plo~ion i nco exi ting space. pace it ell tartl'd to c,pand: the gala,ie!\ are , eparaling bccau e- the pace between chem is inctca · ing. To think about thi · , it help to u ea ~implified mo<lcl of an expanding Univer , uch a the one ho\\ n on the next page. THE EARTH I SPACE 0 Big Bang 9alc1>0 es move apart as Universe expands .A A model of a two-dimensional expanding Universe Abo\'c, Lhc Univc~ i rcp,~scntcd by Lhc ·miace of a balloon. llnaginc Lhat you arc on one of Lhc gala.,ie!) as the balloon inllatc . All the othc, a ppear to m o\'c awa, fro n1 , o u. The more di lant the, ru ', the fa tcr the, recede. Thb a ppli~ whcrc\'cr ,·o u at ,. ~ o ingle gala ,'Y is at I he centre oft he cxpa n...ion. E Estimating the age of the Universe sing red shift, sc ientists ha,·c measured the ra te at,, hich the gala xies apf)\:a r to be m o, ·ing apart. They re present this using the Hubble constant, ~ v = speed al which a galaxy is moving a,,ay fro m Earth " d ;:; distance of the galaxy t ro m Eal'th Diflcrc nt mc thom, o f n1easming H 0 ha,·c produced differ "Ill t ult . but 1 m anv . d entists now agr\!c o n a va ]ue of 2.3 x 10- per (.."Cond. Assuming tha t at th ~ Big Bang, th ~Em1h a nd galaxy were at the sam e point a nd run e scpan1tcd a t a consta nt rate, and using time - dis tance/speed : a g.L' of uni, L'l'-iL' . d 4 explain some gravitational effects. I lllllL' lo sep;.u-alL' :;; - - t· H0 ing the \'alue of H 0 a bo\·e gi\'c · the age 1 0 Expanding faster There Is evidence that the Universe's rate of expansion 1s increasing - an unexpected result because it was assumed that gravitational attraction would stow it do-Nn. The most likely cause ,1s thought to be a repulsive force produced by dark energy (see spread 12 .4). This can't be detected directly, but it as needed to ru, 4.35 x l 0 17 4 million 13 billion 14 billion 1 (4 X 106) (1.3 x 10 °) (1.4 X 10 1°) Which of the above numbers could represent a the separation between two neighbouring galaxres, in lrght years b the separation between two neighbounng stars. in light years c the distance from Earth to the most distant galaxies observed, rn light years d the age of the Universe, in years. ·, or 13. billion ,·ca1 . 2 light from distant galaxies sh~ red shift. a What 1s meant by red shift? b What 1s thought to be the cause of the red shift? 3 What evidence is there that the Universe may have started with a Big Bang? a What is the connection between the Hubble constant and the age of the Universe? b What assumption does this connection make? c If H0 is found to be 2 .5 x 10·18 /s. what value does this give for the age of the Universe? 0 Related topics: Ught, radio waves, mk:rowaves 7.10-7. 11; grcW1tat1onal attraction 11--4; distances of galax1es 1.1.6 ; dark matter and dar1< energy 12-4; Edwan Hubble 12.4 F rt er questions •• ' 1 hght from the Sun '' 'Ecirth's ax:is The diagram sho\\S 1hc Eaa'lh und 1hrce cilics , B , C on the arth's ~urfocc. a late: (i) "hich citie arc in d~, ·light; 11 I (ii) \\ hich cit\ recei\'c:-. the n,o t amount of light during tht.· dav. [ll b late ho\, long it \\ould take it\ C to return to the !'--ame place again as the Earth pins on it a,b. [ l] \\JI~ 2 The diagram sho\\ the Ea11h in four <lifler'\:nt posi tion:s in its 01 hit around thl! un. ssume that the Earth i.., ulways I he same distance from the un. ~ ®~ ,,,,. ... ' - ~~ ----.. . . . s Q ... G) ~ \.:J ouator "r<_ \,. . __ --@ 0--___., ,.,/ s- •.., s a i \\'hen the a rth is in posit ion I, it is sun1mer in the northcn1 hemisphere. \\'h, i thh,? 12) ii \\' hat i the sea on in the northern hcmi..,pherl.! "hen the Ear·th is in . . -'.)')· posll. .lOTl 3'. pm,Hmn iii \\'hat b the season in th • southern hcmbphcrc \\ hen the Emth b in p~ilion 3? llI b Thl! order ol some planets out\\ anb rrom the un is as follO\\:-i: Mct'CUI} \'cnus Eanh Mar . Jupiter at urn ranu~ How would vou e,pl'Ct the a\'erage da,-tirne temper.Hua~ on ,anus to compare" ith chut on ~1ar ? E,plain your ans\\l~r: r21 3 a I Earrh .. 1111 ,\10011 Cop, the sentences h ·lo\\ and sdcct one or h\'O words from the bc)'\l!S aho\·c l<> complete the sentence-.;, Each "or<l can be used once, mor·e than once 01· not at all . i The _ _ _ _ takes 24 hour to spin on its own a:\is. [I] ii The _ _ _ _ takes 36- days to orbit the____ [I] ill he _ _ _ _ take-., 27 da, to orbit the____ [I] b E,plain "h\ i in sun1mcr, c.Jayt imc lasts longer than night, [I] ii \\ c can M.'C the Moon, [ 11 ill the shape of the ~1oon appear to change o, er a four \\e<:k petiod. [I] \\ JF. 4 a 'fhc bo, contain the name~ of eight ol the nine planets in thl! olar \stem. art h \; cptune Ju pit ·r a turn Mer ury ranus 1\ame the planet \\ hich has not got ils name in the bo,. [I] ii \\' hich planet takes about 36- da\"s lo complete its od>it? [ ll ill \ \'hicl1 plan "t has the hortc t orbit? [ I J h • \ \' hich star do all the planch orbit ? [ I J \Vhic h planet ha the long c t orbit? [I] vi \ \'hat is the shape or each orbit? [I] b i \ Ve can sec the \l oon. E,plain \,h, . (2) ii \ \'e can sec ~H11~. E,plain whv. (21 ill On on1c nig hts \\C cannot ' ' an\ ta1-.,, E,plain\\h\. [2) c Cop\ and co,npl<:tc each sentence b, choosing the corn.:ct \\or<ls from the bo,. You ma) use thl! \\Ords once, mon.· than once or not at all . i black hole gala,, ystem ~1ilk, \\'.. , star The un is at the centre of the _ _ __ which is pa11 or a _ _ _ _ al led th• _ _ _ __ This is all part of a much larger S\stem called the _ _ _ _ " hid, scicnfr•,ts think began with the _ _ __ \ \'hen a supcr111a-, h .. tar c, cntuaJI\' collap e , a _ _ _ _ i lorn1ed .. t it~ cenux-. [6] 8 a 5 Astronomer, think that the Uni\ c,~c is c,panding. Givc one picce ol i:, idcnce upporting thb idea. [21 E,plain what b meant b, Co mic ~litTO\\'a, c Background Radiation. The un is po\\ cn~d b, nu dear fu-,ion. .ot dr.iwn to s ) The diagram sho\\ s l he orbi ls of ~ome bodies around th" un. Th• arTO\\ ho\\~ the dilection ol the Earth:"' orbit. a Choo ing I rom A , B, C and D , ,tatc which body is i a comet f I1 ii Venus. [ 11 b Cop, the diagram and mark on t h " orbit ol an an'Ow to how the dilcction in " h ic h it 1no,·e-,. [I] c i Describe the sha~ of the orbit of D . f I] ii amc the lorcl! \\hich keeps D in its orbit. f 11 E\:plain what is ml'ant b\' nuclear f\.l"iion. . [21 9 Jt b a \Cl"\' clear night. Luk· is looking up and :-.ccs the Milky \Vav, a ha,, band ol light aero the night -,k,. \\'hat in the A,1ilk~ \\'ay produces this ha,, bane.I of light? [ 11 b Thc ph1nct Vcnu "i is also seen as a bright sp • k ol light. E:\plain \\ h, \' •nus ~hine~ a brightly. \\'JFC 6 The ,un b orbited b, dgh l planet a \\ ell a d\, ar f planet~ and other objL-cb,. a GiH.· thl" two main diffL·r-x.·nces (apart from tcn1pcr11Lurc) between the four· inner· planets and the four out •r· planets. [21 b Apart from a dwarf plan •t, Ce1 •~. "hat dsc orbits the un between the inner and outer planet ? (1J 4 c cn.:-s takL·s 4.04 x I 0 hours Lo orbit the E un. Calculate i Ls orbital spL>t!d in krn/ hr; assun1ing that it has a circular or bit of radiu~4.l3x 1o ' kn1. (21 7 Cop\' :.md con1plete the pa sage bdow, rn,ing \\oil.!-, trom thl" bo, (,ou <lo not ncL-d to u c them all). acc1~tio11 di c gr·avit • nebula Big Bang planet tar supcn10,a protostar gala,, The oJar v ten1 lonned in a huge cloud of ga and du-;t called a _ _ _ _ Thi contained remnants from the c,plosion (called a _ _ _ _ ) of a n1uch older· star: In thl" cloud, - - - - started to pull matcr;al tog•• her into clump~. At the centre, th • biggest clump (called a - - - - ) got hotter and hotter umi) fu,ion tarted and it "'-.-came a _ _ __ . Around it a hugl.', rotating _ _ _ _ had fonnec..l. In this, mate,;al ,,as starting to [71 dun1(X.xl together to form the____ [2] . [2] Su«'IQ nor to scale c The diagram ho\\ the orbits of \ 'enus an<l the Ea11h about the un. i \ Vhat causes these planets to orbit the un? 11 ii uggc t why the orbit time for Vcnu 1c~~ than for the Eaath. [2) d A \ear later Luke looks up into thl" k, from the san1e place ancl al the samc time of night. i op~ th • table and put tick~ in th • bo,c that \\ottld lit in" ith hi ob c1,ation . [ 1) r in the same position Venus ~1ilk~ \ Va, ii in a nc\\ position ,plain Luke\ obs •1, at ions. [ 21 \1l~G Use the list below when you revise for your IGCSE examination. The spread number, in brackets, tells you where to find more information. Revision checklist Core Level 0 The Earth is a planet in orbit around a star 0 0 D D 0 0 D 0 0 D D 0 0 D D D 0 D D 0 266 (the un). (] I. I) The type · of rJdiation emitted bv the un. (11.1) How the Earth' rotation causes da\ and night. (J 1.1) The tilt or the Earth' axi : why a year ha c.lifi •rent ea on . ( I l. I) How the Moon orbits the Earth. ( 11 . 1) Why we sec diflercnt phases of the Moon <luring the cour co[ a month. ( 11.1) \\'hat the olar ystcm i • ( l 1.2) Ho\\ the un contain mo t ot the ma of the olar , . tcm. ( 11 .2) The order of the planet in th' olar ) ~tern. ( 1 1.2) The four inner planets a~ small and rock); the four outer planets arc gas giants. ( 11 .2 and 11.3) Moon , a tcroids, d\\arf planet , and con1ct . (11.2 and I 1.3) How the un' gravitational pull keep the plan 'h in orbit. ( I 1.4) How gra\'itational rorcc weakens with distance. ( 11.4) Ho\\ the planets and moon were formed. ( I 1.5) \ \'hat an accretion di c i . ( 11.5) The un i a n1cdium- ilcd tar in a gala\:\ of billion of tar called th' Milk, \ Vav. ( 11.5) M •asur;ng astronomical distanc •sin light yea~. ( I 1. -) How the distances bch\·een stars corn pan:s with the di ta nee between gala.,ic . ( 11.S) The Unhc1 c i made up of billion of galaxie . ( 1 J .5) The •vidcncc that the galaxic arc ru hing away from ·ach othet~ ( 11. 7) How the expansion of the ni\'ersc support.., the thcof) that it started,... ith a Big Bang. ( J J.7) Extended Level As for Con! Level, plus the following: □ How to calculate orbital speed, knowing the radius and pl'riod ( Lime) of an orbit. (11.1) □ The Hnk between a planet's distance fron1 the un and the pc1iod of it orbit. ( J 1.2) C The link between a plan 't' di lance h'On1 the un and its urface teniperaturc. ( 11 .2) □ Interpreting oth ·r data about the planets. ( I 1.2) □ How some objects in spacl', including comets, ha\·e elliptical orbits. ( 11.4) C How the pl:ed of an object in an elliptical orbit change . (11 .4) C How tat are lorm ·d in a nebula. ( 11.5) □ \ Vhat a protostar is. ( 11.5) □ How sta~ are powcrt!d b~ nuclear fusion reactions. (] 1.5 and I 1.6) □ \\That happen to a star at the end of it life. (11.6) C \Vhat r\!d gian~. upcrno\'aC, neutron ta1 , and black hole arc. ( 11 .6) □ How th ' brightness ol some supernovae can be used to estimate ho,... far awav other gala,ics ar~. ( l 1.6) □ \\'hat Cosmic Microwave Background Radiation i , and \\ h it i important to cicnti t . (I 1. 7) C How r •d hilted light can be u ,cl to c timatc the sp<.~d al \\hich a galax) is moving away from Ear1h. (11.7) □ \Vhat the Hubble constant is. (l I. 7) □ How the Hubble con~tant can be used to e titnatc the age ol the nhcrsc. (11. 7) Thi ancient tone circle at Stonehenge in Wiltshire, Eng1and, \Vas buih before 1500 BCE. It builder left no ,vrittcn records to explain il pu rpo c. Il may have been a centre for cer monie!'i a ociated ,vith death or healing , but the alignn1cnl of the tone also ugg st that it could have been used to observe the n1oven1cnts of the Sun and the Moon and for identifying th ' Cason . chapter 12 267 Forces and motion On Earth, unlt!~s thcrt! i a force toon!rcome friction, moving things cnmtually come to rest. Over 2300 years ago, 1his led Aristotle and other Greek philo ·ophers to believe that a force \\as always needed for motion. The more speed omcthing had, the more force it needed. BuL in the hca\'cn~. the un, Moon, and ~tat obc,cd diflc1 "nt rule . The~ mo,·ed in circle tor e\'er and ever. The e idea \\ere gl"nerallv accepted until the earlv 1600 , when Galileo Galilei tarted to come up with new idt!as about motion . From hi · ob ·c,-vation-, Galileo deduced 1hat, without fricLion, sliding object, would keep Lhcir speed. Also, all falling objc t~. lig ht or hca\·), would gain speed at the same stead\ rate. .& It is said that Gahleo investigated the laws of motion by dropping cannon balls from the top of Pisa's famous toiwer. There is no evidence to support this story. Hov\le'Ver, Galileo was born in Pisa, Italy (in 1564), and studied and lectured there. Our prc:,ent-day idea about force and motion mainlv come hom I ·aac e\\1on, who put forward hi , three laws of rnotion in 1687. Our definition of force i ba ed o n hi . econd law: force - ma · x acceleration. e,,1on al ·o reali7ed that 'heavenly bodi~' did not obe · different rules from l!\'CrYthing ... else. The motion of the Moon around the Earth was controlled by the same forcc grjvity - that n1aclc objects fall do\\ nwards on Earth. ewlon is upposcd Lo have had this idea \\hilc watching an apple tall from a Lr\!C, although hi · rnathcmatical treatment of gravit\ \\a much more complicated than thi i mplc cxpe1ience uggc t . In 190 ... , Albert Einstein put forward hi special theory of relativity. From this, we now know thal, near the speed of lig ht, Ncwlons !-.Ccond law is no longer \'alicl. Ho\,cvcr. al the spL-c<ls we normall~ nleasu~ on Earth, 1hc law is quite accurate enough. Energy and heat The m odcnl, scicntifit: meaning of cnc,m aro ·c in the call) l 00 \\'hen cicnti L and enginec1 \\Cl"C dc\'cloping way o l me~uling the pe1forn1ance of team engin~. team e ngines u ed iorces to mo,·e thing . They did "''ork. To do thi , they had to pcnd energy. So jt made ense to mea ·ure energy and work in lhe same unit.s (we now u e the joule). ► A modern repltca of Stephenson's Locomot,on. The onginal, built in 1825, was used on the world's first pubhc steam railway. The development of steam engines like this led to advances in scientists· understanding of the relat1onsh1p between wor • energy, and heat. 268 HISTORY O K YID AS \Vith the idea of energy cstabli~hec.l, people soon realizL-<l Lhat energ_\ could cxi ·tin different foam · - clectlical, potential, kinetic, anti ·o on. However. the la,, ol con c1,ation ol cnet'g\ wa not de,elopcd until 1 47. Today. \\Clink heat ,,ith energy. Howcve1: ·cicntisb once thought that heal "as an in, i iblc, ,, eight le~ lluid called 'calotic' which flowed out of hot thing and wa qucc1ed h om olid when the-,. \\Cl'C n.1bbcd. In the 179(}.;,, Count Rumfo1·d did ome cxpedmcnt~ which ·ugg1..'Stcd that the calo1ic theol) wa~ "mng. \ Vhilc boring cannon ban •ls, he found that he could get an endless suppl) of heat b, k<..~ping the bon:rtuming. rr heat \\"''1~ a Ouid, 1hen the ~upph ~hould run out. ln.,tl'a<l, the amount of heat sc'-'mc<l Lo be <lir~ctl~ linkec.l with the amount of,, ork being done. The link between work an<l hear \\as U,,ul~ e ·tabli ·hcd in 1849 b~ Jame Joule. He loun<l that it al\\ay took 4.2 jouk · ol work to producl' l calorie ol heat (an old unit, equi\·alcnt to the heat 1 'QtlirccJ to in rca 'the temperature of I grnnl ol water b~ I C). Howc,·cr, Jou h:'~ work did not C'\plain what heat wa., . A Boring out cannon barrels made them hot. Count Rumford discovered that the amount of heat produced was related to the amount of work done during the boring process. \ Ve now know that materials an! made up of particle~ (atoms or mokcuks) which an: in a ~talc or ranc.Jom n'\olion , and that heat is associated,, ith that motion. ln a solid or liquid, Lhe pa11ides, ibratc. l n a gas the~ mo\'e about h :eh at high pccd. The higher Lhc ten1pcratu1~. the la tcr the partich.: mo\'c. The randon1 motion or the pmticlc~ i called thermal activity, and the encrgv which an object ha~ b •cau~ of it is called internal energy (1 he ~um or the ki ncl ic and potential energies of all l he particle~). 0 0 0 0 0 0 0 0 0 0 .. higher temperaru,e 0 0 0 0 0 0 0 0 0 0 0 0 thermal cne1gy (heat) 0 o· 0 0 0 0 lower tempercl:Ure 0 0 0 0 0 0 0 0 Tf a hot obje t i put in contact with a colder one, a~ abo,·c, energy i trJ.nsfon· xl from ont.! to the other because or the tcmpcrutun: diflcrcncc. This cnl.'1~ i~ called heat. o internal encrgv i~ the loltll amount of cncrg~ due lo thcnnal activit,, while heat r'\!pn.- scnts an amount of energy 1n111.!>{ent!d. Ho,, c,·er, lor hnpl idty, both can be called thermal energy. ◄1 ln engines. releasing thermal energy by burning fuel is one stage 1n the process of producing motion. Light and radiation Over 2300 yea ~ a go , rhe Ancient Cn..-c ks knc\\ rha t 1ig ht tra\'ellcd in ~truight Iinc~. Th<.: Ron1an~ used walcr-fillcc.l gla,~ ~phen:s Lo mag nify thing s . Bur it wa · no t untj] the 1200 · that gla s lcn cs were first made , For s pcc tadcs. The telescope \\'a!) i n,·cntc<l in the earl) l 600 . l n the atnc centurv, ncll di covered 1hc la,, o l refrac tion, Hu, g hen ugge tcd that lig ht wa · a fo n11 o l wa\'e motion , and Tewton dem o n trated that white light wa a mi~tlire o f colour . ~ewlon al~o tried to explain the natu1·c of 1ig ht. He thoughr rhat light was made up o f million~ of tin, 'corpuscle~• ( particles). One of Newton's expenmen1s. Newton passed white sunlight into a glass prism, and produced a spectrum. When he recombined the colours With a second pnsm, he obtained white light again. He concluded that the colours must be from the whi te hght and not produced by the glass. In the early I 00 , Thomru. Yo ung: in\'estigated the interle re nce and diffrac tion of lig ht and ·ucce. lully u ·ed the wa\'e theor~ lo explain th ese effects. From his results, he was also able lo calculate a value for the wa,·clcngLh of light. Young's \\ork seemed lo pul an end Lo C\\1 o n's 'corpuscles', bul these wcr.: Lo appear lacer i rl ano ther form . omc matctials give ofi electrons when thl') absorb light. 'fhi ' i~ called Lhe photoelectric effect. In 1905, Ein tcin wa able to c,p)ajn it b\ a uming that light con i ted o l panicle-like bm t~ ol wave e ne rl!\, called photons. Light, it cemed, could behave like wave and particle!',. James lcrk Maxwell \\as the fi~L to put forward th<.: idea that light was a t~ pc of e lectromagnetic radiation . He <licl this in 1864. From hi · Lhcoretical ,,ork on ck-eerie and magnctk field , he predicted rhc c,i tence o f electromagnetic w._l\'C , calcula led what their pccd hould be, and found that it matched the pced of light. Hi equatio n al o predic ted the exbtence ot radio wa\'e , although ·real' radio waves wen! not detec ted until the I 80:,,. X-rays were discO\'Cl"\..--d by \ Vilhclm Ro ntgen in I 95, hul their elec tromagneti c nalurc was not cstabli~hccl until 1912. .A. Mane Curie m her laboratory Jn 1896, Henri Becquerel dc1ectecl a penetrating radiation coming from uranium salts. He had disco\"er·cd radioacth.rity. Laler, Marie uric sho\\'cd Lhat the radiation came from \\'ithin the a1on1 and wa~ not clue to f"l.'°ac tion~ with othl'1· material ·. In 1899, E1ne l Rurherford in\'e tigatl'<l rjdioactivit~ and idcntit'ic<l two typl: · of radiation, which he called alpha and beta. The folio,, ing year, he discovered gamma ra\' . Toda\, \\e kno\\ that \\'a\e , Mach a~ gamn1a radiation , can behcwe like partjclc , and that pa11icle can al!->o behave like \\"a\'C . ic:nti~t~ call t hi · "'ave-partide duality. HISTORY OF K YID AS Atoms and electrons The word 'atom' comes from the Grcekaromos, meaning indi\'i ible. 1'hc fir l modern u..-,c of the \\01-d "~ b~ John Dalton, who pul fo1,\'ard hi · atom ic thcot"\ in 1 03, in order to explain the ru)C!) go,·e111ing the proportion in which different clcm ·nt~ combined chemically. Dalton ugg~tcd that all matter consh.ted or tin) pa11iclc calk"CI atom!), ach ,tern "nt had it.!-. own type of alom, and atom. of the so.me clement were identical. Atom could not ~ cn:alc<l 01· de~trO) eel, nor could Lhey be broken into ~mailer bit~. Bul what \\'Cl"e atoms made of? The first clue~ came in the I 90s, wh1.m scicnLi~L~ were studying the conduction of cfo~tricit\ through ga-..cs. The) found that atoms could gi\'c out in\'i~iblc, negatively charged ra, . . J. J. Thomson in\'estigatcd the ray · and deduced that the) were particle · n1uch lighter than atom . Thi ~wa in I 97. Thom.son had di co, c1\.'<l the electron. A Ernest Rutherford (right) and his assistant Hans Geiger, in 1912. They are stand ng next to the apparatus which they used for detecting alpha particles. Tf an atom contain x1 ek-ctron~. it mu ·t al ·o contain po ·itive c harge to make it ek"Ctricall~ neutral. But when! \\as this charge? Jn 19 11, a team led b~ ErncM RuthcrfonJ directed alpha particle!-. at thin gold foil. They found thal most pas~ed slraight through but a [cw ,,ere <lent.-ctccJ at hu ge angles. To explain thi , Rutherford suggested that each atom 1nust be largeh· empt~ pace, whh it po itiv~ charge and mo t ol it ma concentrated in a tiny nuclcu . ◄ The Rutherford- Bohr model or the atom (with nuclear --- e proton } nucleus:o r et.itron In Rutherford' n1odcl (pictm --) of the atom, clc tron orbited the nuclcu like planet around the tm. nfo11unat ,t\', 1h ~ model had a seriou · Oaw: according to cla~~ical th1."nry, an orbiting de tron ought to radiate cncrg_\ continuou.sl) and spiral into the nucku.s, so its orbit could not be !-.table. In 1913, Neils Bohr u~ed the quantum theory to ~oh·e this problem. Accortling to Bohr, ck-ctron.') \\en: in fixed orbiL-, and could noL radiate continuo~I). The) could onl~ l~c cne1~ by jumping to a lo\\ er oa bit and emi1ting a quantum ('packet') ol electromagnetic encrg) - in other word~. a photon. ing thi model, Bohr \\'U able to predict the po~ition~ of th' line in the hydrogen spectrum. Howe\'cr, his cal ulat ion~ did not \\01·k for elements with a more complicated electron stru turc. To dea] with this p1·ohlen1, scientisl~ laLcr <levdope<l a mathematical, wave-mechanic.s modd of the atom. The Ruthe, lord- Bohr ,nodcl of Lhc atom aid nothing about what wa in.!)ide the nucleu . IIO\\C\'e1~ in 19l9, Ruthcrlord UM-~ alpha particle to knock po itiveh charged pm1iclc out of the nucleu~. Th· c ,,·"'re proton . In 1932, Jame~ had,dck disco,·cr·d that the nu lcus al.so conlained neutrons. In re cnt year.-., experiments with particle accclcratm~ have suggested thaL protons and neutrons a~ mac.le from particle~ called quarks. particles included). The picture is not to scale. With an atom of the size shown. the nucleus would be far too small to see. Richard Feynmann giving a lecture at the California Institute of Technology. Advances made bit Professor Feynmann in quantum electrodynamics woo him the 1965 Nobel Prize for Physics. 271 Year dates It as becoming more 0 common to give dates in the form 300 BCE and 1600 CE (or just 1600) rather than 300 BC and 1600 AO. The letters ce stand for 'common era' and see for 'before common era'. Magnetism Around 2600 y~r · ago, the Ancient Greek kncw thal a certain type of iron ore, now kno\\n as magnctilc or loc.lcMonc, <.:ould alln1cl small pieces or iron . The\ found the ore in a p]acc called Magnesia, which is ho" magndism got it name. The Chinese had al ' O come acros · the nnste1iou · ore and. by 200 BCE, knew that a piece ol lodc~tone, H free to tun1, would alway point in the ame direction. Bv around 00 CF., the Chinese had di ·covered how to makl.! magnetic ncec.llc!'\ by stroking small piec~ m· iron\\ ith ]od~tone. The fir:..,l compasses probabl~ consisted of a magncrizcc.l needle supported b) a str-aw lloating in a bowl of water. Howc\'c1: the \\ ere not rcaJJ~ suitable for use on hips. Compassc~ \\ith pi\'otcd needle did not appear until the 1200~. ► No signs of a mountain at the North Pole. At one time. sailors thought that a huge magnetic mountain here might be the source of the Earth's magnetism. At this rime, no one rcall} undcr.-.lood why a compass needle points north. me sailors lx.-lic\·cd that there was a huge mountain of lodeslonc at the I orch Pole, whose force wa · so strong that it would pull the it·on nail out of a ·hip'~ hull. Then, in 1600, \\'illiam Gilbc11 publi hed the re uh ol hi experiment with magnet . Ile introduced the term n1agnetic pole and ugges ted that the Earth it eJt n1ight beha,.,. like a bar magnel. But wha1 cau. ed magnetism? The an w~r to that would come fmm an unc.ler...landing of electricity. Electricity The Ancient Creeks also kni:w of the str~nge pro~rtks or a M>lidificd r\:.sin called am be1: \\'hen rubbed, it attracted du ·t and other small things. The Gree"- ,,ord for amber j elektro11, from which the word elccuidl) comes. .A. Amber Our modern knowledge of el"'ctlicit\· really beg-an in the 1600~, when expedmcnte1 · . tarted to inve ligate amber and other rubbcd matedals more closely. They found thar il was po!-tsiblc to produ e repulsion as well as aur.iction, and that Lhcn: were two different kine.ls or electric charge . In 1752, Benjamin f-rJnklin carried out a famou - and cxlrc,nely dangerous - experiment in which he flew a kite in a thundc1 torn, and got parks to jun1p from a kev attached to the line. The park were ju t like tho e produ ed by rubbing an1be1: I lere wa e\'idcnce that lightning and eJecuicitv were the same thing. l thb time, •h.: l tical :,.pcrimcnt~ wcr ' ,, ilh ·Ma tic ek"Ctricitv' - charge~ 1 on insuluton. that could he tr<1n~fen d in :-.uddcn ium~. HmvcYer, in I 00, Ale. sandro Volta discovcn.-cl Lhat L" o metal~ w ith ~alt water bctwcl!n them could cau~ a continuou..., flow ol charge in other word...,, an electric current. 1 He had made the first balll'r\. \ Vi thin -o \ea1.·, Lhe dt.-cttit: moL01~gl!nerator. cHtd kunp had all bttn invented. l l owe, e,: no onl· ha<l .. n~ L'\ idencl' to e,plain \\ hat --lectaicit~ rcall~ \\._ until J. J. TI1om~on' di o,·et, oi the electron in J 97. from thi , we now kno\\ that the cun "' nt in a cit uit i a no\\ of electron . Elect~omagnetism ... UnLj) thl' L·ad~ 1 OCb, dl'cu·icil~ and magnl!Li~m ~ gardccl a~ l\\O difll'rent phenomena. Then in l 20, in D ·nm.. , k, Han~ Ol't--stcd demon tr~ued that a compa~~ nct"'Cllc could be dcncctcd b, an clccwic current. The following \ 'at~ Michael Farackn uc ceded in using th1: lor e rmn1 a n1agnct on the ClltT~nt in a wi~ to p1·o<luce 1·olation. He had mad• a \ "Cr) !-.imple Imm of electric motor. Later, in the I 30., he di'i O\~red electromagnetic induction, the l!ffl.'t:l in which a, olLage is gcnerat<:d in a conclucto t by mov ing or ,ary ing a mag netic fid<l around it. Toda\ 's genl.'1·utor and L1~ut!lo1 mc1 make u l.' of Lhb idea. \\<:t~ Faraday's first transformer, In Lhc 1860. . Jame~ CJe, k 1\1a.,,,dl linkcd clecLricit! and magnL'li~n, made in 1831 rnathen1aticalh. Latct, toU o \\ ing the di~co\~r, or the dct:tron, the cau..'ic of magnetbm ~came dem: ~ an ck tro n o rbit in an atom , it produc1.: a magnctk field , rather a~ th-- cun\~nl in a coil produc~ a fidd . ln m t matl'ti ab, the ,·ariou~ 1 --Ids m'C in random direc tion5 and cnnccl each other out, but in a magneti.1. xl maccrial, ~ome of l he I iclds 1i ne up and reinfm ·c each other. ◄ AA aurora, another example of the fink between magnetism and electricity. Charged partJdes (mainly electrons) streaming out from the Sun are directed towards polar regions bi/ the Earth's magnetic f eld. ~en the particles hit atoms or mofccules in the upper atmosphere, light 1s emitted . ... and beyond Ek-c tric an<l n,ag nl!tic lorcl.'~ are M> do~eh rdaLl.:d that thcv arc da~scd a~ electromagnetic forces. The tor-cc lh:.u hold atom~ logethl'r al'c o( thb l\ pL'. BLH three othc1 kind of tm ce al o operate in the nalural \\ Oriel. Gra\'it\' L th mo t lan1iliar. The other~ arc the weak nuclear force . r~pon!-.ibl ~ ror radioactivit), nn<l the strong nuclear force ,, hid, binds the pa11iclc~ in lhe nu lcu~ of an aton1. oda\', physici~t~ ar • cJc\'doping model~ Lo link thl:'sl! lorcc!-., but gra, it~ ~main~ a problem, and the search i~ still on £or a ~atisfac tory unificd-rid<l rhcon that combines alJ the "-no ,,n force · of nature. 273 The centre of the Universe? The ancicnl \icw of the Ea1·lh was lhat it was nat. Ho\,e\\.!1; b\ about 600 ucE, Grc-ck nlarincr had ob crvcd how the po ition of the ·tar altered a the-,. ·ailed no11h or outh, and realized that the Earth' urface mu l be ctu,·ed. Around 350 RCF.. Arb.tot le believed that the arth was a ' lationary pherc at the centn: of the ni\'e1-sc. The un, Moon, planel~. and stars lay on trcln.,.parcnt, crystal sphere~,, hic.:h rotated about rhc Earth, so Lhc\ mo,·ed in perfect cin:lcs. The idea that the 'hca\'cnly bodic 'nlLbt mo\'e in perfect circle around the Earth was to cau c difficuhie for man, ccntmies. \ Vhen ,iewed from mth. the planet do not move aero the~"-,· at a teach rate, and ometi mes app1.>ar Lo mo,·c badcward" and forward . Around 150 F., Ptolemv amc up "i.th an claborc.1Lc explanation for this. The planet.,. ,lid move in perfect cirdes, but ~ometimes they follo\\ccl small circles superimposed on a larger one. Ptolemy's explanation Copernicus's explanation Jupiter (moves mo (0earth Jup1 er moves 1n a circle around a pomt, w+uch itsel f mO\·es 1n a ewe e around the Earth Thi'\ ,s the motion we observe. slowly than Earth) As the Earth moves c1roun<f the Sun, our viewpoint changes, It •~ tl'Ms that Causes Jupiter's apparent motlOO. Tt wa. not until the I SOO that the vie\\' of Ari. totle and Ptolemy were ·eriou ly quc ·tiont!d. The pe1·son n!sponsiblc was ricolau · Copcrnicu , who clcci<lcd to take a Iresh look al the problem of the <>bscr\'ccl motion of lhc plands. l n 1543, he publi~hcd his theory Lhat the un musr be at the centre of thl" Uni\'cr ·c, ,\ith the Earth and planet · moving around it. O,cr the ollo\\h1g year , rhi idea wa · trongh oppo ed b, the Church, which in i ted that the a11h mu ·t be central. Later, Galileo ·uppo11ed Copernicu ·~idea. , but was f orccd to renounce then1 or ri k torture and execution. Jn 1.610, he had obscrv1.>d tiny moon · mo,·ing around Jupiter cvic.lcnce that the Earth was nol central co all ohjc · b, in the hem t!ns. A Galileo using a telescope he designed and buil t himself. 2'/4 During the late I 500s, obscrvar ion ma<lc b) 1:Vcho Brahc grcaLl~ inc1'\..'a ed Lhc amount of accurate data on the po ition of the planet ·. During the 1600 , the evidence (or the Cope111kan model became O\'er\\ helming. Kepler e. tnb1i hed the law~ of planetary orbit , Jewton publi hed hi theory of gr~l\ilation, and put Kepler's la,\. on a firm mathcma1ical basi HISTORY O K YID AS ◄ When William Herschel built this reflecting telescope in 1789, it was the largest in the world. It could be raised or lowered by pulleys. and there were rollers under the platform so that it could be turned. Caroline Herschel, William's sister. was also an ex.pert astronomer. She discovered comets and nebulae. and made a huge catalogue of her brother's observations. 0 Sun, stars, and galaxies B) the lat .. I 600~. it was ch:ar that the star~ were similar to th.. un, but much further a\\U)- In the late 1700s, \\'illiam Hersc hel used a largl! telescope Lo study ho\\' the stars\\ crl! distributed. He concluded that the un \\as near the centre of a huge, len ·-shaped !-iystem of star ·, which he called the Gala '· B-,. the early 1 00 , a ·tronomc1 Dark matter and dark energy Less than S% of the Universe seems to be made up of ordinary matter as we know rt. The rest ,s dark matter and dark energy Nerther can be detected directly, but their existence has been suggested in order to expf ·n gravitatiooal effects seen in galaxies, and how the Universe is expanding. Observations and mathematical analysis suggests that the rate of expansion is increasing and that dark energy is the most h ·ely cause. n1aking incrca inglv accurate ~timatcs of the dh,tances to th .. ·tan;. The ·e \\Cre ba cd on the folio,\ ing principle. During the course of a ,car, us the Earth move~ round the un, our , iewpoinl in space changes, so nearb~ stars appear to mo\'e against the background of ,·er) di tant star~. This apparent movement is called parallax. B-,. measuring it, the distance to nearb_\ tar can be calculated u ing trigonometr_\. \\Crc In 191 , Hmio,... haple) mapped the r ..lativc di tance of star duMcr and found that the un \\a.Snot at the ccntn: of our Galax_\ after· all. And in the 1920s, Ed,\ in Hubble clisco,·ercd that our Galax~ was not alone. There were mill ions of other galaxies in the ni\'cl"!oie. Hubble also made another ·ignificant discover~ about gala:\.ics. From the altel'cd \\a\ elcngth oi their light, he concluded that thev mu t be ru hing away rom each othc1: Thi di co, crv led to th' dcvclopn1cnt of the Big Bang theory - the idea that, billions of )Ca~ ago, th .. whole of :spac ~ and C\'CT) thing in it~, artcd to expand from t1 s inglc, atom-:sii'cc.l conccntrution of mat1c1· and energy. E,·idcncc :suggc:sts that the Big Bang occurred 13.8 billion) car~ ago. A The Hubble Space Telescope is in orbit around the Earth. It transmits pictures back to the ground which enable astronomers to see distant stars and galaxies without the distorting effects of the Earth's atmosphere. A larger replacement is due to be launched rn 2021. 275 c.400BCE Democritus suggests that thete might be a limit C. 350BCE 1852 Kelvin states the law of conservation of energy. to the divisibility of matter. (Atomos is the Greek word fOf indrvisable.) 1864 Maxwell predicts the existence of radio waves and other electromagnetic waves. Aristotle suggests that the Earth is at the centre of the Universe. with the Sun. Moon. and planets on crystal spheres around it. 1879 Swan and l:dison make the first electric hght bulbs. 1888 Hertz demonstrates the existence of radlO waves. 1894 Marconi transmib the first radio signals. 1895 RC)Otgen discovers X-rays. 1896 Becquetel discovers radioactivity. Hero makes a small turb111e driven by Jets of steam. 1897 Thomson discovers the electron. Ptolemy suggests that the Earth ,sat the centre of the Uriuverse. and that the Sun. Mooo. and planets are moving in perfect circles. 1898 M. Curie discovers radium and polonium. 1899 Rutherford identifies alpha and beta rays. 1900 Planck proposes the quantum theory. 1905 Einstem uses the quantum theory to explain the photoelectric effect, and publishes his special theory of relat1v1ty. 1911 Rutherford proposes a nudear model of the atom. 1913 Bohr uses the quantum theory to modify Rutherford's model of the atom. C. 2408CE Eratosthenes estimates the d.ameter of the Earth by companng shadow angles in d1fferent places. CE c. 60 c. 150 c. 1000 Magnetic compass used In China. 1543 Copernicus suggests that the Sun 1s at the centre of the UnNerse, with the Earth and planets moving around it. 1600 Gilbert suggests that tt e Earth acts like a giant bar magnet. 1604 Gahleo shows that all failing objects should have the same. steady acceleration. 1916 Einstein publishes his general theory of relatiVlty. 1621 Snell states his law of refraction. 1919 Rutherford splits the atom and discovers the proton. 1644 lomcell1 makes the first mercury barometer. 1924 De Broglie suggests that part,c~s can behave as 1654 Guendce demonstrates atmosphenc pressure. 1662 Boyte states has law for ga~. 1678 Huygens puts forward his wave theory of hght. 1679 Hooke states his law for elastic materials. 1687 Newton publishes his theory of gravity and la'--VS of motion. 1714 Fahrenheit makes the first mercury thermometer. 1752 Franklin performs a hazardous experiment with a kite to show that lightning is electricity. 1938 Hahn discovers nuclear fission . Herschel discovers the shape of our galaxy. 1942 Fermi builds the fust nuclear reactOC'. 1800 Volta makes the first battery. 1947 1803 Dalton suggests that matter is made up of atoms. Bardeen, Brattain, and Shockley make the first transistor. 1957 First artifKial satellite. Sputnik I. put into orbit. 1958 St Clair Kilby makes the first integrated circuit. C 1790 Young demonstrates the wave nature of light. waves. 1925 Schrod11ger wave-mechanics model of the atom. 1927 Lemaitre suggests the poss1b1hty of the Big Bang. 1928 Geiger and MOiier invent thear radiation detector. 1929 Hubble discovers that the Universe 1s expanding. 1932 Chadwick discovers the neutron. Cockroft and Walton produce the first nuclear change using a particle accelerator. 1821 Faraday makes a simple form of electric motor. 1825 Am~re works out a law for the force between current-carrying conductors. 1960 Maiman builds the first laser. 1963 Fir~t geostationary communications satellite. 1827 Ohm states his law for metal conductors. 1969 First manned landing on the Moon. 1832 Faraday demonstrates electromagnetic induction. 1971 Intel Corporation makes the first microprocessor. 1832 Sturgeon makes the first moving-coil meter. 1977 First experimental evidence of quarks. 1840 first use of the w"Ords 'physicist' and ·soent1st'. 1990 Hubble Space lelescope launched. 1849 Fizeau measures the speed of ~ght. 2012 Higgs particle discovered. Joule establishes the hnk between heat and work. 2019 New definitions for kilogram and ott,er units. Source: rhe 8,ogri!phkal Encycloµedia of Scientr~rs. published by the lmt,tute of Physic.$ ZJ6 C. - c,,ca (dbotit ) Tht= \\ orkc r in~ ide Lhe cage is quit, arc, despite the 2.5 n1illion volt parks fron1 the huge Van de Graaff gen rator. Th ele tric di charg '~ st.-ike the metal ba1 , rather than pa s b t\vccn thcn1, ~o the cage ha ~ a ·hielding effect. fn fact, if ~afet " pro cdu1·e~ \\' C1·e ignored, sonic of the expcritncnt done in a -chool laborato1 ., \\'Ould be much ,norc dangerous t hnn l hi~ one. chapter 13 277 \ hen can~ ing. our phy~ic · c~pcrimcnts, you need to be able follo,\ ing: • I la ndle equipment and material ntclv. lo do chc • Follow instcuction · carefully. • Chunge how you cntTY out each step of an e~perin1enl, depending o n what happened thc time bcfore. Here are ome rcmindet about how to work ' afeh with different type ol equipment: Bunsensandtripods • If a bunscn burner is alight, buL not in use, ahvay~ lca\'C it on the ycllo,\ flame ~cuing ~o that the Harne can be ecn. .A A yellow bunsen fame is easier to see than a blue one. • Make sun~ that hunsen~ and tripods han~ a heatproof mal unclcrnca1h. • Gi\'e a hot tripod plenty of time to cool down he lore attempting to move it. • Don't attempt to mo,·c a tripod when then~ i a beaker n: ting o n ir. Glass thermometers • Don't pul glas thermometers when: they can roll off the bt!nch. • Keep gla~ ~ chcn11omctc1 awa) from bun en flame . • • • upporl thcrmon,ctcn. safely: sec Safe support bclo\\. ~tercurv, u ed in some the1mo me tc1 , j to~ic. If a Lhe1mometer brea ks and mercury nm out, don'l handle it. Glass tubing • e\er attempt 10 push g lass tubing (or g]as~ thermometer ·) through a hole in a bung. 'fhe laboratory technician ha a ~pedal tool for doing thi . • Always handle hot glas~ tubing with tongs. Rest it on a heatproof mat~ don'c put it straight on the bench. • Hot g la · tubing can ·tay hot for a lo ng lime. Give it plenty of time to cool <lo\\ n ht;?fore you allcmpt lo pick it up. Safe support .A In experiments Uke this, make sure that the apparatus is stable enough to suppo« the heaviest load. • \ Vhen clamping a te~t•tube, don't O\'Crtighten che clamp. And make s ure that 1hc dan,p has soft pads to touc h against 1hc glass. This also app1ies when damping a g la ·s Lhcrmomcter. • In C).pcrimcnts where )OU ha\'c to suspend a load, male sure that the uppo11ing damp ·tand i ·cable enough to take che hca,·ie t load \ OU ,, ill be u ing. You ma\' need to weigh it do\\ n for thi , a ~ho,\ n in l he diagra n1 on the le h. PRACTICAL PHYSICS Electricity • B~fon.: making any changes lo the wiring in your circuit , al way off the power 01· di~connccl the battery. • Rcmcm her: low \'Ohag • circuit~ ma) not gh·e you a ~hock, hut they an cau~c burn~ if the CUffL'nt is too high and a\\ ire O\'Crhcat~. • i\:cvcr make a dirt-et connc Lion acros., the terminals of a hallcl}. Don'1 put wir~s or tools whc,~ the) might connect across the terminals. • If a mains appliance is raull.), M\ itch off the f>O\\l!r and pull oul the plug. Don't change the [uS(:. Ask the ]aboratol) technician to <le-al \\ ith the fault. • Ek·ctrica] fires: ·cc Fire below. wi1ch In man\ modern labo,-.,uorics, the main · cirt:uics arc protected b~ R Ds (residual current <le, ice ·), o the d ·k of ·hock · is reduced. But. .. • U someone ha been dectrocuh:<l, and is still touching the faulty appliance, don't touch the pet ·on. \\itch o(J the J)O\\ er and pull out the plug. • Emergency! But the first job is to switch off the power and pull out the plug. Eye protection • AJwa) · \\'car eye protection (e.g. afct) goggk: ) when: - tretching metal wire or pla~tic cord - breaking or grinding olid (e.g. rock ample ) - heating liquids - dealing with acid~. alkalis, or an, other liquid eh •micab, that might ~plash. Light • Don't look <lircctl\' into a laser beam or other ource of bright light. Don't tand where la ~r light might be reflected into vour e)C . • If )OU need to tud) the un' in1age, project it onto a car<l.. c\·c r look through a telc cope or binoculat pointing tt"aight at the there i a filter in front. un - C\'en il flammable l1qu1d Radioactive sources • The radioactive our c used in c hool labornt01ic ·calcd. hould ah,av be • Raclioa tiYc ourcc houlcl b .. k "Pl w ,11 away from the bodv, and ne\'cr placi:cl where the~ ari: pointing at people. Fire • Don't heat nammablc liquids (e.g. mcth\•latc<l pirit ) over a bun en. If heating i ' rcquiroo, a water bath hould be u ed - \\ ith hot water heated well a\\ av h~on1 the expcd ment. • Don't thro\\ water on burning liquid · (e.g. mcth, lated pidt ). mother the fire with a fir' blanket or u ea carbon dio"idc cxtingui her: • Don't throw water on elccuical fire . Switch off the ~upply and u c a carbon dioxid • cxtingui her: • The only safe way to heat a flammable liquid is to use a water bath 2'J9 Thi~ ~P• ~a<l ~houkl help ~ou plan an cxpclimcnml procc<lut\!. The han<l\\1 itlcn nott..: · show p:.ui ol one :-tu<lem' · commenca1, on hc1 paocc<lurc. Presenting the problem tart b,· dl"-Cribinp. the problem )Ott are going to in\e.,cigate. and the main features or the n1et hod , ou will u~e to tackle it. ' '1 I am going to Investigate how the resistance of nichrome ~ wire depends on lt5 length. I kna..1 that resistance can be calcult1ted with ' this equation: voltaee (in V) resist.an~ (in U) = - - - - - ~ nichrome wire cu~nt (in A) So to find t.he re$l5tance of a length of chrome wire. I nee.a to pot the wire in a circuit. then measure the ~It.age 4 ' I I ~ l I length >. across It and the cun-ent In it. I wi do this for different ~ le~ths of ·chrome. j I think I can predict how the resistance will vary with length. If the length of wire lsdoul>led. the current (flow of electron5) hm~ to t,e pushed vetween twice as many atoms. So I would expect the re$istance to double as well. In my experiment. three of the key variables are: length of nichrome wire - to t,e measured with a ruler markealnmm volt, ee - to be m~su~ with a voltmeter curret1t- to be measured with an ammeter Making a prediction You may ha\'c: an i<lc:a of what )OU expect to happen in , our cnquia,. This pt ~diction is called ,our hypothc i . You hould ,, tile iL do,, n. It ma, not be right! lt i~ just an idea. The ain1 ot vour p1·ocedurc h. to li:st it. Dealing with variables Ouantiric~ lik1.: length, ur..-cnl, anc.l ,oltagc arc called variables. They can ,:lwngl! lrom one situation to another. it. From the voltmeter and ammeur ~ings. I ~ n Key variables ]'hc..,e arc..• the ,ariable that can altect \\hal happen in an e"\pcdment. You mu l dccidc what thcv arc. For example. in the nichrome,, in: cxpe1·imcnt. 1cngth is one ol the kcv , ariablc~ bt:cauSl' changing lhc lcngLh of \\ in! calculate the resfstanu. change~ the rL~i~tancc. I will take more seU>of reaak'l9s. 5hortening the wire t,;, 5 an each tfme until It 15 only 10 cm long. You must also decide ho,, to mca."urc lhe, ariables. and o,·er \\ har range. ror t::-.amplc:, in planning Lhc nichrome\\ irL· c:,pe1imcnl, ~ou \\oul<l ha\'e to: • decide\\ hat the highc t \'Olt..,gc and cu11~nt \..tlue:, ~hould h: (~'\kt\ n1u"t ~ con!>idct-ccl he1"(') dccid(... what length of wit'\.. to u~c. I 5hall $t:8rt wit:h 50 cm of thin nJchrome wire, put a volt8ge of 6 V across ft. and measure the current In For con~nltnce, I wil provably keep tJie ~It.age fixed at 6 V throughout the experiment. PRACTICA PHYSICS Controlling variables me \ariables don't hm·c to be measured, but the~ <lo need to be controlled. or cxa1nple, in the nichro1ne \\ ire expetimenc, )OU 1nlght \\ant to keep the wh-c at a tead, temperature, in ea c the temperature aff1..1et the t\! i tanc ". ome n1riablc~ can be difficulL to control. In \ our experiment, you rnay want to u~c the same thickness of nichrome \\i~ each time, but this depend on how accurately the "ire wa manufacturoo. You must take foctm like thi into account,, hen deciding how reliable your re uh ar ". A fair test \\'hen doing an l'Xpctiment, , ou hould change ju tone ,aaiablc at a tim .. and find out how il There are t'M> more variables I rleed to control: temperature - I know from reference boo 5 that the resistance of nichrome changes with temperato~e. So I wlll use a large beaker of cold water to keep the temperature of the nichrome steady. aJ;:un~·P.r (thickness) of nichrome wire- thl5 could affect the rc515tance. To make 5Urc that I have the same d ameter all the time. I wiO use leneths of v,fre taken from the same reel. and check each piece with a ~uge aff~.acts on .. other~ If lots ofn1riabl~ change at once, it will not be a fair tcsl. For ex.ample, if you want lo find out how the length or a win: affccl~ its n:sist'1ncc, it wouldn't be £air to compa1~ a Jong, thick wire,, ith sho,1, thin one. before usin9 it. ,________________ ___ _, _-~---_-_-_-_-_-_.::-_;:-:-:-~~.::-::::::_::-1 Final preparations I wOI set up this circutt: Decide what L-quipmcnt you ncc<l, ho,\ ) ou will an-ange it, and ho,, )OU will u ~c it. d.c.5Upply To hdp your planning, \OU ma~ nl'c<l to carry out a trial run of the experiment. Befo1-.: you do thb, make ure that all \'our pro edure are ate. + Pr'-!par .. table for your n:nd i ng before) ou tart your experiment~. Look at the ncxl spread on gelling the evidence before doing th i!-,. j Equipment needed: ~tmeter (0-6 V). ammeter (0-3 A). 50 cm of 0 28 mm diameter nichrome wi~e.... nichrome: volt.ige current resistance cm V A n 45 40 - nichrome coll - - - - - - - I --1 water I am not sure how big the nwxlmum cummt length 50 I - - - will be, so I will do a trial run of the experiment fl rst. I will start with, n ammeter that can mea9Ure several amperes. but may be al71e to change to a more sensitive meter for the main experiment. Safety: 35 I must make sure that the power supply is 30 switGhea off before I remove the nichrome wire 25 20 to change its length. This !>prcad ·houkl help you take and rL"cord 1nea!>urcmcnts co11~cll). Units voltage \Vhen you write dO\\n a measurement, remember to include the unit. For example: V \'Oltage 2.3 V lf ,·ou juM write down '2.3', vou ma\ not be able to rcrncmbcr whether thi \\'ru, uppo ed to be a \'ohage of 2.3 V or 2.3 n1V. 2.3 1.1 A When recording readings in a table (see spread 13.2). remember to include a unit in the heading at the top of each column. \Vhen \\Tiling mea urements in a table, \ 'OU don't need to put the unit afler each numht'r. But be ~urc to include thtt unit in the heading at the Lop of each column. You can sec an example on the left. Uncertainties No meru.uren1ent i exact. There is alwa) ome uncertainty about it. For example, you may only be ahle 10 read a \'Ohn1etcr to the ncare:-.t 0.1 V. ay thaL you measure a \'ohagL" of 2.3 V and a cun~nt of 1.2 A. To \\'01-k out the 1e ~btance in ohm!> (0), ~ ou dh i<lc rhe \'Oltage b~ the ctartcnl on a calculator and get... 1.9 ) 6 666 7 Thi~ ~hould be re ordcd a~ 1.9 n. nccrtaintie~ in your H>ltage and currcnt n:adings mean that you cannot ju~Lif~ including any n1orc figures. ln th i case, you arc giving the 1'\..'suh Lo two significant fig ures. - - - - 0 - - -- - Take enough readings For a graph, you houlcl have at least fi\'e set~ of r~adings. A You can only read this voltmeter to the nearest 0.1 V. • ol all cxpcrin1cnts gi,·c )OU rc-c1dings for a grc1ph. Somctimcs, you ha\c LO measun.• quantities lhal don'L change - the diameter or a wire ror example. ln ea -~ like thi , )OU hould repeat the mca url'mcnL at ll'a t chrc-c timl: and find an a\'cragc. Repeating a n1ea urcmcnt help you pot mL take~. It al ogive ,·ou ome idea of the uncertaint~. Look at lhis example. The diameter of a wire \\a me~ured four tim~: 1.4 1 mm 1.34 mm J. l 9 mm 1.30 mm You can work out them cragc like thi ·: a,eragc (1.41 1. 19 · 1.30) - - -1.34 --- - - - = l. 3 1 mm The odginal four number!> ranged frun, less than 1.2 lo more than 1.4. o, the last figure, I, in the a\'cragc or 1.31. i complctcl) uncc1 rain. Therefore, , ou hould write do\\ n the, a\'erage diameter a 1.3 111m. PRACTICAL PHYSICS Reading scales On many in ·trumcnt~. vou have lo judge the po~ition of a pointer 01· level on a sculc and work out the n1casurcmcnt from that. Here arc some \\UVS o making sure that you takl! 1h e corf"\?cl reading: A Using a glass thermometer to mca u1·c the tempctatu1~ of a liquid: kcc t he liquid well ~tirred, gi\'e the thermometer titne to reach t h e tcmpcratt and kc".. P the lan1p in the liqujd whHc vou take the reading. B ing a ruler: be urc that t h l! cale i right along~ide the point you are tn ing to mc.>asurc. (Error~ due to an incon-l!ct line of. ight an: calh:d parallax cn'U~.) J\1easuring a liquid level on a scale: look al Lhc lc\·d of the liquid's flat ~urface, not it, curved rncni ·cus. D Reading a meter: look at t he pointer and ~cale • quarc on'. (The pointer n1a, have a tint end like l hat ·hown here, o that , ou can lo at it edge on.) A 9u---- 20 C 0 an ~-ou t"Cad the instruments hdow corTcctly? T he am,\\C~ an.: on page 31. 1 3 2 4 s I have uS&l my ~It.age and cu~nt re.adi"les to cslcultlte the resisu nee of ~eh length of nichrome wire. No-.v I shall use these values to plot a graph of reslst.ance against length. Length Is the Independent variable (the one I chose to change). so it goesal0t19 the bottom axis. Resistance goes up the side. This page ·houl<l help ) ou Lo analyst: your <lala and draw conclu ion ' trom it. The hand,, 1itten note ~ho\\ part of one tudent' commrnt~u, on her enquiry. Drawing a graph A graph <.:an hdp you sec trend in , ·our data. Choosing axes 0 1.:cide which , ariablc lo put along the bottom axi!). sually, iL i~ the one you chose to vac~ b, et amount~ - thl' length of nichrome\\ ire, for t.'\~u11ple. Thi i the independent variable. Th'-' resbtance would be the dependent ariable hecau~' it~ valu~ depend~ on the length you cho e. It goes up the side axis. Choosing scales heck your highe~L reading . then choo c thl' largl-sl scales ,ou can tor) our a.,cs. Labelling axes long each a·d , \\Tile in what being mea...,ured nnd the units being used. 0 10 20 30 40 so length/cm The point$ on my graph are a litde sc.a~ but I think that the lile of best flt is a straight line. The line ought to go through the origin. If the we has uro length, there is no metal to r ~ t the current. so the resistance should also l76 zero. I have rcjcc~ one point on my graph. ln my table, the cWTent reading for that point 5eem5 far U)o low. I prol1abty misread the ammeter. h, Dra\\ing the best line Because of uncertainties, Lhe points on a gr..iph \\ ill be une\'cn. o don't join up thl' point ! 1n tl'ad, <lra,, lh4..• -;Lc-aight line or Mnoot h crn, e that go~ clo ~l to mo t ol tht.'m. Thb i called a line of best fit. Belon~ \OU draw it: • • De ide whether the line ~hould go through the ongm. D~ci<lc whcLhcr an) n:a<ling~ ~houlcl be ,-c1ectc<l. Some may be so far out that they an: probably due 10 mistal.c rathe1· than uncertaintic . Cl.' if )OU can find out win · the~ occutl'cd. From 1hc ,,a~ point · ~caLterabout a linl' of bL-st fit, ~ou can Cl' ho\\' reliable A5 the graph 15 a 5tra1!3ht bne through the ongrn, the reslst.ance of the nichrome wire 15 In direct proportion to Its length. This agrees with my onglnal hypothesis that tfoublif19 the length of wire ought to make it twice as difficult t-0 push electrons through. l his, )OUt reading •.u~. But for \ ou need plent) of point~. Trends and conclusions From the ~hape ol ,our graph, \OU can draw onclu~ion~ about the data. The ~impk~t lo11T1 of graph b a traighl line through l h" origin. A graph of resi~tance against length ol wire might be like this. If M), ii means that if the length douhles, the rcsislancc douhl~s... and so cm. Tn this case, n:si.'oilancc an<l ll'ngLh an: in direct proportion. H )OU thin"- that \our gTaph uppo1 t \ou1·original prediction, then a, o and e~plain )Olli' rea~on . Thb page hould help, ou decide how reliable YOlll' condu~ion" are, and how )Olff procedure could be in1pro\'ed or e\:tcndcd. Reliability The points on the 9raph are uneven. But 5 they zig-zag at random, I am fairly 5ure that. without uncertainties. they would lle on a straight line. There are several rea5on~ why the points may have t,ecn oo scattered •. To get a more rellat,le graph. I need to find a more accurate method of measuring ~515~ nee... In n:aching your conclusions, n.:mcmbcr tha1 there arc uncertainties in your measurements, and \'ariahlcs that you may not han~ allo\\ccJ for. )Our results can nC\l'1· prow! \our original pt'-."<litLion. You must decide ho,, far the, ~1tppor1 it. H you I hink that your re uh~ m~ unreliable in any wa~. !-.CC if you can explain whv. You may han~ some results\\ hich <lo nol agn:c \\ ith the other · ancl look like mi lakes. Thc~e arc called anomalous results. Tt) to c~plai 11 ,, h.._,t c...'au~cd them. Suggesting improvements To extend my enqull)', I coula flna out how the resistance of the nichrome win, depends on the tliameter.M Ha, ing complet<..--d your procedure, ~uggcsl wa,·s of impro, ing it so that your conclusions are nlorc reliable. Looking further ugge t . omc further work which might produce C\lra C\'idcncc or take your pro cdurc further. Writing your report The student's commentary was designed to help you understand the different stages of an procedure. It includes far more detail than you would normally put in a report When producing your (JINn report. these are the things you should include: Planning • A descnpt1on of what the procedure is dbout. A pred1ct1on of what you think will happen, and why. A hst of key variables, and a descnption of how you ..~11 measure or control each one. A hst of the equipment needed. Diagrams sh01Nn)9 how the equipment will oe set up. • A description of what you plan to do. • • • • Analysing and concludmg • Graphs and charts. • Calculat1ons based on your data. • A conclus,on. including details of: - what you found out - 'h'hether your findings matched your p,edictioo. Evaluating Gettmg evidence • A description of what you d,d. including comments about any diff1cultres and how you overcame them. • Tables showing all measurements. including units. • Comments about. - how reliable you think your results were - any anomak>us results, and thear possible causes - how your procedure could be improved - further work that could be done. Here are some suggestion~ for practical \\Ork. Some an: full investigations. Other~ a~ shorter exercises to help you develop your l.'xpcrimcntal skills. Measuring newspaper Plan and a1TY out e:-.peri mcnt to mea ure: a the thicknc: ·s of one ·heet of new paper b the mass of one ~heet of ncw~paper c the dt!nsily of rhc paper u~cd. ·u,r1 by 1hi11ki11g about the {ollou·iug: If a ingle ~hcet i · too thin to mt:asun: accurate!~. ho\\ can )OU i mpro\'c the accuracy? Wet or dry? The rnaker ~ o{ a well-known brand of soh tis ~uc paper clainl that their ti ~ues are ju t as trong wet as dn. Arc 1hey right? Plan and earn out an enquiry to le t their claim. tar/ b,· 1hi11king about the follou•i11g: Vhat i meant b, the· trcngth' of a tL ~ue? Do vou need u ea whole tL uc? \i\fhen compadng ti ue , how can you n1ake ·ure that your test i · fair? 1 \ Fine or coarse? Coarse gla pap r C andpaper') rub~ through a wooden urface n1orc quickly than fine gla pnpe1: Bul doe it produce more fdction? Plan and earl) out expt>riml;!nts lo find out. lllrl by 1hi11ki11g about the {ollowi11g: How can ,ou me-a ur..: tht: frictional force when gla ~paper i · rubbed on \\ood? llow can you keep the gla paper pre ed again t the wood? \Viti the [01 c u cd to pre s the g)a paper again t the wood affect the r~ult? How can you make sure that your test i fair? /: I I / I / I / . t / I l • I I / The period oJ "ing ,night be aHcctcd b\ th~ c factm : the ma of the bob, the amplitude ( ize) of the wing. 1he length of the pendulum. Plan and can-y out an t!nquir~ to find oul which facton; affect the period. I ·u,r1 by 1hi11ki11g about the {ollowi11g: The period of your pendulum will probably be a t:ouplc of ~cconds at mo t. How arc\ ou going to find the time ot one \\ing accurately? Ho\\ arc ,ou going to mea ure the j7,e ol the wing? I J. . 1 I ~-:=::;:> one comp!ete swing 286 The time of one con1plcte "\\ i ng of a pcndulu m is called i L'i period. I ' f Pendulum otc: make urc that the top of the pendulum tring b fi1·mly held o that there i no movement al that point. f Funlzer " 'ork: Find out how Lhc period of one pendulum compan..-s wiLh anoLher of rour li1ncs the lcnglh . Is the1-c a simple connection between rhe length and the period? Docs the connection work for other length · a ' well? PRACTICAL PHYSICS Stretching rubber A con1pany ,,·ant to n1arket a cheap ·pting balance for weighing letter.-.. Their de!-iigner suggcMs that, to ~,·e money, the) could use a rubber hand instead of a spring. Their technician says that thi~ would~ unsati~faclol') because rubber band~ change length and 'springiness' once they han: IA:en lretchL'd. \Vho is co1n~ct? Plan and can') out an enquiry to find out. Find the mass Plan ancJ carry out an experiment to find Lhe mass of a Jump o[ Plasticine (or some other solid). You arc not allowed to u ·c a balance "ith a m~ cale ah-cad) rnarkcd on it. And \OU arc not allowed to u c lottcd ma e or 1~ than 50 g. Further work: Take the problem a stage ftn-ther: Plan and c.:an~ out experiments to measu~ a much smalkr mas~ ~uch a~ the ma~s o( a pen or pcnc.:il. Thi~ time, you can use a !--elect ion of standard masses down to S g. Stan by 1lzi11ki11g about 1/,e /ollowin~: Your original dl: ign will probably not be sen iti\'e enough to mea urc a mall m~. Can it be n1odificd in on1e ,,a, lo n1ake it 11101-c en itivc? Bouncing ball Son1c table Lennis ball ha,c ,norc 'bounce' Lhan othct . Plan and out an cnquirv to compare the bounce of two table tcnni ball . CalT) rart by tl1i11ki11g a1Jn11111,c /ollou ·ing: \Vhat is meant by 'bounce'? \ \'hat do you need to mea!-iurc? \\'hen compating the balls, how can )OU make ~ur"l! that your lest is foir? Parachute design The diagrmn on the light ~how a in1plc n1odcl parachute. Plan and carry out an cnquit')' to Hnd out if thct • is a link between the de ign of 1he parachu1e and the speed at which it falls. ·tart by 1/zi11ki11g a!Jo1111/,e following: Shape and area arc two pos ible fcaturc~ of the design. \ Viii you inn.~ tigate both? How will you make ure that )Olli· te ts arc fair? How will ) ou ,, ork out the pccd or Iall? Double-glazing In cooler countri~. people tit doublc-glaLing in their hou ·c bccau ·c two la\ct of gla~. with air between, arc uppo~ed to lo~c thcnnal cnc1~ (hc..iat) more Jowly than a inglc la)cr. But doe double-gla7ing cut down 1hcm1al energy loss? Plan and earn out an enquiry to find out. rart by tl1i11ki11g alJOul the /o/lo\l'i11g: How an.: you going to ~et up a double layer of gla:·s ,, ith air between? \ \That ,, ill )OU u~c as a source of thermal cnerg)? How,, ill you tell whether the now of thermal energ~ i~ n:clucecJ ,,hen the extra la~e1· or glass is added? \ \'ill your test be fair? glass PRACTICA PHYSICS Salt on ice During winte•~ alt is often prayed on the road to melt the ice. Pure ice ha · a melting poinl of O °C. Adding ah to ice affecl · lhe melting point. Plan and can-y out experiments to find out hO\\ the 1ndting point of ice changes when alt is mixed in. Find out if there i · a connection between the melting point and the concentration of ~ah in the ice. (The concentration can be n1ea ured in gra1n of ah per cn13 of ice.) Star/ by 1hi11ki11g about the follo\l'i11g: How will }OU make sure thal the sail and ice are prop!rl~ mixed? How arc you going to measure the melting point? The speed of sound Jn the diagram on the left, someone i holding a \ibrating tuning fork above a mea uring cylinder. Sound \\,a\·c travd down the cylinder and back, and make 1he air inside \·ibr..ite. If the lt.mgth of lhe air column is exact!~ a quarter of the\\ a,·dcngth of the sound, the air\ ibr~tions are strongest and the air give out it loudt.-st note. The cffcc.:t is called rCM.>nancc. Ieng of air column The pced of ~und i linked to it frequency and wa,·elength by thi equation: pccd (ml ) = frequency (Hz) x wavelength (m) .-- ing the inf01mation abo\·e, plan and can:' out an enquiry 10 find the ·peed of sound in air. tllrl by 1hi11ki11g about tlze fulluwing: As a measuring cylinder has a fixed length, how will )OU vary the length of the air column in~ide? Apparent depth The person in the diagrc1m on the left is looking at a pin on the bottom of a beaker of water. Light rrom the pin is refracted (bent) when it leaves the w•j tcr. A · arc ·ulc. the water looks less deep than it really i and the pin appear ' closer to the ·ur1acc than it reall) b. Plan and carry out an e'\pcriment to find the apparenl depth ol some water in a beaker. Su1r1 by 1hi11ki11g about tlze following: If )OU look at a pin in some \\ater, it i · an image of the pin which you arc seeing. How can you locate the position o thi~ image? Could you u ·ea imilar n1ethod to that u cd to find the po~ilion of an i1nagc in a mirror? - -. Two pa;rs or one? PL-oplc claim that two pairs of socks arc warmer than one. But docs an extra pair cut down the loss of thermal cncrg~ (heat)? Plan and carry out an enquiry to find out. (You d o nol ha,·e to u ·c warm fccr a )Our ourcc of then11al energy!) 288 1ar1 by 1hi11ki11g about 1/te {ollowiug: How arc you going Lo tell Lhat one object i~ lo ing heal tnorc rnpidl\' than another? Ilow will you n1ake ut~ that \ otar test L fair? PRACTICAL PHYSICS Image size and distance ....·-~- 1mageon -- convex lens 0 I r~y box - - - ~~ . - __--c-;: ---~------- ~ ..,... ------ Place a bright object\\ ell away from a convex lens as in the diagram, and ~ou can get a dear image on a screen. lf you move the object do ·cr, the ize and the po ition of the image both change, and )OU need to mo\'e the ct~cn to get a clear image again. l there a connection between the ilc o[ the image and it di tance from the lcn ? Plan and car11 out an cnquit, to find out. Current-voltage investigations Plan and can)' out experiment to find out how the crnTcnt in each of the following depend · on the ,·ohage aero ·· it: 1> nichrome wire, kept at constant tcmpcrdture 2) the filament of a lamp 3) a sem iconc.luctor diode. by 1/zi11ki11g alXJlll Ilic /ollou ·ing: How will you \'ary the \'Oltagc across each omponent and measure the current in it? \\'hat checks must you do to make sure that the current in each component i~ safo, and doc not cau ·c damage? tar/ Making a resistor Rc i ·tor · arc u ed for keeping \ oltagc ~ and current~ at correct levcl in electronic circuit . sing nichrome..: \\ ire. make a 1-c ~i ·tor with a rcsi tancc of 5 n. tart by tl1i11ki11g about the following: How do~ the length of wire affect it · rcsi ·tance? How i · resi ·tance calculated? \Vhat circuit will you use to test the nichrome? From your mca~un:mcnt~. how can) ou w01·k out how much wire you nccc.l? Thermistor investigation Thcrn1i to1 ha\' a re i lance that vmi~ con~iderablv with tcn1pcraturc. They can be u ed as ten1perature ·en on,. Plan and carry out an cxpcrim .. nl to find out how the resi~tance of a then11istor n1ries between O°C and 100 °C. Star/ by 1hi11ki11g about the {ullowing: How will )OU change and contl'ol the temperature of the thcrmi ·tor? How \\ill) ou n1casurc the re i tancc o( the thcrrni tor? How will) ou n1akc ure that your circuit do n•t heat up the thcrmi tor? -------:, t ssue paper -- card \.·11th square hole an it Thi · ~p.-cad should help you ff you have lo rake a p1 actkal LL'Sl in ph\sic!-1. The Lest i the same at both Coa c and E.,tcn<lcd Lcvd. You \\ill not need anv "-nov. ledgc of ph, ,ic be, ond Core Le, et. There are t" o typka I quc~tion!', on the oppo~ite page. In~tcad of d oing a practical l~t. , o u ma, ha,e- to ~it an ahcn1ative-to- practical examination papc1: Your teacher\\ ill be able to tell ~ou which form of a~:-,cssm ~nr applie~ to \'OU . There arc son1 ~ :-,an1ple ahc111:1tivcto-pn1cti al quest ion!'. in •c Lion 15 ( IGCSE practice quc~tions). Apparatus used in the test In your test. you could be asked Lhe following: •• •• • • 10 can out experiment · invol\'ing 1ca.~uring phy ·ical quantitic ·uch a~ length, \'olun1e, or force . Cooling und h(..>ating (for ''\ample, Question I on the next pag •). prings and balance (for e, amplc, Qu~~tion 2 on the next pagt.:) . Tilning motion or osdllalions. Electric circuits. Optics cquipn1cnt uch a mirror , ptisn1s, and lense . P~eparing for the test &:fore raking a praclical test, then.! an: ccrlain things ,ou m.~d to be familiar with. Th~sc are Ii LL'<l in Practical pre paration on p, ge 292. MoM al ·o appl~ if }OU arc taking the alktnath·c-Lo-practic-aJ paper. Go through the list and check them one by one. During the test •lake • • • • • • Ufi' that you can do the following: Take plcnt, of reading . \ \'hen you r 'cord )Our reading~. rcmcn1bcr to include the cotTect unit ·. 1f you arc putting )Our re~1dings in a tahlc, th ~ column heading~ should al~o include 1he con-eel unit . Record readings or r~~u lt~ \\ ith a suitable dcb,1J·e • of accuracy. Identify an) anon,a]ous rcsuJ ts. Ju ·tit) ) our conclrn,ions b)' rden ing to ~our data. Idcntif') any po ~ible causes of unccrtaint\. For more information about ony of the above, see page 292. s: rthe q ,:)stions e 1 In this experiment, you will investigate th' clTccl of insulation on the cooling of watc1: f thermometer thermometer 2 insulation Wclt~r bec1kcrA-:..-:..-:l______ water bcak~rB-::1:1,_ _......_"-.._ bcakC?t A a i ii ill iv Suggest l\\ o condition~ that you had Lo ke~p thl" ·a1ne so that the co1npaii ·on bet \\ecn beaker A and beaker B i tail: (2 J De clibe one pn.-caution that )OU took to make sure your temperature reading · \\'Cl\! as accurate as poss iblc. [ ll In this e).pcti1nent, vou "ill i1n estigate the reh·action ol I ight a it pa sc.: · through a rectangular tran pan:nt block. bctlket B Pour 200 cm 3 ol hot water into beaker A. 1\11.?asun! the starting t<:mpcrc1turt! of the hot water. Record this tempcratun: in Table 1.1 tor time L - 0.0 s In11nediatcl) 'tart the ·topwatch. In Table 1.1, 1 xorcl the tc1npcratm 'of the wat 'r 8 e\'Ct 30 · until you hm c eight scl~ of n..-a<lings. Rcpi.?at steps i 10 iii using beaker B . Beaker B has insulation around iL but no li<l. tls beaker A (no insulation) beaker B (with insulation) IH IH 0.0 X y D C N plain ~per Fig. 2.1 a - i ii iii [3] Table 1.1 b Complete the mL ing unit · in the colrnnn heading in Table 1.1 ll l c i Plot a graph ol 8 (v axis) again~• t (x axb) for hc:akcr A. Draw the line of b~sl fit. f 41 ii Plot a graph of 8 against I for beaker B on the same axL'S you ust:d for beaker A. Dt~\\ the line of be t fit Jor beaker B. [21 d oc ~ctibc what yorn· re ult · ·how about the eltccl ol in ulation on the cooling of watc1: sc data from \Ottr tabl, and graph in\ our answci: f2l (0 OUP· this may be reproduced ror class use solely for the purchaser's institute iv v vi Place the t~ctangular block, large t foce do\, n, in the n1iddlc ol a piece ol plain pap •1: Draw around the block and Lhen 1'\!mon: it. Label ABCD . Draw the no1mal 1\1 al the centre of ~ide AB. Label the point X where the normal l\fN cro e ·idc AB. Continue ~o that it cro~c · idc CD. Label the point Y where M crosses side CD. Draw a line EX al an angle of incidence i 30 to the let t of the normal, as sho\\ n in Fig. 2.1 . Place the paper on a pin board. Place one pin P 1 on the line EX clo~c to point E . vii Place another pin P2 at a uitablc distanc' fron1 P 1 on the line X . 291 P AC ICA P SJCS b i viii Place the rcctangu lar block back in the same po it ion on the plain paper. Ob er"\e lhe itnagc:, of the cwo pin~ through ide CD from the position of thee-,.' in Fig. 2.1 , so lhat P 1 and P 2 appear behind one anothl.!1: ix ii r21 Change the angle of incidence to i 50 and repeat tcp av to a i. Mca.-.ure the angle ,J and th' length/ when I 50 . r21 d talc whether ~our results suppo,-t the c Place two mor .. pin , P 3 and P 4 , betw' ·n vour e-,. c and the rectangular block. Make sure that pins P 3 and P 4 , and the images of P I and P 2 appear bchi nd one another. x Label the po it ion ot all the pin P 1, P 2 , P 3 and P4 . Remo,·c the block. xi Dra" a Iine that pa c through Measure the angle ;J bcl\,een the line joining position~ P 3 and P 4 and the line Z1 . Mca ure the h:ngth / bet\\ ccn Y and Z. [olJowing ~uggt.•slion: 'The angle u i~ alwa\ equal to the angle of incidence i. c ,our re ult to .iu tii-y your an wee ( 1) e De c1ibc on· precaution that ,·ou hould take with this experiment to make !->Ure that your n..~ulL"i arc as accurate and reliable as po. sible. ( I] po itions P3 and P 4 and continue th .. line until the point whc~ it mcct!-1 the normal M . Label this point Z. f3] Use the list below to help you prepare for your practical test. The page number, in brackets. tells you where to find more information. Pr · al pre ration □ \\' hen using meter or other in trumcnt \\ ith calc on them, be able take reading that lie between the dhi ion on the calc. (page 283) □ Calculat' in1ple areas and volume : fo1· cxampl ', the area of a rectangle or triangl •, or th' \Olum' of a n..-ctangular block. (pag !S 20 and 296) □ Alto\\ for lcro c1To1 ,, hen making m 'a urcn1cnts. (pag' J 7) □ Record readings, or <lo calculations, with a uitablc lc\'cl ot accurac, - and not include too man) ignificant figure . (page 2 2) Core and Extended Level heck lo make sure that \'Ou know ho,, lo do each oi the follo\\ ing. ~1o t of the e al o apph if you aa~ taking an alternative-to-practical CX_amination pap ·r. □ Idcntif) kc, \ariable . (page 280) □ Explain why certain \'ariab1es should be controlled. (page 28 l ) □ Mca urc length to the ncarc l half millimetre u ing a rule. (page 296) □ Mca-,un: angle to the near-c l half degree u~ing a protracto1: (page 296) □ Include the correct uni ls with your rc-adings. (page 282) □ Mca.."iurc time using a Mopwatch or stopclock. (page J 7) □ Find the a\'eragc , ·aluc of sc,eral similar reading~. (pages 2 2 and 29-) D Measure mass using a balance. (pages 14 and 22) □ Draw a line of bc~t fit on a graph. (page 284) □ □ Find the gradi ·nt of a graph. (page 30) □ Read otf new vaJucs from a graph line. (page 295) nderstand direct and in\ crsc proportion. (page 295) If mca uring the ma ., of a liquid, allow for the n1a of it container. (page 20) □ Mea tn-c the volume of a liquid u ing a measuring C\lindcr. (page 20) D □ Mca-,un: a force, ~uch a weight, u-,ing a pt ing balance. (page 38) D Ora\\ circuit diagram u ing , mbols. 292 (pag !', 178 and 321) Asun1maryof the mathcmal ical concepts and skills required for IGC E cxan1ination . eh pter 14 293 For JGC E L'Xatninalion , )OU will lll'l'<i ·omc bask skills in malhcmatks. The folio,, ing arc t\ pical ot what i required. Adding, subtracting, multiplying, and dividing You should be fan1iliar with the syn1bol-.; +, - , >- , and 7 and the processes they reprc ·cnl. This ma ·ound ob, iou~. but ic includes undc1 ~tanding the link between dh·ision an<l ractiorr. as described HL'Xt. Using fractions and decimals A half can of course be writLen as~ (sometimes p1;ntcd a.~ ½ or 1/2). However~ you should also understand thac il mean · l 7 2 Improper fra tion~ are those with a bigger number on the top than the bottom: for example.~~ , which nH.~an 48 :- J 2. You hould be nb)e to ,,•rile fraction u. i ng deci ma 1 . o. one ha 11 i 0.5. Decimal · may ha,·e ·evcrul numb1:1~ after th1: point. However, you ·hould under.,,tand Lhal 0.489, for example, is smaller than 0.5. Using percentages You hould under tnnd that percentage are fraction of one hundred. o, tor example, one half is - 0 . which b -ore. The percent svn1bol "r reullv mean · I O0 • • 'di, idccl by I 00'. Using ratios Ratio~ are another wa~· of exprc~ ing fractions. Tf ~on1e app]e are being shared between two people in the rutio 2 : 3, then: art! - 'parts' to divide up, so one per ·on get~ 2 of the to,al, and the ocher gets 3 of the total. 5 5 If there were JO apple , to sha1\!: one person \\ ould get : ) I 0, which is 4 apple ; the other pc, on would get ~ x 10. which i 6 apple . Working out reciprocals 1 is called thl' reciprocal of the nurr1bl'r. For example: number The rccip,ucal of 2 is!, or 0. - . 2 The rcciproc-Jl of JO i / • or 0.1 0 You may have to work oul reciprocal when prepadng reading for a grnph. Many calculator~ ha Ye a pecial key for doing thi . 294 MATHEMATICS FOR PHYSICS Drawing and interpreting graphs and charts Graph~ arc a way of pre cnting ·et of scientific datn ~o that trend or laws can mon! ca~il~ be s" "n. For mo1·c information on how to prepan! a graph anc.l draw a line of best fit, sec spn:ad 13.4. You should be able Lo read off nc" ,alue from a graph line. Finding \'aluc bct,,ccn c:d ting point i called interpolation. Extending a graph line to c timatc new \'aluc beyond the mca urcd point i called c ·trapolation. Data can also he present ·d in chart~- A table is one form of chart. A pie chart is another: il shows Lhc c.li ITcrcnL propol1ions or percentages making up the,, hole. From the example on the right, you ~houlc.l be able to <lec.lucc that 25° t of the people at a football match ~upp011ed the a\\'a~ team. A Proportions of home and away supporters attending a football match Understanding direct and inverse proportions Look al the sets of \'aluc~ for X and Yin the 1ablc on che righL If X double~. X y Y doubles; if X t1iplcs, Y triple~. Also, <li\'ic.ling Y by X always gi\'cs the same 1 4 2 8 nun1bcr (4), and a gr'1ph of 1r against X is a Mraight line through Lhc oiigin. These all indicate that X and Y are in direct proportion. Thi · can be c:\pt~~~d in the form Y :< X, ,,hct-c et; i the \ mbol for 'directl) proportional to'. 3 4 ow look at the ~et of ,·a lucs for X and Z on the right. In thi case, if X doubles, Z hal\'l.!S, and so on. And 1111dtiplyi11g Z by X always gi \ ·c s the ~ame number ( 12 ). He~, Zand X an: in inverse proportion. The table al o include · a c.:olmnn for the t~ciprocal · of X. ote that Z and at~ in direcr propo11ion. , another wa) of e~pre ing the in,·c1 e proportion bet,vccn Zand X i to wlitc: Z C( X Understanding indices 1/x ½· You hould know that 2 3 n1ean 2 x 2 x 2, and that I 0 4 mean 10 x 10 x 10 x 10. The tiny number · ' and 4 ar' called indices. For mon: ad,ancc:d work, it is useful to know about nc:gaci,c indice~. For example, I 0- 4 mean~ blO Understanding numbers in standard notation In standar·cl notation (also callee.I standard ronn, or scientific notaLion), number~ ar\: expressed u~ing powers of I 0. For example, l 500 is written as 1.5 >t lo >. Using standard notation, you can indicate how accurately a value is "-nown. Thi i · e:\plaincd in prcad J. I . Using a calculator You n~-cd to able to u c a calculator c.:orrcctly. f'or e:\ample, lo work out a 7 value for 6 x , vou would kev in thb: 6 x 7 ❖ 1 1 : 3 = 1I x 3 • • A~ a result, the cakulator c.li~play will ·how this: 1.2727273 Working out an average If vou have, ay, five in1ilar reading , and need lo find the a\'~ragc, you add up the H\'c readings and dhide the total by-. ( ee also p1·ead 13 . . ) 12 _ _ _, • - - 16 z 12 1 2 6 0.5 3 4 0.33 4 3 0.25 MATHEMATICS FOR PHYSICS lf a calcu]ator displa_ reads 1.2727273, you mu~L be able to inlcrpn!l this torn:ct]). lf the original numbers came from c:<perimental data, ou c.:ould not ju ·tify gh1ng the re uh o accurately. 1.27, or 1.3 if you round it up, would be more appropriate. You should ah,o be able to intcrprcc high number · on a calculator: or e'<ample, 2.5 >.. 109 will probably be di plaved as 2.5 E 09, or _ju t 2.5 09 Making approximations and estimations You shou]d be ab]e to check\\ hcLher a n:sulc is n:asonab]e by doing a rough ~timatc withouc a calculacor. For example, if you dh ide 12 by 2.9-, ~ou should rcali e that the answer wil1 be ju~t o\'er 4. So, i( the calculator di play 40.67, vou have made a mi take in keying in the number . Understanding units !lo c mea uremcnt have unit a well~ numbc1 : for example, a ~pecd of l 0 nl/ . \ hen giving a result, you mu t al way include the unit. For more about unih, ~ee spread 1. 1. rectang e Understanding number accuracy para eogram You shou]d undc~Land che significance of whole numbers. You ma~ count 12 ' Ludent~ in a room as an exact number, but if a length mea urcment is gi\'en a~ 12 rn1n, thi · onl) indkatc~ that the \'aluc lie~ somcwhct~ bccwecn 11.5 mm and 12.5 rnm. Manipulating equations If .vou are gh·~n an equation like thi ·: Z - X y you should be able lo rea1Tange it to gi\·e Y - Z x X, and X - ; Understanding the terms for shapes, lines, and angles As weJI a · the circle, sphcn:, triang1c, square, and cube, you need to know the term ·hown in the j ir ·t three <liagr,;.1ms above left. h af('d ;:;; / ) hX b b Using the links between length, area, and volume You hould be able to calculate the area of a rectangle, the ai~a of a tightangled triangle (see left), and the \·olume of a rectangular hlo k (see spread I.-). N Using mathematical instruments The basic instruments are a ruler for measuring length, a protraccor for measuring angles in degree ( 0 ), compa · ' L"S for drawing cirdes, and a set ~quarc tor use in dra,\ing right angle . s Knowing the points of the corn pass The dfrcctjon~ north, south, cast, and we t arc called the points of the compa s. To make ~urc you know which i which, look at the diagr-an, on th' leit. eh pter 1S 297 1 The diagran1 ho,, the ma ~ of a mca uring C\ tinder b ~tor .. and after a liquid is poured into it. cm an 200 200 A the current u ed and Lhc work done only B the lorce ust:d and the distance 1no, 1.:d onlv C thL" ma of the bo:\e and the cun·ent used onl) D the work done and the time taken onlv 5 The diagram sho,,s two forces acting on a small obje l. 3N 100 100 mass= 90 g ..,__ liquid mass= 190 9 \\'hat h, thl.! density of the liquid? A 100 g/cm3 B l 30 g/cm3 160 190 D l 90 g/cm3 C 100 g/cm' 130 160 2 A motot'C\cle accelerate from rest. The graph how ho\\ it pecd change \\ ith time. SN \Vhat i the I ultant force on the object? 2 • do,, n ward B 2 ~ up,,ard C J't.: do,,nwards D 1' upwards 6 How long. appro·\imatel~. docs the Earth take si,eed to rotate once on it o,, n a.,j ? A 12 hour B 24 hour C I month D 36 clan, mi's" 30 o.._________________ 0 10 \.\'hat di ta nee do ..~ the rnotorc\ clc travel before it rcachc a tcad\ pc~xl? 3m B 30m C 150m D 300m 3 \Vhich typ'of pow~r tation doc. not us .. steam from boiling,, ater to tum the generators? A coal-fired B gcothcm1al C h\ droclcctric D nuclear 4 An electric motor is used Lo Iift boxes onto a lorn. \Vhich of the iollowing values would \ ou ust.• to calculate the power of the motor? 7 \\'hen a car is tr..wdling along a road, the tcn1peraturc oJ it t, 1 "s increase . \ Vh, doc the air pre u1 • in the l)n: al o incrca e? A Th• molecules in th .. air expand. B The molecules in the air· hit the ~ides of the l\ rcs less often. C The moJcculcs in the air increase in number. D Thi.: molecule in the air move at a higher pced. 8 A vacuum flask has two walls of gla.')s \\ ith a , acuun1 between the two wall . \Vhich l\ pc of heat tran fer arc reduced by the , ·acuun1? A conduction and con,ection onl~ B conduction, con\'ection. and rndiat ion onlv C convection and radiation only D radiation onh 9 A fin: alarm is too quiet when it rings. The fire alarm i adjusted ·o that it produce a louder ound at the a1ne pitch. \\'hat dk'Ct doe5 thi ha\'c on the an1plitudc and the frcqucnC\ of the ound produced? A B C D 13 The p .d . and cun-cnt n!adings of four electric hcaten. arc shown in the table bclo\\. Which of the hcate~ ha the highest n: i lance? A amplitude frequency B larger larger same larger C D Sc1me same larger same p.d. / V current/ A 110 110 230 230 4.0 8.0 4.0 8.0 14 \ \'hich of the following shO\\ ~ the corTl!Ct order of planets from the un? A ~1ars Venus aturn B Mercu, • Earth Jupiter Jupiter C atu111 1crcut .' Earth • cptunc D Vcnu 10 \Va,cs in a ripple tank spread out when thcv pass throug h a gap. I Uranus aturn -1.ar aturn 15 A transformer has 200 tun1s on its pdmal)· coil and 400 turns on its sc ondarv coil. An alternating voltage of V is applied across the p1i1nar~ coil. -o I \.Vhat is the name A diflrjclion B rcflL'Ction or this cHcct? secondary coil 400tums C ref r-.lction D radiation. \\' hat i the, oltagc aero the ccondat'\ coil? A 25 V B SO V C 100 V D 200 V 11 Son1e of the wave.~ in the ek"Ctron1ag n •tic spectrum an~shown: 16 A sample contains 800 mg of a radioactive lorlg • - - - - - - - - - - - - w;rvelength • - - - - - - - - - -short rad10 waves 1nfrared - i p X-rays What arc the names of wa\'c P and wa\e Q? waveP waveQ ultraviolet C gamma microwave microwave D ultrav1olet A B --~gamma 12 \ \lhich component has a resi~tancc which decrease~ when the temJ)C!ralUn! incn:ascs? A filament lanlp B relay C thcm1i tor D tran former Q isotope. The isotope has a half-life of 6 davs and decays into a stable isotope by L'mitting alpha particles. \\' hat ma of the i otopc i till radioactive alter 18 dav ? A O mg B I 00 n1g C 200 mg D 400 mg 17 A loudspeaker emits sound \\"aves of frequcncv 640 Hz. The, tnnd through cold air at a ·f)\:ed of 320 m/s. \\'hat is their wa,dength? A 0.050 m B 0.5 m C 2.0 111 D 20 m Multict, ·r~ 0 (:a~tiori~ ( xtended) 1 The g raph how how the p 'cd of a motor )cle change \\ ith time. ~ mA 30 o.....- - - - - - - - - - - - - - 0 10 \ \'hat i the acceleration ol the n1otorcyclc du ting the first 10 ccond ? A 0.33 m l 2 1 B 3.0 m l!->~ C 150 m/s 2 D 300 m/s 2 2 A car of m~~ 1000 kg a ccelerate at 2 m /s 2 alo ng a traig ht, flat road. \r\'hat i the r • uhant force a c ting on the car? A 0.0020 B C 2000 D 5000 6 Th· tabl' how the p •rlonnancc of four di ltercnt electric motor . A B C D input power / W 200 300 200 100 output power / W 160 210 150 50 \\'hich motor ha the highe t clt'ici 'nc,? A motor A B motor B C motorC D motor D 7 Air i trapJ)\.."CI in a ·calcd \ lindcr at a pt m of 1200 kPa. The pi ton i pulled out lo,\h o that the air •xpands lo three tim •sit!-. Yolumc. Assume that there is no change in the temperature of the air~ , / -oo 3 The table g h ·e infonr1ation about the length of a p1ing when diftcrent load arc applied. 0 1 2 3 22 32 42 52 What is the spring cons1ant of the spring? A 0.03 1 1\/m B 0.10 / m C 3. 1 m D 10 ~ /m 4 \r\'hic h or the following enct·g) r •sourc es dot.~ not have the un as its main source of cncrg\ ? A geothermal B hvdroclcctric C oil D wind 5 \\'hic h o( these units is thc same a the watt (\\')? A J B J/m 2 C JI D J/ 2 300 ➔ air piston \\'hat is the nc,, pressure of the air? A 3600 kPa B 600 kPa C 400 kPa D 200 kPa 8 Copper is a better thcrrnal COllductor than gla . \\'hich tatcn1ent explain \\ h\ ? A In gla , the atom vibrate n1orc quickh than in copp•r. B In g lass, there are fn:c proton!-. that tran!-.fcr the thermal energy. C I n copp r, the atoms arc furthcr apart than in gla . D In copper, there arc tree electron that tran f 'r th' thcnnal 'nerg}. 9 A Ion') with a mas!-. of 3-00 kg has I I 00 kJ of cncr·gy in its kinetic en erg\ sto1·c. the spce<l 0£ the lo~. A 2.5 m/ B 6.4 m/ C 25 ml D 630 m/s alculate 10 An object i \icw"d through a con\'CX lcn which i being u ·ed a~ a magnifying gla s. X I 14 The table how data about the Eanh' orbit around the un. F I I ob,ect pnnopal fOC\IS \Vhich tatcmcnt de ctibc the image? A The image i re'- I and at po ition X. B The image i real and between the lcn and the eye. C The image is \'il'tual and al position X. D The image is \'irtual and bct\\ccn the lens and the c,c. 11 T\\o wire , X and Y ar' mad· ol th' am' metal and are at th • am• t •n1peraturc. Y i twice as long as X and ha" t\\ ice the crosssc tional an.:a. X average radius of orbit / km 1.5 X 1cf orbital period / s 3.2 X 107 \Vhat is the a,·eragc orbital speed of the Earth? 3 A 1.3 X 10 m/s B 1.3 m/s C 29 m/ D 29000 m/ 15 A transformer has 200 tun1s on its pdmal)' coil and 400 turns on its secondary coil. The alternating current in the primary coil is 4.0 A and the \'oltage aero the pdnlal')' coil i V. -o pramary coil 200 turns secondary coil 400 turns A(_)_________) \ hat i the cun·cnt in the econdar coH? A umc that the tran former i I 00f't efficient. A 0.5 B 1.0 A C 2.0 A D .0 A I V 2A 21 \Vhich tatcmcnt about re btancc i corTcct? A X and Y ha\'C the same n..~ istancc. B X has double the resistance of Y. C ' has four times the n:sistancc or Y. D X has half the rl: i tancc of Y. 12 \Vhich component, used in electronic circuit , allows current to no" through in one di re tion onl,? A diode B re i tor C thenniMor D tran'-.£ormcr 13 Three rcsiston, arc arranged in chi combination in a circuit. 16 An unMablc nuclcu ha 137 neutron and 8 proton . It dcca, bv emitting a ~pat1iclc. How n1an\' n 'Utron and p1·otons do• the nudcu~ have after emitting the ~-particle? neutrons protons A 136 88 B 136 89 C 137 87 D 137 89 17 A low mass tar, uch as the un, expand to forn1 a red giant ,, hen mo t ot it Jn drogen ha b !en convened into helium. \ Vhich of th • lollo,, ing will th • un b •con1e near the end of its life? A black hole B neutron star C upernova D \\ hite dwarf \ Vhat i the total 1 i tanc' o[ the th, A 6H 8 9H C 12 n !C rc~i tot ? D I U 301 s IGCSE Theory questions c 1 Drop~ of water fall fron1 the co111er of the r or of a bungalow. akulate the a\'cragc ..,pct.'<l of a drop of \\alt.'r. [3] d E~plain wh\' it i better to calculate the a\erage tin1c 101 5 d1u1~ o( water to tall rath ,r than ju..,t I dtnp. [ 11 2 a De caibe the dilte1 ence bet\\ L~n ma~ and [21 b A tudcnt wants to mca u, 'the dcnsitv of a small, irn:gularh shape.~ ph.~c of iron. he is giv~n the l'quipmcn1 in Fig. 2.J. \\ eight. drop of 3.0m cm3 Fig. 1.1 A student uses a ..,top,, a1ch to I imc how long it drop of walcr 10 fall from the roof lo LhL' ground. "fhc ~tudent: • ~t the ~top\\atch to .1eru • stm1... the ~topwatch "hen a drop of \\atcr lalls Imm the roof • stops the "itop\\illch when the d1·op of water lands on thc ground • n:pcaLs thi method (or anothcr four drops of takes ---8 r01· a \\ i.llc1: a 10 he ..,tudcnt record~ hi re-,uh in Table 1.1. drop number time for one drop Is 1 0.70 2 085 3 0.91 4 0.79 5 Table 1. 1 Fig. 1.2 shows the r ·ading on the student's stop\\alch for the final drop of ,,·a1c1·. ..... J!!!!!!!l6 - 4 .J!!!!!!l 2 Fig. 2.1 "an1c a piece or equipment, not sho\\11 in Fig. 2. J, t hut l he s t udcnt will use 10 mca..,ure the mass of the piece or it-on. [ 1l c Dcsc,;bc ho\\ 1hc student dctcrmines the volume o[ the piece of iron, using the equipment in Fig. 2.1. ( 31 d The~e an: the tudcnt~ n.: uh,: • ma,, ol i,un - 23.6 g • \·olumc of fron 3.0 cm Calculate the densit\' of ir·on. l r 3 Fig 3.1 sho\,: the distancc-timt.' graph or a c,clist tran~lling to hi.., (lit.·n<l'~ house al po..,i lion . . .... . ....... I I 1111111 I I I I I I ■ ■ I I R· _J Q omplctc Table J.l with tht.' time shown on the ,Lopwatch in Fig . 1.2. [ 11 b Calculate the a\e1~1ge time it take~ Jor l drop of water to fall hum the rool to th~ ground. [21 302 100 0 .t ■ I p I I I I I ~ ,, ✓ 300 • Fig. 1.2 ■ /, 400•• 200·• • s 500 · distance Im ■ 1 I '' I I I .• " " " i . . 0 10 20 40 .... .. . .. 30time/ s .... .... .. . .. .., . Fig. 3.1 . I I . 50 60 TT1 ,■ ■ ■ • • • 70 •••• Ill ■ • • ■ ■ ■ ■ ■ • ••••• ■ ■ I ■ ■ • A Describe the n1otion of the cvcli..,l during: i section P [I] ii sL-ction Q [I] b tah: the total di tance tr~n died b, the a c, lbt to hb frj •nd'~ hou~c. [11 c late the total time il take~ the c,cli~t to tr11\d to his friend's hou"ic. [ 11 d akulatc the a\c11.1gc spcec.J of the c,clist o\'er the\\ hole joun1c,. [ 1l e In \\ hkh M:Ction of the joU111c, docs the C\ di t tra,d the ta k t? E,plain )Otu· an"i\\~I: r11 a I Q NS Calculate the momentum of trolley A bdon.: the collision. [ I] b Cakulate the momentum of trolk•, B before the colli ion. [ l] The trollc,~ ~tick together when the, collide. c Calculate the \·c locit\ of the l\\O trolle\~ aftc1· the collision. [41 7 (Supplement ) Fig. 7 . 1 sho,\~ the spced-tin1e graph of a olid ball falling towards the anh. 140 120 4 Fig 4.1 shows the spcc<l- timc graph (or~• car. .. . R" s. 100 60 speed 80 50 m/s 60 40 speed mJs 30 .,.__ _ _~ 40 . Q 20 20 p 0 10 0 o...........__._......_.,__,._._.,_ 0 10 20 30 40 so 60 10 20 30 40 SO 60 70 80 90 100 110 t1me/s t1mM a Fig. 7. l Fig. 4.1 Describe the 1no1ion of the car· du,·ing the [I] b (Supplem ent) alculatc thc accclcration of the ea,· bctwccn / - 40 an<l r 60 s. (3 J c Calculate the total di..,tance travelkxl [41 d alcul~\lc the a\cragc spc •d of the ca1· O\'Cr the whole jornTIC\. [ l fin.t 40 s. Dc~cribc thL' motion oi the ball bct\\Ccn po ition R and po:-.ition S. [ 1J b The ball in Fig.7.2 b dnn, n when it i at a po~ition R. Add lwo an·o,\s to the diagram to ~h ow the forces acting on the ball. Label ea<.:h an·o\\ \\ ith lhL' name of the force. 5 A rectangular brick has a mass of 2900 g. Fig. 7.2 C 6.0cm 11 cm a Cal uk,tc the, olume of the btick. b Calculat,. th,. dcnsit, of the bdck in kglm \ 8 a r2J rJl E~plain the motion or the b,111 bcl\\L'L'n position P and posit ion R. Use ideas about fortes in ,our answL'r. (41 tatc t\,o conditions ncc<lc<l lor an object to be in equilibrium. F ig. 8 .1 hows t\\O tud1.:nts, 6 (Supplem ent) Fig 6 . 1 ho\\-, two LI ollc\' ha:-. a mass ol 200 g. Trolley B ha~ a mas~ of 300 g. 0 .25~ F ig. 6 .1 (2) and B , it ting 8 colHding. Trol lcv (31 p rvot Fi g. 8 .1 Each scudcnt sits I. - rn ltum the pi\ot. b Caku late the moment ol student A about the phot. (2] c Calculate the n1omcnt ol tudcnt B about the ph·ot. (21 d (Supplen1ent) Calculate" hen: anoth ·r student of Wl!ighL 250 ,, ill sit to balance the scc... aw. [3] 9 A bucket of water ha a mas or 4.5 kg. Gt'a\'i tational field Mt ·ngth = 9. :i X/kg. a Calct1 latc th • weight of the hu kct of watet: f 21 b (Supplement) The bucket of\\ ~llcr h angs r10m a sp1·ing. The spring docs not e,cccd its limit of proportionaliL, . i Define the term 'limit of propo11ionaJity'.[ 11 ii The un tretchcd length o[ the spring b 15 cn1. Its length incrca c to 35 cn1 ,,hen the bucket of water hangs fron1 it. Calculate the ..,pring com,tant of thi.: spring. [21 10 An aeroplane of ma 3.1 I 0-; kg accelerate unitorn1h fron1 r1..~t along a runwa). a i ~ ame one cnerg, store that inc1enses as the a •1·oplane accelerate..~ along the runwa~. ii a me one cncr""g\ store that dccn:a.scs as the aeroplane an.-d erales along the r11 l'l.tllWa). []] b (Supplement) The aeroplane ,~ache a speed of 70 m/s on the ru nwa, alter 25 . i Calculate the a, crage accclenu ion of the c acroplani.:. [21 ii alculatc the n.:suhanL force acting on Lht· aeroplane ,, h ilc it i~ accdcr.iti ng. [2] (Supplement) After the aeroplane take ol , it gain~ height and then fliL~ at a com,tant height in~\ circular path around the Earth. i \ Vhat is the direction of the n:~uhant lorcc acting on the aeroplane\\ hen ic is rh ing at a constant hi:ighL? [ 11 ii The spi:cd o[ the aeroplane in<:r\.•asc · but it height abcHe the Earth remains constant. talc ,,hat happen~ to th • ,i,e of th • r-~uhant lot c acting on the aeroplane. f 11 11 (Supplement) Fig . 11. l show~ a c, I indcr 20 m below the su1face ol the ,,atcr. - - - - - - - surface of water 20m ~ OOmm a Th' den it, of water i J000 kg/ m 3 and the acceleration of fn:c fall is 10 m /~2 • Calculate the prl!ssurc that the water exe1 ts on the Lop or the c, lindcr. [ 31 b The t:\ linder ha~ a radius of 800 mm. Calculate the lorce the\\ atcr e,erts on the top ol the c, linde1: [4 I 12 A tudcnt sch up the simple p ·ndultm1 in Fig. 12. l. The p •nc.Julum ~\\ ings hackwat·d'> and lon,ar-ds h~L,,ccn and C . iM.ilMiill-~W/ SU pport ,,, ,, , ' ' ' A/ ' string '\ C • ~ 4 .0 cm - pendulum bob B Fig . 12.1 a The ~tudcnt rncasurcs the time tor the pendulum to "ing h on1 A to C. De clibe ho,, the ~tudcnt detcn11ine thb time as a curatch as po~sibl •. r21 h \ \'hat ar·c the nan1c~ of the l\\ o H:.-tical forCl.'.., acting on the pt..'ndulum bob,, hen it is at position B? [2] c (Supplement) The mas~ of the pcndulunl bob i 150 g. \\ hen the pendulum ~\\1ng , it i 4.0 cm higher at po~ition than at po ition B. Gt'1\ itational field trcngth - JO , 1kg Calculate the change in gravitational potential cnc•"ID of the pendulum bob between A and B . r4J 13 a Describe the diff~1'\.'nce ~l\\ L'Cn rx:ne,,ablc and non-rene,, able energ,. ( 2] b i late t\\O advantages of rn,ing nuclear fi ion a~ an cncr~ n.: ourcc. r21 ii talc t \\ o disadn'lntagcs ol using nu cleat· fission as an Cnl!l"g\ l"CSOUl"Ce. [ 2 l c Other than nuclear and solar, state one renewable energ, 1t: ourcc and one nonrcne\\ able energ) tt: ou1"C('. [ 2] I d ( upplement) Fig 13.1 sho\\ s solar cells arrangL-<l in a n:ctanglc. 1111 ■111■1■11 111111111 S d A 12 \' batten po,H~rs the electric.: lift. Calculate the cu11·ent llo,,ing in the lift. [2] 16 J\ group of students use the t.•quipment in Fig. 16.1 tocomparc ho,, well rodsoi 12 m ditlc1~nt material conduct heat. ■11111111 2.6m Fig. 13.1 The solar cdls ,~cci,e 250 \ \' ol energy from the ull per qua!'\.~ metre. 'f'h<: cdls pt oduc.:e a cun-cnt of 2.4 A and~• potential dine, cnce o( 0 V. Calculate the cHicicnc, of the ~olar cell~. r·1 talc the narnc of the gal:::L\\ that thl: Eanh bin. [I] b D1..-:,cribc what i meant b, r xt~hi It of ch.-c1ron1agnctic radiation. f2l C The spl'cd of ligh l is 3.0 X 1 n1/s. alculalc the tin1e it takes light to n.:ach Earth from the ull if the distance bl.'t,,ccn thl' Earth and the uni 1.5 x 10' km. [2] draw,ng pin 14 a o~ 15 Fig 15.1 A man pu~hc~ n cupboard toward a van at a constant sp • 'd. Fig. 16.1 E:\:plain how tht.· tudcnh \\ ill use this equipment to dcte1u1 ine ,, hich material b the best conductor of heat . [ 11 b ( upplement) o~~cdhc the d ifl c":ncc hc1,H.'Cn thermal conduction in coppc1· and in plastic.:. [ 4] c (Supplement) Describe wlw thermal conduction i~ poor in ga~e~. [ 1] a 17 Complete the table bv writing T if the ~latement is true and F ifth· ~tatcmcnt b fal e . [2] m or (F) statement The Earth orbits the Sun ooce in app,oximately 365 days The Moon orbits the Earth once every 24 hours. - electnc 6ft The strength of the grav1tat1onal field around a planet increases as the distance from the planet increases. Fig. 15.1 a The lrictional Force acting on the\\ heel-., ol the cupboard b SO . \ \'hat i the site or the torcc that the n1an pushes the cupboard with? f ll b An ck-ctric lift mo\'cs the cupboard a \'Cl"li t1l distance or 1.7 n1 fn>m the ground to thl' , an's floor le, cl. The ,,·<:ight of the cupboard i~ Calculate lhc work done to lilt the 18 Fig . 18.1 ~how~" fixed \'olumc of gas in a ealcd container. I .--o .. cupboard. [2) c The po" er or the ck-ctric Ii It b 0.20 k\ \'. alculatc the time it take:-. forth' dcctdc lift to mon.• the cupboard to thL" ,an\ noor lcn~L [3] Fig. 18.1 gas molecule a Explain how the gas mokculcs c...:ei1 pn:ssurL" on Lhl.· walls ol the container. [ 11 b he ga i heatt:d. E,plain \\ hat happen lo the pn: urc of Lhc gas. (2J c ( upplcment) A fix~xt mass ol ga.s at a com,lant t.:mpcral urc has a volum • of 1200 cm ' . Thi: pn:ssut"C or the gas is 4000 kPa. akulatL' the, olunu.• of the gas al a prL"s..,un: o[ 2500 kPa. [3] 19 Thc planets in th~ olar \'Item diff,r in site and composition. a D<...~cr-ibc th~ differences in the site and composition ol the lour planets ncai·csl the un con1pan:d lo the four planets lurtllL'sl from the un. (21 b Explain the difJcrencc in part a using an accretion model tor Solar , stcn1 formation. [41 b The student heats -oo g of water in a beaker until it ·tart~ to boi I . The star-ting ten1_pcratm (' of the \\ atcr b 15 C. The pecific heat capacit, of \\ater i 4200 J/kg' C. Calculate the amount ol h 'at enc1·S' supplied to th' water to in n:asc it.., tcmpcn1turcto 100C. [4] c talc l\\O wa,s in which the c,aporation of a liquid i dil lc,~rll from "hen a liquic.l boils. [21 22 A sound wan: is produced al Q. The sound \\ an: travels Lowa re.ls thL' \\ al I. 0 path of soon d wave 20 (Supplement) A Mudcnt sets up the c,pcrimerll in Fig. 20.1 . t~rmometer SO w electncal heater ,_.,_ 2 kg iron block Fig. 20.1 Cx:sa;b,: how the student uses th 'cquipn1ent to detc1111ine the sp«."Ci rte ht.-al capacit, ol iron. In ,our am~\\er, incluc.lc an, equations the student ,,ill neec.l Lou ·c. [4] b The student calculalL-..., the ,alue ol the spccilic heat capacit, of iron to ix' 620 J/kg. C. The Lruc ,aluc of the pccific heat capacitv of iron b 4""0 Jlkg . E,plain ,\11\• the, aluc calculated h,· the student is higher than the true ,-aluc. [I l c uggL'Sl ho,, the student could improve the accurac~ of the ,alue the, oblaincd (or the [ I] ~pedfic heat capadt, ot iron. a 21 ( upplement) A student pours a sn1,1II an1ounl of water onto a table outside on a ,,ann, sunn, c.la\'. The water slo\\ h c, aporatcs. a Explain "h the table in contact with the \\atc1 cool do\\ n. Use idca about (31 306 a Explain \\ h, a pcr~on standing at R hears an echo. [ 11 b A ound wa,·c is a longituc.linal \\.l\e. De cribe the dilkrence bct\\L-cn a longitudinal \\3\C and a tran ,c1 ~e \\a,e.(2J c Th' ound wm c ha~ a spct.~ of 330 m/~ and a \\a,·clength of 0. 0 m. Cal ulatc the ln:qucnc, of Lhc sound wave. [31 23 The diagram sho,,s a ruy of white light incident on a gltw, pri-.m in air. The path of onh the 1\:.'lractcd red t"a\ i hown in ide the p1hm. a Draw,, rn, to show the path of the l\."Cl light ,, hL'n it emcrg~ lrom tht: pri"irn into the air:[ I] b On th~ same c.liagram, d1c1\\ a rav lo show the palh of ,iolcl lighl in the prisnl and \\hen it emerge~ lrom Lhe pli~m into the air. [21 c ( upplement) The rdr..1cti\ e index of gh1.-..s ror I l.'<l light is I. -2. The angle of incidence of the white lighc i 50 . Calcu1atc the angle ol r~fraclion of the ,~d lig ht in tlP glas . [31 d Ara,· of light enters an optical fibre at end M . The light undergoes total internal n:fkctjon a it ll~l\ds through the optical fib,~. M 24 (Supplement) The table ~ho\\ data about the planet in the olar v~tcm. Planet Orbital Orbital distance duration Average surface Gravitational field strength at / million km / years Ear th 1SO 1.0 lS surface N/kg 9.8 Jupiter 779 - HO 25 Mars Mercury 228 58 ~--~ 12 1.9 0.20 - 23 170 4.0 Neptune 4490 165 14 Saturn 1420 30 Uranus Venus 2870 108 84 -200 - 140 -210 460 temperature I °C. 0.60 I N light ray Complete thl! path of the light l'i.l\ until it emerges Iram end . [ 2] e (Supplement) The optical fibre material hn a rdracthc indc\_ of 1.5. Calculate the dtical angle. r31 tudl'nt A and tudent B ~Land 250 m fron1 a rlat wal1. tudcnt ha~ a stop,,atch. tud 'nt B clap!-! her hand~. Dc..~crihc ho" lhc ~tudent~ dctcrn1inc the sp1:cd of sound in air. Includl! an equation in )OUrans\\c~ [3] b Tht.: Luc.lent look at traces ol t \\ o souncl \\'a\e~. and Y, on an osdlloscopc. 26 a 4.0 10.4 10.4 9.0 a Gin:· one t •ason whv th • aYcragc ~urlac • tcn1peratu1 • of Uranus i.., le s than lhc a,cr.1gc srnface tcn1pc11.1tur'-!' of the Ear1h. [ J l b An object ha~ a mass ol I O kg. Explain on which planet the object" ill ha\-.: the greate t \\ dght. (2 I c Cal ulatc the circumference or Jupiter·~ orbit around the un. [21 d alcult'ltc ho\\ man\ time!-! bigger lhc Ea1·th's a,cragc orbital spct.!d is con1parcd to Jupiter's. [3] I .I a I ,\ r l l r1 I l I ' ', y X tudent A sa,·s that ,,·a,·e has a highl'r pitch and i louder than \\'a, c Y. I tudent con~ct? E,plain our an ~\ e,: [2] 27 There arc 7 region in the ckcLromagnctic pecttum . 25 A student hi ne-, a ray of light from a 1 '",. bo~ at to\\ ard~ a mi11-01: The rav of light i r 'lle t1..'Cl b, the minur towards Y . radio waves p z infrared vis,bJe light ultraviolet X-rays Q tatc the names or r •gions P and Q in the de tr·omagnctic ~pcctr·um. [ 21 b late which ~gion is used in electric gl"ills and tclc, ision r~motc c.:ontrolkrs. [ l] tatc \\ hich region is UM..-xl in ~curily C n1arking~ and ~tcrili ing water: [ l) a a Lall' the na1nc of the dolled line Z. b Late the narne of angle Q. c Dc..,cribc the relation hip between angle and angle Q. [ J] [ J1 P [1] 28 (Supple m e nt) The diagram shO\\~ the po~ition of a con\ ex lcn and an object QR. pos,t,on of conve>t lens R F p,incipal focus ► ► ~ 1~) ► ► principal focus principal axis a Draw l\\O ray lrom R that pa through the lcn~. U c the t\\O ra, to determine the pm,ition of the image. On the diagram, mark the po!-iition of the image and label il I. r21 b Describe h\O charactctistics or the image tormed. [21 c Dl: cribe how a divergjng lem, can be u ed to co.,- ·cl hon-.. . ightl.'C.lnc ~- 30 a A student sets up a circuit using a voltmett..•r, an ammclcr, a cdl, an<l a fixed resistor. D~l\\ ._\ circuit <liagran1 of the circuiL the ~tu dent \\ ill et up to dctc1111inc the 1~..,btance ol th, fixed n:si t01: r3l b The potential di l h:1~ncc aero., the r\.'-,i-,tor b 10 V. he cun~nt through the rcsi tor b 0. 10 . Cnlculatc the •~~i.,tancc of the rcsh,to1: [31 c ( upplement) Dn1w an arrow on vour· cin:uil to !-iho,\ the din1ction of the con,·t..•ntional current. [ I] d (Supplement) Calculate the tinll· it tah.c tor a cun-ent of 0.10 A to tran fer a charge of l.4C. [3] 31 A \tudent sets up a cir·cuit to inYcstigatc the resist an c of an unkno\\ n componcnt, X . Component y (31 29 The diagram ~ho\\S two ray~ of light, X and Y , from an obi<...-cl 0 . The two 1·a,!'> a1 'incident on a plane min"01: a talc the nam • of component Y . [ 1l b ( upplement) The student uses the circuit to takL' n1casurcmcnts of the curn:nt thr·ough X and the polenlial <liflc~nce aero s X . he plots a CUl1\.'llt- potential <lifkrence g1 aph her 1\.' ults lor component X . or current a Draw the normal to the miTTor at the point \\her: .. nn X 1-cache the min'Or. [ 1I b Dnn\ the path of 111, X alter· it rcachc!-i the nlirror. potential difference [ I] DL~CriiA: l\\O charactcti ties or the image f01 rned b the plane Jllili'ot: [] J d (Supplement) Draw the path of ray Y alter it ,-..ache!-> the n1irr01: ~ .. the paths of ra, X and ruv Y after the\' reach the mill"or· to locate the image of the C object 0 . Label the in1age I . 308 r31 talc thl! name of component X . I Il ii E,plain the shape of chc cun ·nt- potentjal di llc1~11Cl.' graph lor componl.'nt X. U e idea~ about ten1peratm-e and 1 ~i tance in i your ans\\Cl: f3] 32 ( upple m e nt ) The diagram shows two parallel conducting plates connected to a high-voltage uppl\'. 34 The cliagran1 shows a tr-ansrormer. r-----~:::a...- X secondary primary voltage ♦ high-voltage supply voltage secondary pramary co,I coil a conducting plates a b c d An clcct1ic ridd is pn.:scnl bet,,ccn the conducti11g plates. D • ctibc what i incant b, an clectlic field. [ l] Dra\\ line on the diagram to -,ho\\ the ck'Ctric fi ·Id pattern bct\\ccn the t\\o conducting plat •s. D1-aw an arm,, on one line to ..,how the direction of the dectric fidd. [2] A piece of 1'\.'sistance "ire is used to join the t\\ o conducting plates. A charge of O.o-o C p~se-, through the ,,ire in 25 s. Calculate the reading on the am1netc1: (21 The potential difl ,,-cncc ol th • hi gh-,oltag .. supph is han ged to 2000 V. akulatc the nc,, reading on thi: amrnclcr if 300 J of energy is supplied in 1- s. [3] 33 F ig . 33.1 sho,, an c,pu iment :._, student et up to in,cstigate the magnetic lidd due to a lllT •nt in a ~tr~ight wir•. cardboard I I I Q) compass -!.... tate the name of the part of the transforn1cr lab ·lied •. [ 11 b ( upple ment) E ,plain how l he transf01·mc1· work-,. [ 31 c A Mudent fills in a table about transfonners: input output voltage I V voltage I V step-up or step-down A 20 60 8 100 40 C 230 1500 step-down D 70 20 step-down step-up step-up \\'hich two rows in the table has the student filled in incon-ecth? [ 2] d The student finds out inf01mation about the hig h-, oltage trans1ni ion of dcctJicitv. ,oltag(' ac1u~s plin1an coil - 10 000 V numb •r of turn on prima,, coil - 4000 number of turns on sccondar~ coil 200 current through ~cconclarv coil = 2-0 A 1 Calculate the ,·oltagc across the econ<lan co il. [ 3] ii (Suppleme nt) Calculate the cun·ent through the p1ima1, coil. A~un1c that th' trunsrorn1er b I C clfici 'nt. r31 iii late l he ad, an lag ' ol using hi gh[21 ' ohagc tnmsmission of clcctri it\. oor 35 Th• diagram ~ho\\:-. a bar magn ·t next to a circuit containing a coil of,, irv and a ga hanomctc:1: D ~ clibc how the ~tudent use;'\ thi-., equipment to dctcnuinc th • magnetic field pattern produc'-"CI by the cmTcnt in the wit '. [31 b Draw the patti:rn and din: tion ol th" magnetic field a1uund the,, in: in Fig. 33.1. r21 c ( upplement) The student n.:,e~cs the <lil'\:ction of the cun~nt in the,, ire. Dc-.,cribe the elk-et this has on the magnetic field around the ,dn.:. [ 1] a •I I • •I •• ~p •• •, •• •' • •• f # # •' '• ' a I is A sLu<lenl lllO\ e~ thi.: bar magnet into lhc coil. Explain ,, h, the galvanomett·1· bridh deflect to the ldt. [2) 303 b uggL'sl one wav LhL' student can make thL' gah anomctei- <leflccL 1urthcr to the left. [ 1I c uggesl one wa, the tudcnt can make the gal\'anomcter deflect to the lig ht. 11] d (Supplement) As the bar mag net approachc.., the coil of wfr \ encl P of the coil a ts as the south pole of a mag net. Exp la in \\ h) cn<l P ha., l his polarity. [ 11 36 ( upplement) The Huhhlc com,tant dcsc dhi:s ho,, last the uni,·crsc is c,panding and can he usL-<l to csLimate the age ol the ni,cn,e. a tale the definition of the Hubble con tant and an L-...,tin1ate of ih CU11'CIH \aluc. (21 b A gak ~, b 1110, ing awa, lro m the Earth at asp '(.xi ol 1.6 x 10::; ml-.. Calculate th' dist~mcc from th • arth to this gala,~. [21 c The gn1ph sho\\s th • rdationship bet\\ ccn the spL-cd of gala.,ies Lhat arc n10,·ing a\\ a, from the Earth and thdr<listance lron, the Earth. he \aluc or the Hubble constant can al o be e'\pre.,sed in km/s/Mpc. 'th" graph to show that the ,aim: of the Huhhl • constant h. appr·o~imat •h [21 6 7 kmls/Mpc. Calculate the reading on the ,ohmcLc1· when the thc1misL01· has a resistance of 4.5 kn. I 3] 38 Radium-226 i~ the mo~t ~table i otopc of 1 adjum. Radiurn-226 ha~ a proton number of and a nucleon nun1ber ol 226. In nuclide notation, radiun1 i \\l;llcn a : a i [ I] late the , ·alue of A. ii late the , ·aluc of Z. rI] iii Calculate the nmnber ol neutrons in the nucleu'> of rL dium-226. l2) b R.adium-228 i another isotope of radiwn. E,plain what is meant b, the tcrn1 botopc. r21 (/) .......... E 20,000 ~ ........ "O 10,000 0. circuit C )R,1 30t000 QJ QJ In,, hich ci1·cuil i~ the current the samL' though both n:~i to1 ? [ I] ii (Supplement) In\\ hich circuit i the potential dHlercnce the ~ame acro~s [I] both rcsbtm~? iii Cakulatc the combined r •sisHmc 'of the n:sislors in circuit A. iv ( u pplemenl) Calculate the combined fL~i~tancc of the re i~tot in circuit B . [3] b (Supplement) Circuit C contain a the1 mi tor and a 1.5 kn I e i tor in "crie . Th 'l'C is no CUIT'nt th1oug.h the ,oltn1ct "I: a i (/) 39 Thc graph ~ho,,s the de a,· curve of radioactin: isotope 0 400 0 100200300400500 distance/ Mpc 300 count rate 37 T\\o fhed tL'si::.toa . ar ~ conne tcd in a circuit w ith idcnli al balle1 ·ics. counts/mm 200 ------1--~......,__ 10 300 0 cercuit A 310 ----. 300 0 ,___ ClrCUlt 8 30 40 t,me/ mins ....,_-t 1000 t,....---t 100 0 20 a i ii Define the ternl half-life. I IJ Detcrn1inc the half-Ji le ot radioi otopc.:from th, g raph. r21 IGCS b Another radioisolopc, B. starL"i with the same count rate of 400 count~ min. Radioi otope B ha a long.er haU-Jirc than rudioisotopc A. D1 a\\ al ine on the graph to ~ho\\ the decay Cll I'\ c of radiobotopc B. 12] c ( upplement ) ,.\ scicnt bt wanh to dctc1minc the half-Ii fc or radioisotope C. The background radiation mL"asttrL-<l b, a detcc.:tor "hen no radioac.:ti\ c isotopes arc pl\:sent is 30 count~/m in. The cicntbt mo\·c radioi otopc C closer to the d lcct0t: The t'\:ading on the dct ~tor incn:ascs lo 1 '"0 count!',. min. Arter 20 da,s, the count rate is 50 count,/min "lien radioisotope C is at the same distance from the dctccto1: Cakulate the hall-life of radioisotope C. [4] americ1u m QU S 10 S alarm air inside smoke detector alpha r adiatton alpha detector smoke c A bean, ol <1-pa11iclc-, enter an electric field bctwt.--cn two charged plat~'!-.. ____.i__..,<.._ negatively charged plate beam of a-particles 1 40 Thn.· c t,pcs of nuclear crnissions arc: alpha radiation Ix-ta radiation gan,ma radiation a i tale which of the three nuclear en1is~ion" ha~ th • g1'\:atc t ioni,ing dk"Ct. 11 I ii late" hid, or th' three nuclear cmission!-i [I] has the lo\\~st pcncll a ting abilit,·. b 1 Desc1·ibl! ,, hat is nlcant b, the term [I] background radiation. tale t\\O OUl'Cl.~ or background u radiation. I 1] c (Supplem ent) A beam ~ panicle, en tcr a mugnetic fidd between the pole~ or a strong m~1gnct. P AC JC I < (positively charged plate ketch the path of the beam of, -paniclcs bctwt.'t'n the charged plates. [ 11 42 (Supple m e nt) a tale the tin1c, in \t:-a1 . , that it take-, light to tn\\'cl 10 million light, •tu-~ in spnc '. [I] b Calculate the time, in ,car , it take for light to travd 1.9 10 1' km in space. [21 c Complete thc diagran1 to show the life cvclc of a star: [6] int ~1 . tcllar cloud of duM and gas .. ~ or ppartlcles ~t~u / 41 (Supple m e nt ) ,\ mcl'icium-24 J is ra<lioacti, c. An amcticiu m-24 J nucleu., <leca\ to a neptunium nucleus b, cmiLLing an n•pa11iclc. a Complete the equation to show the d~"Ca\ of americium-241. 12) ➔ . p ' lo\\ mass EJ Ocsciihc the path of the 1 pa11ich:" in Lhc magnetic fidd. r3J 2 1 : Am i) + o b Th~ diagram ~how:-. how an1 dcium-24 I is u~"'<I in a household ~make ala11n. sc the main ~cqucnce star ~ iv) ii) ,. '. superno\-a planctarv nchula and iii) ·• \') or 1 <liagranl., to dc"icr;bc how the smoke al.um "arks and c,plain \\ h, the smoke alarm rings \\hcnthcrcisafoc. (21 high ma ta.- \'i) 311 If ,ou do not take a practical examination, ,ou will sit an alternativ ..-to-practical paper instead. Her .. an: some •xamplc.~ oft~ pical questions. For sonic of them, ,ou will r :quire grap h pap •r. IGCSE Alternative-to-Practical Question~ 1 A student b in,·' tigating "pring . The tudcnt measures the unstretchcd length /0 ol th • spring in mm. he attaches the !-.pring to tl clamp, as shown in Fig. 1.1 . -o-e damp stand d Plot a graph of C\:tcnsion e I mn1 (x-,l'.i.) against load LI , (,-a,is). Draw a line ol bcsL fit. (-1 e A student suggcsls thaL the length / or the spring i dirL'Cth proportional to the load L. h the tudenl corn~ct? Explain your [l) r ~e, our graph to dct ·rminc th • c~t 'ns ion of the :-.pr ing "hen a load ol 2. , is added. [I] 2 A student wants to detcrrnine a \'aJut.' for the accde1·ation or free fall~Fig. 2.1 and Fig. 2.2 how the equipml·nt the student :-.cts up. L---.,..........1-- clamp Fig. 1.1 The stud 'nt: • hung" a load/.. on the spring • mcasun:'-\ the nc\\ length/ of the spring • calculates the extension e or the spring • 1'\..'pcals the mt:thod "ith diilerent load . a On Fig. 1. 1. dra\\ the pm., ition where the ~tudent \\ould place a ruler in order to accurately mcasu1 .. th' length/ ol the spnng. U] t Th' un~trctchcd length of th '~pting i 4- mn1. The :-.tudcnl n: oi·ds her mcasu, •menL in a table. load LIN 0.0 1.0 45 48 2.0 50 3.0 54 4 .0 57 5.0 60 b Com plcte the in the table. l\\ o I \ I \ I \ I \ I \ damp 0.0 missing column heading [2] c Calculate the C'\tcn ion of the- spring for each load added 4'nd wri l .. ~ our 1· "-suits in the table. f31 312 I \ I \ I I I cj bob Fig. 2.1 \ \ \ \ c:> Fig. 2.2 Th<.· ~tu<lenl :-;ets up the equipment"° that the length / ol the pendulum i actualh 44 cn1. D ~c1ibc ho,\ the Mud ·nt pre, ·nt~ a parallax cnor wh ~nm ..a. uring the length/. [ 1l b Th ' student mo, c:-. the bob to one side slighth. hi..' ,·ck--ase" the bob and m<!asun:s the time t for 20 complete oscillations. The time, b 'iho\\ non the.: ~topwatch in Fig 2.3. [2J a \\'l'itc down the time I shown on the stop\\atch. [I] ii The period T of the pendulum is the time for one complete o dilation. Cakulmr the pc1iod To( the pendulum. [2] ii c To dctcn11ine a valu • for the ace ·lerati nor fr ·c lt1l1 g, the student rn.~d~ the valu • of i Calculate T 2 to a ~uitable nun1bc1· or significant figun:s. Gin~ the unit. [I] ii Calculatt: the accdcration of lrL"C fall .~ u-,ing the equation: r-. Fig . 3.3 sho,,~ the \·oltmct •1·r·ading for s1.:ction JL of the win:. ~ 1 V 3 '\ 4;!/ r g = d Fig. 3.3 uggcst t\\O in1provc-mcnt that the- tudcnt could niake to the exp "timcnt. "in: aflL'Cb its •~sistancc R. The tu<lcnt set up thl: circuit in Fig. 3.1. pow<?r A J L c i R U] V I ii talc the unit of n:sistance. [I] d Using the n:sult~ in Table 3. I , prL"dict the •~si ta nee of the same piece ot \\ ire \\it h .. length o( I. - m. f I] ----o sourcl] :0___...,,___ I( r [21 3 A stud1.:nt inn~stigatcs how the length/ of a Fill in the mi sing pot 'ntial di llet ·nee rca ding for ~ect ion JL in Ta bi e 3. J. 11 Calculate the 1 •~i~tancc R of each section ol the ,,ire. Use lhL" equation: M 4 A student inH.'sligatL~ if the l'l:!-ii tan cc or a \\ ire dc~nds on the metal from\\ hich thl' \\ire is n1ade. The following equipment i a\ailable to the Fig. 3. J The tu<lcnt mea~un.: the current / through the\\ ire. He al o mcasm~s thL' JX>lcntial diflcrcncc \' act section~ JK, JL, and .JA.1. The student's n1casm "mcnh ar" shown in Table 3. J. section of wire t/cm VN //A JK R 0 .95 The r •sistancc is calculated using the equation: . Jl potential di/]eri:11ce re~,,,a,,ce - - - - - - - - 1.9 JM Table 3.1 a stud "nt: an1m 'lcr conne ling leads pO\\Cr supph re~istancl.' wires made ot diflL"rcn t mL"lals s\\ itch , ariable t ' i tor voltmeter ing Fig. 3.1 , c.:ompktc the length column in Table 3.1. [ I] b i Fig. 3.2 ho,\~ the an1mctcr reading for all t111· 'C st.--ctions of the ,, ire. 02 0. 1 0 -7 03 A / 0.4 0.5 Fig. 3.2 Cornplctc the current column for c-ach M."Ction wi l h th • r ·ading shO\\ non th' ammct •1: rI l , 11n-en1 Plan an cxpcri1ncn1 to inn~~tigatc i I the resistance ol a ,, ire depends on the metal from \\ hich the\\ ire is made. ln \ our plan include: - a diaga .. n1 of the circuit ~ou" uld L't up to dete1111in > th • l ~i~tancc of each metal wi, .. 3) - a dcscdption of ho\\ you \\ould perf o,~m the c,pc1·imcnt, including an, mca..,urcnllml~ \ OU \\Ould lake rJJ - kc, \aaiabh.: that )OU \\ould nt.~d to control [2] - a table to dh,plav \ our h:ading and cakulmcd ,-aim: , including column headings (\OU do not n .. xl to \\1itc an, , ·ading.-.. in your tabl '). (2) r 313 5 T\\ o students <lo an c,periment Lo c alculate the 6 A student is inn.•stigating the cooling using lhe equipment in Fig. 6.1. speed of ~oun<l in air. student A or \\ater student 8 thermometer wooden bkxk hd insulatio Fig. 6.1 I - - - - - - - d -------' The stud •nt pou~ 200 c m 3 or hot water into the insulatL-d beaker: He cove1·s 1he lop of the beaker \\ilh a licl. a The thermometer in Fig. 6.2 shows the temperature o( the water in the beaker at the tart o l the cxpcrin1en l. The stud •nh tand a diMancc cl apa11 . tu dent B tart.~ the stop" atc h \\ hen she \C •s studcnL hitting the wooden block.~ together. tude nl B stops the stopwatch \\hen she hem ~ the ound made bv the wooden block... and record~ the time intc1,al t The student-. repeat the c,pcrin1cnt liH~ timt'""· The, r ·cord the re ults in a table and alculatc th • spL~d of sound ,,. t/s V (m/s) ~-~ 344.83 , .1 9 336.13 1.12 357. 14 1.11 360.36 1.20 333.33 IO }0 ?) M> 'tO 60 I I • I I I Fig. 6.2 \ \'tile down the starting temp ' f1lturc D., ho\\ non the th •r·momctcr in Fig . 6.2. rl l b The ~tudcnt n1ca tar's the tcmpc11ltt11\! Oof the\\ atcr "\ •r, 30 s a!'-. the water cools. He n.: orcls th<.: 1·cading!'\ in Table 6. I. r21 tls I)/ 0.0 86 30 80 Estimate the disLance cl bcLwcen the two 60 76 studcnL,. [ 1] b uggest a uiLablc piece ot equipment that the tudcnt u~ to mca-,urc the dbtancc d. [ I] c Cnku late the n1can, aluc lor the sp ' ..d of sound from the :,,,tudcnts' results. [21 d In the table, the students n.-conk-d their· values £or the speed or sound,· to ft\e signiricant figures. E.,plain ,, hcthe1 this i a suitable ntunbc-r ol "ig nHk anl figure lor the students toll~. [ 1] 90 73 120 71 a 314 1.16 C Table 6.1. Complete the n1issing unit in column L\\o in Table 6.1. [ll u akulatc the cempcraturc drop D.0 1 during the [i1 t 60 s. f I] ill Calculate the tempc.:raturl.' drop ~ 02 [I ] bct\\een 60-.. and 120 -... iv E,plai n wh) ~ l/1 i dill c1 •nt from ~ 02 • [ ll c The student n:peat., th • c,pcrimcnt. uggcst two changes that the saudcnt could make Lo the equipment to make the \\ater cool down tllOI'\: quick!\'. r21 .. chapter 16 315 In most ca,cs, the equation.., below arc gin:n in both word and s,mbol form. -~= IO i\/kg - IO rn/ 2 (Ea11h's gravitational fidd strength) Stretched sprinq load density = nla~ · ,olu.-nc >' cxt~n ion kt (acceleration of free fall) Density, mass, and volume spring com,tanl Pressure nd force D~~,ur, _ force ' area c Ill I' \I Speed PrPssure in a Liquid average ~peed mo\'cd = distance .tJn1c taken - pre. ure dcnsitv x g x dcp1h Acceleration accdc1-alion change in \'cloci l, tin1c taken Temperature Kelvin 1enlpc:ralun: = temperature in Comoressin ases ·- 273 u,· (l - - ill Fo1· a fi~cd mtt-..s of ga at constant temperature: Force, mass. and acceleration [orcc: F prc~~urc 1 x \'olumc 1 = prc:ssurc2 n,a~s x acceleration • volun,c2 /J1 VI - p.:!\I.:! lll<l Momentum Work momcnturn - mass ,elodt~ \\'Ork done = force \\' Impulse distance mo\'cd in dire tion ot force Fd impulse ... force ..- time - change: in momentum Gravitational potential ener y gravitational potential energy = mas.\ < g x height Weight ,, eight - n1a \V PE - mg/, xg Ill~ Kinetic ener ment of a force moment offorcc - rorcc aboul a point 316 kinetic cncrg, pcrpcndicula.di~tancc from poinL KE ½x mas~ x vclocity2 /2'm· 2 1 REFERE Energy and temperature change p.d., work done, and charge cnergv ~pccific heat tcmperatut~ = mas:,. x x I trans fen-ccI capacitv c 1angc E CE p .d. - woa·k done \\' h \I c argc 0 IIIC~{J Resistance. p.d. (voltage), and current p.d. cun"Cnt Power work done po,,·cr - --cime taken encqp· transferred time taken Efficiency . . c f hc1cnc, · \I I R Resistors in series .... useful work done = total cncrg, input uscf ul energy output total energ., input ... and in parallel m,cf ul power output I total powc,· input R Waves RI R .. Electrical power pccd - frcqucnc, x ,,·a,·c lcngth po,,er - p.<l. x current - cun·cnt1 x re!)i~tancc P P inc of angle of incidence cncrg\ tran-,fcn-ed - po\\cr x time = p.d. sinl' of angle of refraction Sin I II l 2R Electrical energy Retraction of light refract i,·c index \II E >,.. cun-~nt x tin1c \lit SIil I" Total internal reflection lira nsformers . o f cnt1ca . . I ang1c = smc output \'oltagc output turns input voltage \l, input ttn11s II , v,, ,,,, SIil C I • ref ntctin.~ index I -II Current and charge current ch'1rgc time For 100% efficient transformer: I 0 I po,,cr input - power output \I/II ,, \I' I \ 317 SI units and prefixes Elements For implicity, mnn) o t the rarer elements have unit hl.!en omit1c<l from the table below. kilogram atomic nwnber (~roton number) element metre m time second s 1 area square metre n,2 2 volume cubic metre m3 3 force newton N weight nev\iton N 6 pressure pascal Pa energy Joule J 7 8 work joule J power watt w frequency hertz Hz p.d., e.m.f. volt V current ampere A resistance ohm H charge coulomb C capacitance farad F 19 te m,perature Ketvin degree Celsius K C 20 4 5 9 10 1, 12 3 14 15 16 17 18 22 25 meaning hydro~n helium lithium beryllium boron carbon mtrogen oxygen 26 27 neon sodium magnesium alum1n1um silicon ~hOSQhOrUS sulfur chlorine argon ~otassium calcium titanium manganese non cobalt G (919a) 1000000000 M (mega) 1 000000 (106) 29 copper 1000 (10~) 30 ZlrlC I 00-1> 1 35 38 (10 47 48 bromine strontium s.ilver cadmium 50 tin 53 55 iodine caesium tungsten P'atinum gold mercury lead radon radium k (kilo) d (deo) To c (cent,) Too m (m1lh) ,, (mrcro) n (nano) p (J)ICO) 1 1000 1 (10 28 2 ) 3) 1000000 1 (10..9) 1000000000 l 1000000000 000 Examples 1 ,,F (m crofarad) - 1o-6 F 1 ms (rrullisecond) - l o-3 s (10 12 ) 74 78 79 80 1tometre) - l 01 m 1 MW (megawatt)= 106 W 82 86 Note ·micro· means ·m1ll1onth', ·m1ll1' means 'thousandth' 88 90 • G, µ, n. aod pare not required for Cambridge JGCSE exammat1ons. 92 318 1km 94 chemical ~mbol H He u Be B C N 0 F N Na Mg Al Si p 5 Cl Ar K Ca T1 Mn N1 Cu Zn Br Sr Ag Cd Sn I Cs w Pt Au Hg Pb Rn Rd thorium Th uranium P'utonium u Pu Electrical symbols I 't\11 res 0 ® w res cr<m. ng om ng + term amp ' -----11 SWitCh ce ---1 r--~rbattery (~~ral ce s ~ ~ res tor varldb e resistors - + 0 DC power supp -----c;n----therm stor E3 ~IC t>I heater fuse transformer dodc M G I I motor generator -- ,----J earth 0 "'\., 0 0 am J_ votme·er ammeter r...i _____/. ~ 0 AC po-.vcr supply ,, -----<=J--g t-dependent ,c-s stor (LOR} ❖ t>I l~ght-cm tt g d ode (LEO 9~ =D re ay co a d S'Nltch be Resistor codes The resistance of a resistor in ohms (H) is normall~ marked on it using one o f Lhcsc codes: The resistor 1s marked with coloured rings. Each colour stands for a number: black brown red orange yellow green blue violet grey white 0 1 You 'read' the first three r:ings like this: number of naught~ 2 3 4 5 6 7 8 9 R27 means 0.27 n 2R7 means 2.7 H means 3000 S! 5K6 means 5600 S! 47K means 47 n 3K0 red VIO et orange 2 7 000 So: resistaoce a 27 000 Q a 27kU The fourth ring g,ves the tolerance. This tells you by hO'N much the resistance may differ from the marked value: gold ±So/o The resistance is printed on the resistor: silver ±10% 2M2 means 2 2 MU So: res1S1ance ■ 8 .2 Ul The extra letter at the end gives the tolerance: F ±1% G ±2% J ±5% K ±10% M ±20% no colour ±20% 319 1.1 (page 13) 1 I 000 g 2 1000 mm 3 I 0 6 ,,~ 4 6 m 2 5 2 km, 0.2 knl, 20 km 6 S s, 50 s 7 1.5 x 101 m, 1.5 x 106 m, 1.5 x 10- 1 m, 1.5 x 10- 2 m 1.2 (page 15) 1 m 2 kg 3 ~ 4 gram, milligra1n, tonne, micrometre, millisecond 5 a 1.564 m b 1.750 kg c 26 ooo kg (2.6 x 1O'' o d 6.2 x I o-"i s <0.000 062 e 36.5 kg f 6.16 x 10- 10 m 6 a - x 10- ' kg b 5000 mg 7 ma ·s: t, kg, g, rng, ,,g; length: kn1, m, mm, JJm, nm~ Lim<!: s, ms, 11s, ns 1.3 (page 17) 1 a 87 rnm b 95 mm 2 2.3 s b 1i1nc more ~-wings 3 Measure total thickness of all 336 pagL'S, divide by 336 4 a Reading hown \\ hen re ~ult i known to be zero a Using scales 10 mL"'JSurc a weighL ~> 1.4 (page 19) 1 1 1 1 cm 2 10 cn1' 3 106 ml 4 a 200 I b 2 x 10\ cm3 c 2 1O'i ml 5 a 2. 7 g/cm 1 b 54 g c I O cm l 6 red (stain]e · ·) 7 39 kg 8 4 n,3 9 22. >- I 03 kg o~ 1.5 (page 21 ) 1 Crown : A ih·cr, B gold, C mi ·turc 2 a 0 g. t OOc.:m\ 0.8g/crn 3 b 120 g, 48 cm 3• 2.5 g/c1n3 1.6 (page 22) 1 a Yes b o 2 a 2600 kg b 2200 kg c 400 kg Check-up questions (pages 22- 24) 1 mca urc111ent: n1a , tin1e; unit: metre, ccond; ~ymhol: m, kg 2 a 1000 b 1000 c I 000 000 d 4 000 000 e 500 000 3 a 3 m b 0.5 kg c 1.5 km d 0.25 c 500 1n f 750 m g 2500 g h 00 mm 4 24 cm 3• 4 cm, JO cn1. 0.5 cn1 5 a 2·00 m b 2 m c 3000 kg d 2 litre · 6 Band D 7 a k·g b m, km c m 3 • cm ' , m 1 d m • · c glen?, kgh11 3 8 D 9 B 10 1.25 kg/m 3 11 a 0.1 m 3 , 0.05 m 3 b 800 kg c 800 kg/Jn 3 d 1000 kg/m 3 12 a expanded, poly t)rcnc, wood, ice. polylhcne; all le · den e than water b expanded, poly tyrene, wood c petrol\\ ill lloat on waler; petrol le ~~ den ·e Lhan water 13 A only i ~ true 14 a r o; too many ignificanl figure 320 b Time mon: s,,ings c 0.93 s 2.1 (page 29) 1 20 m/s; ac.:tual speed \'alie · 2 \'docity also include ~ direction of tr-:.1,·~I 3 a 64 m b 20 · 4 Runnel' 6. 7 m/s, Grand P rix car 100 m/s, pa · cnger jct 250 ml·. sound 333 1n/s, International pac.:c lalion 7690 m/s 5 lncrea ·es bv . 2 m/: L'Ver\. ·econd, velodtv. , decreases by 2 m/ s e\'ery sec.:ond 6 2.5 m/s7 4 rn/s 2 8 a 12 m / · b 4 4 m/s 9 17 m/s 2.2 (page 31) 1 a Not n10\'i ng b A and B c B anti d 4 m/s 2 c 60 n1 f 3 n1/s 2 a 30 m / b 3 m/· c 6 n11s2 d 150 m e -25 m f 2- s g 2 I m /s 2.3 (page 33) 1 Accelerating 2 a O. l s b 200 mrn/s c 800 n1m/ · d 600 mm/ ·1 3 a 10 n1m b 100 mn\/s c 50 mn1 d 500 mm/ e 400 mm/s f I 000 mm/s2 2.4 (page 35) 1 a 10 m/ b 20 111/ c 50 rn/ 2 a 30 n1/ b 40m/s c 70m/: · 3 a 10n1/s b Onl/ c 30m/~ , 4 a Downwards band c B d, e, and f 10 ml: - g C 2.5 (page 37) 1 a CD b AB c DE d AB c BC, DE f DE 2 See below; will le\'el off al a n1uch lower ·pced than for a ~tone 2.6 (page 39) 1 newton 2 a and b They balance (arc cqua]) 3 a Tenninal ve]ocit) b Air re ·istancc: upw·ct1'd force on parc1chule equal to weight c Equal d Lower because air resistance would be greater 2. 7 (page 41) 1 a resultant force mass x accdcr....:lliun b l Or , 20 2 a l 000 r b 1.2- m/s 2 c Accderntion zero ( teady \'clocity) 2.8 (page 43) 1 a Brake ·, on r"oad b Air resi~lance, engine pat1 2 Lower fuel con umption 3 a Top. ~o that feet grip boa1·d b Bouom, for fa ·ter mo\'emcnt over water 4 a ta.tic~ no hL'ating effect b D~ namic; heating cffec.:t 2. 9 (page 45) , 1 a 50 y, 100 b 10 N/kg (both) c JO m/ L) 1-cs A SW RS 2 a I 000 ~ b I 00 kg c I 00 kg d 370 ~ e 3. 7 mJs1 2. 10 (page 47) 1 a 'I b pwurd force of SOO · 2 Motion caused by equal but opposite (i.e. back\\""'11-cl) fon.:e on gun 3 Ground is pm1 of Ea11 h which has a huge mass so c.:hange in moLion is far Loo small to detect 2.11 (page 49) 1 momentum mass x \ ·c locit, 2 resultant force change in momentum/time 3 a 48 kg m/s IC> right b 72 kg m /s to right c 24 kg m/s to right d kg m/ · Lo righc e ~ f 2 m/s g 0.67 m /s 2 h rorce mass x acceleration i 8 ~ 4 a and b 7500 r 2.12 (page 51) 1 a and b 0 c 12 kg n1/s lo left d 12 kg m/s to right e 4 ,n/ to right 2 a 80 kg m/~ to right b 20 kg m/s lo lcft c and d 60 kg n1/s to right e 3 rn/s to dght 2.13 (page 53) 1 \ 'euor (e.g. force) has magniLude and <lin:ction, caJar (e.g. m~ ·) h~ onl~ magnitude 2 a 17 ~ b 7 ~ c 13 1' al 23 to 12 1' force 3 a Horizontal component 7 , \ertica] component 50 N b 350 . c Fm\:c reducL'd (to 250 N) 2.14 (page SS) 1 Path i at a tangent to circle 2 Ftiction bct,\cen tyre~ and road 3 CL'ntripetal lorcc a le · b le c m01~ 4 a gra\'i~ b electro tatic force 5 a Gr:.1\ ity (weight) is onh force on atellitc, toward centre of Earth; acceleration i in same direction b Lower speed c Lower force -oo Check.up questions (pages 55-56) 1 a pecd di tancc/tin1c b 100 m 2 a i 8 m ii 2.0 s b 4.0 ,n/s c i Incn:asing di tancc lx-twcen po ition ii \ \'eight ha a component do\\n slope, torcc cau cs accdcration 3 a i 101~ 101-cc cau c n1orc acceleration ii force mass • acceleration iii 2.0 kg 4 a 25 b 10 0 1 c Re i ling force (air ,·c istancc) increases\\ iLh speed, o resulLar\l force le 5 a 2000 b i 1200 . ii force ma · x acceleration iii 1.5 m/s 1 c Total c11~g force will increase\\ ich pccd until 1 • ultant force i again 1-ero 6 a b i Both [orccs in san1e direcLion ii Fo,-ce in oppo iLc direction 7 a - km b i 10 m/s ii min 20 s c 2 m/s2 8 a 4 · b rticLion c On L") 1 ~. from rood d 3000 9 a 20 m /s b Graph,, ich speed on, crl ical ax i~ and time on horizontal a.,i c 4 ; reduction in speed d i \'\'eight (gra\'it~) ii Air resistance iii \\'eight; air resistance; equal e lraight and lL'\cl f i ~o change ii Greater lo · or speed 10 a cc bclo\\ b i 1.33 m/s 2 ii (~ X 20 . ~ ] 5) i (5 15) 225 m ... 25 ve,kxity rn/S I ____________ JI 5 I 0 15 tJme/s 11 a and b 30 kg m/s to lert c 10 kg d 3 m/s to left 12 a cntripctal force b Ball tran!ls in straight line at tangent to cirde c Cr..\\' il~ 3.1 (page 61) 1 l\.1agnitudc of force, pcrpendi<.:ula1· <li~tancl! rrom point 2 for pri ncipJc see p60, rorces must balance 3 a 16 1' m b 12 1' m c o; cloc~·wi~c d I e Do\, n\\ ards 4 a 21 • b I O I , 8 . and 3 • lon;cs; 4 m c 2 I foi·ce; 4 m d Yes 3.2 (page 63) . Tension centre of mass-+--,.- 4N cc abo\ e lei t b ho11er legs, ,, i<ler apart cc abo,c right b J ~ 3 cc bcJo\,: 1 a 2 a stab' A s: :z neutr~ 3.3 (page 65) 1 a <."C below b 720 'Im c I O e 420 ~ f i'Cro g 0. - m X d 600 ~ y 480 N 120 N 2 Ye , the~ arc till equal 3.4 (page 67) 1 One that return Lo 01iganal hape "hen torcc (load) removed 2 Point b '\ond which material "on't return to otiginal ·hape \\ hen to1\:e 1-cmo\·cd 3 . o, not a traight line 4 a 40 mm b cxtcn ion/ mn1: 0, 9, 18, 27. 36. 4 • 70 d Ela tic lirnit i~ at cxten ion of 36 n1m c p to 36 mm cxtcn ion (end oJ traight <:ction) f 3.9 ~ g 2. :\ 321 s s 3.5 (page 69) 1 a -o Pa b I 00 Pa 2 a 200 , b 400 , 3 Lurye at\!a of comact with M>il n:cJucc._. pn~ ~ur\! on soil 4 a 00 \: b i and ii c • helo,, c 7-00 Pa. SOO Pa c?--b' r1:ium•.irr DRS ure rurnmum pr(:~~ure 3.6 (page 71) 1 a Le~ b ame c amc d Le " 2 a 24 m3 b 19 200 kg c 192 000 '\ d 16 000 Pa 3 20 000 Pa 3.7 (page 73) 1 Incrca c ,, ith depth, a t in all direction 2 Pr • ,un: in craw reduced ~o greater outside air p,-c..,"'urc pu..,hc liquid up 3 Height of column reduced 4 a 100 mn1 of mercur-v b 60 mm of mcrcm') c I l 3 000 Pa 5 a 96 000 Pa b 0.96 atm c 960 mb 6 a 9 10 Pa b 10.3 m 3.8 (page 75) 1 \101 ~ molccuk~ in each cm 3, so mo1 collisions C\'ery ~c.--c.ond on e,lch m 2 of in~icle ...,urfoc. • of balloon 2 a 12 m' b , .. m 1 3 a Pr'C,..,m-c \'o1ume i.., constant b trairht line (through origin) Check-up questions ( pages 76-77) 1 a ~1oment du" to F produce~ larg •r force at ~honer di,tance from pivot b Larger rorc1.:, rurthcr from ph·ot 2 a 0.4 , m b 1.6 · 3 a I 00 kPa, 200 kPa, 300 k.Pa, 400 k.Pa b 2 m3 4 a Do,, n,,ard force (,,cirht) throurh 1, upward lorcc through A b i 30 m ii 0.3 m 5 b i 10.0 cm ii 14.0 cm iii 2. - , 6 a 100 000 Pa, pr '. urc force/area b Not sufficient to e\'.C •ecl t.•la ·tic limit of windo,, 7 a li ' act down,,ard., from C b Force prcad 0\'Cr 1n~ater area, ,o le,, p1'C,,ure on hce1 c 200 , d the pc1-pcnd1cular dbtance from the phot increa">c~ 'IO the morn ·nt of the fore• inc,~asc.., 8 a the ..,amc a ; mo1~ than; le~., than c 2.5 /cm 2 9 a i 0 ... m 2 ii 2.0 m 2 b 000 , m 2 1 10 a 12 m b J 2 000 kg c 120 000 \i d 20 000 Pa -o 4.1 (page 81) 1 60 J 2 0.5 m 3 a t 0 000 J b 35 000 000 J c -oo 000 J d 200 J 4 I 5 a kinetic, rra, icational potential, chemical b chemical 4.2 (page 83) 1 a -o J b 50 J c hang(.x) to thermal cncrgy(heat) 2 For Im, ..,e • p 4 3 Encrg\ can't be made. 322 Bl-cau..,e of los~c..,, generator can't ddi\l!r enough cn1.:r1t\ for mocor. 4.3 (page 85) 1 a 240 J b 360 J 2 a 75 J b 300 J 3 20 m ,~ 4 a and b 2- J c and d Sm 4.4 (page 87) 1 a 30' <. b \\'a..,tlxl a.., thermal cner ID' (heal) 2 -oo \V 3 a 3000 \V b 3000 J c 60 000 J d 7 5 c li 4 a 6000 J b 300 J c 300 \ S a 6000 ~ b 4000 \\' 6 50 000 \\' 4.5 (page 89) 1 CoaJ, oil, natural ga , ur-anium 2 a Turning turbine~ b Condense ..,team (turn it back to liquid) 3 a Tut binc.., b The1 mal cncrg\ (heat) c : 2000 M\\', Y: 1-00 M\\' e X i, 36l',, Y b 27% 4.6 (page 91) 1 G1, vitational potential energy of,, atcr bch ind a dam 2 a cful cner'g) output (as elcctricil\') b 2scC of encrro in rucl b B C E d A e A f 0 (ud required or burned 4. 7 (page 93) 1 C.. n 't b1.: r~placcd; oil, natural gru,, coal, uraniun1 2 a \\ ind, h,drodc u ic ola1~ tidaJ, gco-thcnnal, wa\'C 3 "C p96: un~ energy tored in ancient plant-, du1 ing gro\\ eh (animal~ get cncrro b~ eating plant-,) ► ancient 1 ~main buritxl and changed into crude oil o,cr 1nillions ol ~c-a~ • petrol c,tractcd from oil 4 Carbon dio,1dc cmi..,..,ion'-;, other pollutant.., 5 tor-age of nudea1 \\ a~CL', po,, er station c,pcn h c to ch."Comtni ion 6 Energ, from hot rock.., (or ,,atl•r) underground; heating, heat source (or po,,er ')lation 7 Enct'g\ radjated from un; ~olar panel~ (for hot \\atcr). olar cdl!) 8 Hvdrodcctlic, tidal, wave 9 Bette, in~ulation, mor\! efficient tran"'po,1. making good~ Ja-,l longer. being k ~ wa tcful ,,ith clccuicit, ctc Check-up que tion (page 96-97) 1 a \\'ound up pr ing, stretched rubb~r band, b Via gcan,•ht~I o that co, gain kinetic encrg\ 2 a i PI:. ii PE KE iii PE -· KE b Changed into thermal energy (heat) 3 a i Ela..,tic potential cncrg, htr.tin cnergv) ii Changed to KE · gravitational PE b 0.75 J c cncrID lo~t a\ thermal energy 4 a \Vind, hvdroclcctric, tidal. ,olar b ~o polluting gasc~ (rom ~ource~ in part a; rc~ourcc, don't run out c Output can be variable (e.g. ,, ind) d building, operating, and maintcnant:c co~l.., 5 a 225 000 J b 22 .. 000 J c 1.2-- m 6 a 3000 , b I 0 000 J c 4000 \ V d 0. ( O"d 7 a kculc 2 k \V; food mhct 600 \V b tclc, bion A SW RS c rood mixer d wa.,te<l as thermal encrg_} 8 a Rc~ources that can't be replaced b Simplest way of rdca.sing cnerg_}, a._, heat (c.g as in a power Mation) c ran 1um 9 a Heating water •steam - • motion in turbines turning generator • electricity h Compared with fossil rucls, \\'in<l po,,cr more cx~nsi\'c, much lower output, \'ariablc, hut le s polluting. 10 a wood yes, no; uranium no, no b ii ot renewable, u ·e may be cau ·ing global wnrming 11 a Oi] (or coal or natur-c1I gas) b energy, bw-ns c ·on-renewable fuel can't be replaced/regrown d (From cop, example, use) petrol, car::-.; ,,ood, burning ror heat; ,,·ood, burning ror h "at; pctrul, car.-. 12 a currenl, ther·mal h kincl ic, thermal c chen1ical, cu1Tent, light d ound, then11al 13 da tic; gravilational; potenlial 5.1 (page 101) 1 a, e and g ga~ b and c olid d and f liquid 2 a Random motion of smoke particles b Bruwnian motion c nioke particles light enough to be mon.-<l by colJisions with indi,·idual molecules in gas 3 Move fo ter on a,·~rage 4 Total kinetic energy of all atoms or mole uk~ in a material 5 .2 (page 103) 1 a I 00 C b 373 K c 273 C d O K e O C f 273 K 2 a Volume increase with temperature b Change of conducting ability (re i tance) with t "mpc1·atur 3 a lower on a\'~n1ge in B b A to B c \ Vhcn temperature ar' l he mnc 5 .3 (page 109) 1 a Particles (atoms) vibrate faster and push each other further apart b To allow for contraction if temperatun: falls c Aluminium expands more l han concrete and would crack i l d M -"tal on on_.. side expands n1orc than difforcnL metal on other ide e More open arrangement or molecule in ice takes up more space than in waler 2 a Bimetal tdp b ·nd ·, o contact · ·eparatc b Right 5.4 (page l 07) 1 a Par1idc (e.g. molecule ) cau c force when they collide with walls (becau e of momentum change) b Pa11icle n10,·c foster, o force of collisions greater 2 Increases 3 Liquid; weaker attraction to hold part id"' together 4 Ga : vcrv weak attractions ~o particle~ not hdd together 5.S (page 109) 1 a Bottoni nc !d to let heat (thermal energy) through, handle n<..~ds 10 n..:.ducc heal now into hand b Th ·v trap air c Aluminium conduct · heal away mor'l! r-c1pi<lly than wood d \ \'atcr is a much heuer thern1al conductor than the air trapped in doth 2 Loft in....,ulation, minerc.11 wool in ca, ity walls, in~ulation around hot water storage tank 3 Thicker lagging, keeping water al a lower an:rage Lcmpcratun: 4 a opper h Length, diam •te1; temperature diffcn:ncc same for all the metals 5 Fr"\!c ek-ctrons present to n10,·e through me1al and carry energy 5.6 (page 11 J) 1 a 'Radiator' cau~cs convection cun'l!nL b Hot air ri~es by convection, can-)ring smoke with it c oolcr air flow~ in to replace hot air rising from honfire d Cooled air sinks, selling up a con,· •ction current in 'fridge e Air can't circulate by convection 2 a and h For explanations, ee diagrams on p 114 3 B; hot water rises, so collccL, from top clown 5.7 (page 113) 1 a and b mall black c si Ivery 2 More energy radiated per second, shorter wavelengths 3 Through metal pipes and fins 4 a Temperature, deleclor <li~tance and area same for all the surface b Plate area, distance, and ,-adiation source same ror both surfaces 5 a Tcmper-c1tun: of sphere will r~isc b Temperature of ~phere will foll 6 a To ab~orb un's 1hcrmal rc1diaLion b To can) warmed water away, into house 5.8 (pag e 115) 1 a 1\.1uch mor"\: of the ,,aLer is doM: to the surface where it can e\·aporatc b lncn.-a~ in tcmpcr.iturc, ,,·in<l aero~ surface (or inc1"\:asoo surface an:a, reduced humidity) 2 Evaporating water tak<..~ Lhcrmal cnerg.} (he-'1l) from skin 3 Rcfrigcrc1lo1~ ~weating 4 a E,·a poration from skin reduced, so k•_s cooling b bn:cze spL'cd-; upe,aporation 5 E\'aporation occur.-. from the smfa e of liquid at all Lcmf)L'ratu~s; boi]ing occun; throughout a liquid at a ~pecific temperature 6 Humid air cooled by glass, so water vapour turns into liquid 5.9 (page 117) 1 \cVatcr used to ea~ thermal encrg_} (heat) in central heating S_}stem; also in car cooling systems 2 a 400 J b 200 000 J c 2 l 00 000 J 3 a 400 J b 42 000 J c - C 5.10 (page 119) 1 a Turning solid 1 b 6 C 2 Energ_\ needed to scpar-.ile particles (molecules) so chat the, form a liquid 3 a 3 300 000 J b 23 000 000 J 4 0.12 kg Check-up questions (page 120-121) 1 a F~Lcr molecules escape from liquid surface to fonn ga ' b Motion o, er ground comprc ' C · air 323 A S\ RS ancl \\ arms it up. Mo]ecules move faster, so rorcc larger when lhey bounce off inside or lyres. 2 8 3 a To absorb un's thermal radiation b To pn:vent loss of thermal cncrg) (heat) which should h ~ absorbed by waler c Pump cin:;ulate~ warn1cd \\ atcr through coil in tank d 2 k \ V e 5 m 2 f i The energy i · frct:/rencwablc ii it i unreliable a~ the un is not always shining. 4 a Flow equal b Reduc" · radiation now fron1 Earth c Rate of emiuing radiation is slightly less than ralc of ab ·orbing il 5 a i liquid ii liquid b i 440 C 6 a e\·aporation b, c, and e con\'Cclion d conduction 7 a In ulation: mineral wool b Hot water ri c by co11vcction, so collecls irom the top down c i kilo ( 1000) ii 3000 J iii I 260 000 J d i 4200 J ii 420 000 J iii 3 C 8 a Larger surfoc' area gives increased heat tran fer rat~ b 12.6 MJ (12 600 000 J) 9 a 80 C b None c Boiling rapid (or expanding \-apour bubble in liquid) 6.1 (page 125) 1 a trc1ns\·crse b 2 m c 0. - m d 2 Hz n 0. - s e 4 m l · f 4 m g l H 1. 6 .2 (page 127) 1 b refraction c, d , and c dif 1-action 2 a Ret1cct b Rcfract (bend) c DiHract ( prcad out) d Less diffraction (]ess spreading) 6.3 (page 129) 1 a Sounds can be heard aero: · a room b ounds can b heard undcr,vatcr in a wimming pool c ound can be heard th r ugh wall 2 a . o medium to cart) vibration b ound waves cliffrnct 3 a OscillaLions (\·ibralions) back\\ar-c.l~ ancl forwards b o~cilloscope displa) i~ a graph 4 Rcnccted ( omc cnerg) also tran~miued through wall) 6.4 (page 131) 1 a und i · much ·lower than light b 1320 m 2 a solid b warm air 3 refraction 4 a 440 m b 1.33 ~ C 82.5 m 6 .5 (page 133) 1 a C b B c A and D 2 They ha\'Cdifferent o\'crtone 3 a Peak clo er together b Peaks higher (greater amplitude) 4 a 20 kH z b l 6.5 m C 0.0 16 5 m 6.6 (page 135) 1 ounds with frcqu --ncy undetectable by human car 2 canning the womb, b1 --aking up gall ton 3 a Mea udng depth of water b Depth calculated lrom time for reflected ·ound pul ·c to return 4 a 40 000 Hz b 2 1 m c 0.035 m Check-up questions (pages 140- 142) 1 a cin:;ular, tran verse b i O ·cillalc up and do\vn ii Tran \' --1 c wave produc' only up and down motion c i 2 Hz ii 0.25 m 2 a I 5 s b i \ \'aJI ii 264 m c ound wa\·c · arc longitudinaJ ancl much r~tcr 3 a \\'aves ~hould have s.a me spacing hut higher p "ak b i If two wave take 0.02 s, one wave tak .. 0.0 l , o I00 wav per ccond ii 3.3 n1 4 a i A il B b i Frmn greater than average to le · than average ii Rcpeatcdl~ backward · and forwards ill One wavelength is distance from centn: of one cluMer of particles lo cenlrc or nexl 5 a Longitudinal - · und, P-\\"a\·c..~. -wave ; Tran "·er~ - light \\< \ "C , ripple , '-1-a, · b By underground rock nlo\·cmcnt (earthquake ) c 66 nl 6 a Compres ion · in ound w~\\"c · pu h ball for\\ ard, then it S\\ ings back b i Gn:acer amplitude (greater forwarch-and-backwards motion) ii More vibrations per econd c 6 0 Hz 7 a 0.4 1TI b 5000 m/~ 8 a B louder than A b C higher pitch than A c B d C e 1.5 rn f 440 H L 9 a Transverse: \'ibrations up ancl clown (or siclc Lo side), at right angles to direccion in which wavt! ll1l\·d~; longitudinal: vibrations backwards and forward , pa1-allcl to dire tion in which wave tra\'cl b akr, can di tingui h between ti uc la~ e1 c Cleaning (or metal tc ·ting) 7.1 (page 141) 1 a un, light bulb b Moon, walls in a room 2 Point light ~oun:;e causes sha11> shado\\, 3 a Reflected b A~orbccl 4 a 1.2 b -oo 5 a red b \'iolet 6 ingle wavelength (and colour) 7.2 (page 143) ,mage :' 1 a cc abo\'c: b Vi rtuaJ c Sec above c Virtual d o: no t"'JY from B striking mirror will reflect in to eye 2 7. - m 7.3 (page 145) A SW 1 a , b, c , and d 7 .4 (page 147) 1nddent ray cc above e 63.5 glass normal refracted ray cc above b Refraction (bending) would be le~~ in water (larger angle of rcfraction compan:d with gla ) 2 a Di pcr ·ion b Viol 't c Red 3 226 000 km/ 7.5 (page 149) 1 For light tnl\clling from gla~~ towards boundary wilh air, ray~ at angle of incidence greater than 4 1 are con1ple.tel) reflected with no 1·efract ion at all 2 a cc below b o; angle of incidence 1c~~ than critical angle 1 a A 3 a CatT)·ing telephon .. ·ignal ·• --ndoscope for looking in idc bodv b In pcti cope, bino u]ar (or rear rctlecto, ' ) 7.6 (page 151 ) 1 a 17.8 b 36.9 2 a 30 b g~atl!r 3 a 124 000 km/~ b 24.4 7 .7 (page 153) 1 a A b A c Point wlrrc parallel rav convc1'g~ after passing through lei)!) d Di Lance fro1n ptincipal loclli Lo cenlrc orkns 2 a Al p1incipal focu b Further from lens, large,· 3 Image is n:al, inn:11ed, same size a~ object, and 2 x focal length awa~ fron1 len~ 7 .8 (page 155) 1 a 12 cm f1 n1 1'n , height 2 cm, real and inverted b 15 cn1 from lcn , height 3 c1n, real and in\·erted 2 a Closer than principal fot:u~ b At Lwicc focal length c loser than in parL b, but no closer than principal fo u~ 3 In a room, focu · image of a di ·tanl window on a Cn! •n and mca u re di Lance from lcn to crccn 7.9 (page 157) 1 Further away 2 Ra,s bent inward~ too much; image is formed in f ronl of the re Lina 3 Rays not hen l inwards enough; image would be formed behind the r•tina 4 a Concav (dh·erging) b Convex (con\·crging) 7.10 (page 159) 1 Transver c \\'U\'Cs; can tra\'cl Lhrough vacuum; ha,·c same speed in vacuum 2 microwaves, S infrc1rccl, ~cl light, \'iolet light, uhr..l\'iolct, -ra, ~ 3 a Light b I nfrarcd c Rad io waves d Ultra, iolct e Micm\\"a\' '" f X-ray!-1 or gamma ray 4 a 100 000 000 H7 b 3 m c l 500 m 7.12 (page 163) 1 Digital - rcpr~cntcd by numbe1 ; analogue continuous \ariation 2 a hangcs det:trical signals into light puls~ b hangc~ Iight pulses into "lectricnl ·ignals c •cleans up' and ampl ifie ignal · d Ea ·icr to maintain power and qua 1i tv; ideal for optical fibre and compute, e Ca11·y more ·ignal ; le s auenuation (enerro lo ·') 3 ConlaCLless t:arcl n:ader~or security Lag Check-up questions (pages 164-165) 1 a peed, direction b Totally internal1) r flc.--cted 2 a and b c below lcft c 20 cn1 d l cn1 11 3 a Sec above right b Refraction c Light wave slo\\ down 4 a and b Diagram should be similar lo that al hou om of p 15 ; size (height) of image is cm 5 Larger, hart her from lens 6 a Diagram hould be imilar co that at top of p 15 b 1\,·o oi virtual, magnified, upright c i t:on\·erging il di\ erging d i conca\'e (di\'crging) ii con\'c~ (con\'crging) 7 a ingle wavelength (single colour) b totally internallv r , ncct •d c Endo ·cope for looking in idc b~dv d Rcpre cnt number c Le allccted bv interference; ea!)ier to boo t power\\ ithout affecting quality f ontat:tle ·· card reader, or sccurit) tag reader 8 a Ra\ travels ~ll-aight through glass with no change ·in dir 'Ction b Diagram imilar to that al top left on page 154; 2 c 2 x JO m/ 9 a An\ three lrom radio wave , micro\\'a\'l"S. infrnrcd, ultruviolet, ?'•rL)S b 1\,o _offrej~ency, wa\'clcngth, penctratmg power c l0 10 a i X-rays ii infrared b i wa\'e ·p~ ..d - wave frequency x wavelength ii 3 x 10 11 I 17 iii n1icrowa,·c 11 a 35 b 42 c uikc KL at more than critical angle but, alter reflection, Ltikcs LM at lc~s than critical angle 12 a i greater than ii the same as iii greater than b i Microwav.. ii ltra\'iolet or gan1ma 8.1 (page 169) 1 a repel b attract c repel 2 a Po it i\·e ( ) b egaLive ( - ) c o charge 3 FrL'C electrons 3'-5 A SV.J RS 4 Po )) thcnc an insulator so c.:hargcs don't mo\'e, copper a conc.lucLor so charges now a \ \a) easily 5 Carbon 6 a Comb b FC\\Cr electrons than normal o le ncga1iv' char-g .. pr~cnt than po ith·c 8.2 (page 171) 1 a E1cctroscope 2 coulomb 3 a End B b Charges being attrac1cd (+and-) an:doser 1han those being rcp ..llcd (-and -) ·o fore"' of attraction i trongcr 4 Refuelling aircra t; earthing aircraft and tanker 5 Two or elcctro~1atic prccipilator, photocopier, la er pri ntcr 8.3 (page 173) 1 a Arrows poi nl away from sphere! b Away from pher c Towards phcr' d 8 "conie I~ (bccau c of How through point) 8.4 (page 175) 1 a 0.5 A b 2.5 A 2 a 2000 m A b I 00 mA 3 a and b cc below c 0.5 A d A and B; incomplete circuil 4 a 50 b 10 C electton I flo-.v "' convent10nal current d:.rectlOrl '------( 8.5 (page 177) 1 a and b \'Oh c coulomb d ampere e joule 2 a An1mctcr b Voltmeter c 8 V d 12 J c 4 J f 2C g J 8.6 (page 179) 1 a 2 n b \\'oulc.J nol heal up withoul resislancc 2 Bulb gets brighter; le re i lance in circuit, so more cun"Cnt 3 a LOR b thcrmi tor c diod 8.7 (page 181) 1 a 16 V b 32 V c 0.75 A 2 B 3 a 2 n b 4 ~2 4 Rc\'er~c; from the graph, the currenc is close lo zero so the \'aluc of VII wi II be \ 'C l')' high 8.10 (page 187) 1 a 1. - A b 6 V (both) 2 a 3 A c 6 A d 2 3 (9.9 n o n> b A (both) 8.11 (page 189) 1 Allo\\ current through in one dire tion onl v 2 Change · a.c. to d.c. 3 a Y b X 4 Reduced to 2 5 Bring a magnet dose 8.12 (page 191) 1 a 2000 \ \' b 2 k\\' 2 920 \\' 3 2 A 4 a 11 J b 660 J 5 a 36 \ V b 21 600 J (21.6 kJ) 8.13 (page 193) 1 Thin wire which protc t circuj l fron1 too high a cun~nl; \\ire o\'crhcat , melts, and breaks circuit if cun-cnL too high 2 So that wire in cable c.:an't still be live when S\\itc:h is off 3 afcl\ : if Lherc is a fault, current nowing to earth blo,\. fuse (or trip · circuil b, ,aker) ·o 1hat circuit i · oil 4 3 A fuse for lnnip and ood mi; c1~ 13 A fu for hairdrvcr and iron 5 lf there i a lault, circuit might o\'crheat \\ ithout fuse blowing 6 witch off at socket; pull out plug Check-up questions {pages 196- 198) 1 a i Electrons pulled from hair Lo balloon ii Positive; equal but oppo itc to charge on balloon b l nduc po ith'c charge on ceiling (i.e. electron · pu hcd awa~. lea\ ing urfacc of ceiling with positi\'e charge) which is altractc<l to ncgati\'c charge on balloon. 2 a i Like charg~ i-cpel il 1\cgative b I{ - 11\ c Diagram same as on p172 bouom left 3 a cc below b Brighter, more current 8.8 (page 183) 1 2 n 2 a 720 mm b 250 !2 c 200 n1m 8.9 (page 185) 1 I n eric · 2 All bulb · gel the full battery \Oltagc; ·e below ir one breaks, others keep working 3 4 a X: 2 A, Y: 2 A b 6 V -,1 I I 4 a 1A b 3A 5 a 4.5 J b 4.5 \V 6 a 6 H h a nd c 0.2 d 0. V e 0. 16 \ V 7 a i Onl) for use with alten1ating cun'ent ii Ft "qucncv: crnTCnt flow backward and forward 50 tilnc per ccond b Two layc, ~ of in ulation c 2. 17 A d i Breaks circujt i[ cun-cnl i~ loo high for ~afcty ii 3 A; ncan!st fuse \'nlue abo,·e ac.:tual CUJTl!nt, olhen\ i~e foull) appliance might overheal withoul A SW blo,,ing fuse e Lower voltage causes lo\\crcu1Tl!nt, so much lower powl;!r output (less heat per second) 8 a 8. 7 A b i 40 \ \' ii 2000 \ V greater than 840 \ \' rcquir"'d but le than 3000 'A' ne'dcd if bulrn, changed c All bulb get the full generator \'ohage ( ·hared i[ in series)~ if one bulbs break~, others keep working (all stop working if in series) d I 90 n e i 50 H z ii Graph has ~aks of only half lhe amplitude (height) but ame pacing 9 a A i amnictcr~ V i · ,·ol tmetcr, B i \'ariablc r i tor b c B to increa e \'oltage in tep ~ mc~urc current each time c 0.4 A d 5 n e 7.5 n f Increases 10 a s A b 2.4 n c 100 C d 1200 J 9 .1 (page 199) 1 orth-s 'cki ng pole 2 a nl ikc hard magnetic material • oft one ea ii) lo e niagneti 111 b tccl (hard); iron ( ·olt) 3 Iron, nickel, cobalt 4 Aluminium, copper~ zinc 5 Bars I and 3 arc permanent magnets, bar 2 is not 9 .2 (page 201) 1 a N i · at top (black) end b pole at right-hand end of magnet; field direction i from 1 to (right [O lclt) C X 9.3 (page 203) 1 a As on p202 bottom righl but with ficl<l dircclion re\'e~ed bt.~au e ball "ry is other wa\ round in quc tion b Higher cun-cnt; more tum on coil c R~, c1 c cu1n:nl direction 2 ~ecdlc lo1,n pai1 of a circle with black end.-, pointing dockwi e 9.4 (page 205) 1 a To incrua.~c str"l!ngth of magnetic field b Field doc n't rl.!main ,, hen current in coil switched off c lncrea ing cun--cnt, incrca ing tun, · on coil 2 a \Vith a rela), mall cuffent through ,dtch can tunl much larger cun~nt onion b Rda) core magnetizc<l, so armalun.: doses contacL~ to !,Witch on motor 3 a To switch off curn.:nl if this is too high b Tri~ (cu~ off) al lowl.!r current 4 a To magncti1e particle in a ,·arying pattern along tap~ b Magneti n1 mu t ren1ain but den1agneti~ing not be too difficull 9.5 (page 207) 1 a Higher cun·cnt, ~trongcr magncl b pwards c Reve~e ClllT"nt direction or turn magnet round 2 A · cun "'nt alten1ate (change direction), force change direction, cau ing vibration 3 a tronger Lut·ning effect (higher force ) b Turning effect in opposite clireclion 9.6 (page 209) 1 a and b plit ring (con1mulator) 2 a i Coil hori1onta 1 ii Coil vcnical b trong r n1agnct. higher cu1Tcnt, more tur·n on coil c Anticlockwi e 3 1otor Gul be u ed \\ ith a.c. 9.7 (page 211) 1 a un"Cnt dire tion reversed band c o cun"Cnt 1 RS 2 a and b Crcall.'r EMF c Current cJin.:ction rcver~ed 9.8 (page 213) 1 nchangcd 2 a pole bccau c it repel the pole of the magnet b AB 3 Edd) current induced in di c create magnetic field which oppose~ motion 9.9 (page 215) 1 a a.c. each side of coil rever$eS it · dir"ction of motion through magnetic field ..,·c1,· half turn b Incrca ·e turn on coil, rotate fa tcr, u c tronger magnet c Horizontal; iaste ·t motion through (ield lines d Vertical; field lines not being cut 2 Fixed coil with rotating clectromagnel, more turns on coil, specially-shaped core 9.10 (page 217) 1 a Galvanometer needle flick b ... ta) at zero c ... flick!-! oppo itc way 2 a . ecdle ddlccLion much more b a .c. induced in coil (so average <lcflection of nec<llc is zero) 3 a 3 V b 3/1 9.11 (pag e 219) 1 More turn on output coil o incrca c voltage 2 a Magnetic field not changing b To reduce eddy cun·cnL~ which waste power by healing core c Because output power [ voltage cun-cnt] can't be more than input power 3 a JO V band c 23 \V d 2.3 A 9.12 (page 221) 1 U ing tran forn1er 2 a Tran (orn1e1 only work\\ ith a.c. b To reduce cur1~nt so that le s po,,cr i~ ]o!,t rrom hc-ating effect in cables 3 In <lcnscly populated or scenic area.~ 4 2640 M \V 5 0.02 \ \1 6 a 2 k \ V b 0.002 \ V Further que tions (page 224-226) 1 a Any l\\O of: reduce turn on coil. reduce cu1Tent, rc,novc core b So that no magneti ·m remains after !,Witch off 2 a and c a magne1 ic material b a magnet d a non-magnetic malerial 3 mTcnt in coil create niagnctic field. ft iron piece attracted together which clo e contac~ and ,, itches on current through motor. 4 a Fis to the right, at right angles to wire b i trongcr ii \Vcakcr ii Opposite direction c A motor 5 a i and ii "'cclle deflect to right iii Larger deflection to left b Elcctron1agnctic induction 6 a Heating cu111 · water into team which pu ·hes turbines round to turn generators b To reduce ct.u-n:nt so that le. ~ powr-!r is lost from heating effect in cable · c 32 000 7 a One that rcduc voltage b Fewer tLu-n on output coU c 1 1.5 V d To reduce currcn t in tran~mission line~ e iron or Mumetal 8 a 90 b i Magnetic fidcJ ii Become magnetized, so will repel A SV.J RS 9 a Each sic.le of coil allcrnaLdy mo\'es up anc.l down 1hr·ough magnetic field so direction of induced cu1Tent keep · changing b i 2 ii 4 c trongcr magnet (or fa tcr rotation) 10.1 (page 227) 1 a, c, and e electron~ b neutron d protons anc.l neuLrons 2 a a nd b 13 c l 4 3 Di fforent numben. of neutrons 4 a b ~ 0 c 2 Ra 5 X and Y are carbon, Z i nitrogen 10.2 (page 229) 1 carbon- 14 2 a, d, f, h, and i gamma b, e, and g alpha c beta 3 Atom · of radioactive isotope ha\'c un~Lahlc nuclei which c.leca\ anc.l emiL rad iation 4 Atoms arc cha rged because electrons ha\·e h >en lo ·t (or gained) 10.3 (page 231 ) 1 Radon gru, from ground 2 Health ri kif radioactive gas i ab~orbcd by body 3 a Ga,nma b Alpha 4 a 2 counts per second b 26 counts per sc ond c amma; it is ab le to pcnctr.ite the lead blo k •:c 10.4 (page 233 ) 1 a Alpha particle b A - 228, Z c R adium 11 d ''?Th ➔ • Ra+ ,.a "' 2 e rac.lium-228, alpha particle 2 a O b - I c Beta parLicle (elect mn) 10.5 (page 235) 1 tronlium-90 2 a 400 Bq b 200 Bq c 50 Bq 3 a Radioactive decav i a random procc b 1.5 hours I 0.6 (page 237) 1 Emitted particles Lransfer energy to surrounding atoms when they collide with them 2 a pliuing of heavy nuclcu into two lighter nuclei b Emitted particle (neutron ) triggering further fi ion ... and o on 3 a Energy 1-clca.sed in a nuclear reactor b Explosion or nuclear weapon 4 a Formcc.l in reactor when -23 is bombarded by neutrons b Toxic, and dust can gel into lung · 1 1 5 a • , + 0 n ➔ ''' ,; Ba + "' K r + 3 r n b Total n1a of product i lightly le than total mas of U-235 nucku~ and neutron. Loss of mass represents loss of energ_\. I O. 7 (page 239) 1 a Joining etc. b 'lucl "ar fission 2 Fuel plcntifttl, n1or ~ energy per kg offucl, lc~s radioacti\'e wa Le, failure i afc 3 Di fficult Lo maintain high temperature · and pre · urc · needed for fusion 4 a Hydrogen b udear fusion c Helium 5 a fusion h burning 10.8 (page 241 ) 1 a Radioacth·c i otop,.. b In nuclear, ~actor, \\ hen table j otope ab orb neutr n or ganuna. radiation c Tracer , imaging 2 a Alphas ·topped, gammas puss straight through, but beta.~ partly ab~orbec.l c.lc~nding on thickness b Reading goes down 3 a Any two from bullcted points on p240 b afer. little r:.1diation emitted after te ting has nni heel 4 a Gamma penetrate food, alphru, don't b tcrilizing n1edical in trument c X -rn~ -type metal te ·Ling, or medical irnaging 10.9 (page 243) 1 In Thomson's model, positive and ncgaLive charges ·pread throughout atom 2 RutherfordBohr niodcl ha ' quantuni energy lc\'el for electron · 3 a . ucleu exn~.m elv mall b Repelled by highl) concentrated charge 4 Alpha · arc po~itivc and arc rcpdlec.l by like charges 10.10 (page 245) 1 a Radiated a photon b horte1· wa\'clength c Onh certain energy level cxi Lwithin an a lon1 2 Particle not n1ade up o( other particle 3 elect1·on ·, quarks 2 1 4 um of fract ional charges = .J.. - - ! 0 , I 3 3 3 5 Charge en1itted - + ) 1 3 -( 3 lions (page s 246-248) Chec k-up que 1 a i nuclei ii electron · iii ,, ave · b Alpha particles 2 a 17 electrons, 17 protons, 18 neutrons h p1·oton~ and neutrons in nucleu , electron~ around iL 3 a i 33 ii 52 b Atom of an1e clement ( an1e aLomic number/e lecL1'0n ' ) but,, ith different ma number (or c.liften:nt numben. of neutrons) c Use fact LhaL lcac.l will s lop alpha and beta particles but not gamma ray 4 a i 1':uclcu of pho phoru -32 ha extra neutron ii ame electron arrangeml'n L b i Electron ii 16, 32 ill ]i me taken for half rac.lioactive atoms to dcCa) (or acti\ ity Lo halve) c i glove~tongs, keep c.listance, scalcc.l stor.1gc ii GM tube, photographic r.tm 5 a Too ea ·ilv ab ·orbed by ti · uc b i 12 hou ii / 6 x origina l \'aluc c Rock~. co mic ray 6 a l\ucleu · b Total of proton · and neutrons in nuclcu~ c ii 8 days d Much longer half-l ife 7 a i Only atoms with unstable nuclei are radioactiv ~ ii a tural ly occun·i ng rad ioact h ·~ niatcrial in oil, rock iii 1in1e La ken for hall radioactive aLon1 Lo deca) (or acth ity to halve) b i 24 count · minute ii 40 hours approx c Gamma noc \ 'Cl) ioniz ing d i beta particle ii I 22 Il 13 8 a i Unstable atom pre cnt, emitting radiation ii En1it radiation \'en do " to cell and can damage/change them b Atorn o t ~amc clen1ent (same atomic number/electron ·) but with dilfer~nt ma'-.s number (or diITcrcnt number.,; of neutrons) A SW c i and ii 6 lii 136 9 a Too easily absorbed by tissue b Tracking plant' uptake of fert ili:,er, or detecting leaks in underground pipe 10 a 146 b Kudcu l 1.01 (page 251) 1 a I day b 27 cfu)~ c 36- days d 27 <la) s 2 a Moon's rotation time same as orbit time b \ Ve an! only seeing mall part of unlit ~id " of Moon c TIit of Earth' axi i toward · un in June o bigg 'r fraction ol each rotation i pent in unlight d More hom · in sunlight, al ·o un~ radiation comes in at higher angle so le s sp~ad out 3 1.07 x I 05 km/h 11.02 (page 253) 1 Jupiter 2 Jupiter 3 Mercury 4 Mars and Jupiter~ tim' for one orbit lie between Yalu for tho c two planet 5 a Fu11hcr from un, o le energy received per quare metre eve1) ·econd b Venus; f u11hcr from un than Mercury bul a,·erage surface tempcr.itun! is higher 6 500 s 11.3 (page 255) 1 inner- Mercul'y, Vcnu , Earth, Man,; outcr Jupitc•~ &.turn, ranu , cptunc 2 Pluto, or Ce1-cs 3 a Very high ·urface temperature, acidic atmosphc~ b o solid surface 4 a Comet orbit is elliptical b un heats comet, panicles of dust and gas ·tream off into pace and refl -'Ct ·unlight 11.4 (page 257) 1 a B b D c B d D 2 a Orbit lin1c n1atchc Earth's rot~1tion tin1e b 24 hour c ending/ n .'Cci\'ing di::-.h on Earth car\ be in faxed position 11.5 (page 259) 1 a Huge cloud of gas and drn,t (in \\ hich stan:. can forrn) b Collection of billion · of ·ta, c The galaxy of which our uni a n1cn1bcr d E,·c1"\rthing - all the sta1 · and gala.,ic 2 a lowly rotating disc around ::-.tar (or planet) into which addiLiona] material is drawn b Be ause of gra\'ilational allraction c Particles of n1auer falling inward · lo t grnvitat ion al potential 'nCl'g\' o gain<..xl kin 'tic energy - f, tcr particle meant higher tcmpcratm' 3 a . uclcar fu ·ion b H)drogen 4 a Di ·ta11cc t1-a,·ellcd b~ light in one year b 4 x 1013 km c x 108 hour.-. (over 90 000 yctln\) 11 .6 ( page 261) 1 Hcliun1 2 Cor" will collap c, outer later wi1l expand and cool (becomjng red giant) leaving a hot, den e core (white dwad) which \\ill eventuall~ 1ade 3 Fusion reactions in superno\'ac 4 Gigantic nuclear explosion of massive star 5 1}pc 1a !-,Up --rnovac all have the same b1-ightne ·s, o di tanc~ can be compared by comparing btightnc 6 . cu tron tar i lo1111cd h n1 cornpre e<l con: o( upcrnova; black hole [orn1ed when grjvit) is so strong that core goc~ on S collapsing 7 Hca,) elements p~sent \\ hich could ha\'e only be made in superno\'a l 1. 7 (page 263) 1 a 4 million b 4 c 13 bil1ion d 14 billion 2 a Inc, ·a <: in wavelength of light fron1 \ 'Cl) distant object b ObjL'Cts mo, ing away i rom Earlh at \ 'CJ') high speed 3 Red shift suggest galaxies arc mo\·i ng apart so may have started in same place; microwa\·e from C\""ry direction in pace may b" t ·d- hiftcd radiation from inglc , . 'nt 4 a Hubble con cant - 1/agc oi unj\'ct c b Rate of ... paration of galaxic · has been con tant c 12.7 billion years Check-up question (pages 264-265) 1 a i A and B ii A b 24 hou~ 2 a i ach place ·pend mor > hours in daylight, un rcachc · higher angle in kv ii Autumn; ,\'inter m umn1cr b Le ; ranu lurther fron1 un o reed, c ' lcs · radiation per m2 per second 3 a i Earth ii Earth iii Moon b i Earth's axi~ tilu.>d towards un so less time in dark during each rotation ii Moon•~ urface 1- ,fleets light from un iii ~ Moon orbit Earth, fraction of unlit part of Moon vi ible fron1 Earth , ·atic 4 a i Venu · ii Ea11h iii Mercury iv un v ~cptunc vi Circle b i Moon rdlects un's lighL ii tar~ give oft own light iii louds and dust in atmo pherc; elTect of city lights c olar ,stem; gala'\); Milkv \ Va\'; Unive1 c; Big Bang; black hole 5 a i D ii B b Orbit in an1e direction a arth' c i E1lip e ii Grtn it) 6 a Inner planl!ls ::-.mall and rock, outer planets large and gassy b steroids c 6.42 x 104 km/hotff 7 nebula; sup "'lilO\'a; gravity; p1-oto. tar, tar; acer 't ion di c; planet 8 a Red hift how that gala.xi~ arc moving apart b Red- ·hifted n~n1nant of radiation from Big Bang c r udci of atoms (h)drogen for L''=amplc) joining together to fonn nuclei of heavier elements 9 a Million of stars h Reflects sun's light c i Motion affected by gravitational attraction between planet and un ii Vcnu travel at higher !)peed in horter orbit d i Venu ' in new po ·ition, Milk) \ \fay in same position li Venus clo~c enough for changing position in orbit to notice, stars so far away that motion appears negligible 13.3 (page 283) 1 47 C 2 36 count econd 3 5.4 . 4 86 kPa 5 0.79 rnV Multichoice questions (Core) (pages 298- 299) 1 A 2 C 3 C 4 D 5 A 6 8 7 D 8 A 9 A 10 A 11 D 12 C 13 14 B 15 C 16 B 17 B Multichoice que tion ( (page 300- 301) tended) 1 B 2 C 3 D 4 A SC 6 A 7 C 8 D 9 12 A 13 8 14D15 10 C 11 A 16 8 17 0 329 A S\ RS ICCSE theory questions (pages 302- 315) All anS\vers should be g iven to 2 or 3 significant figures unless s lated othen.,rise. All ans\vers should include the unit . Allo\v error carried fonvard \ here appropriate. 1 a 0.75 s b 0.80 s c 3. m/ · d to itnprove accur.1c,· I reduce the effect of random error~ 2 a mas~ i~ the quantity of maLtcr in an object; wcighl is the gravitalional force acting on an object b (top-pan / electronic) balance c mca ·urc the oliginal \'olumc of water in the mca uring cylinder (without the piece ol iron); place the piece of iron ea ref ully into the mca~uring cy]inc.ler and measure the new \'olume of water in the mea~uring cylinder; suh1ract the original , ·olume from 1he new , ·olumc to dct 'nnine th' volun1e of th' piece of iron. d 7.9 g/cn1 3 a i con tant/steady/uni form ·peed ii stopped/ not moving b -oo m c 70 s d 7. J m/s e cction Pas the gradient is slcl!per (accept !\p<..:.cd~ for time - 0-20~ and 1in1e - 40-70~ calculated) 2 4 a con tant/ tcadv/uniform pccd b I .5 m/ c di tancc lln\'ellcd = area under graph; di tance travelled in fit ·t 40 s - 1200 1n; di tance travelled between t • 40 s and t • 60 s = 900 m; so total di~tance = 2 J 00 m. d average ~pl"Cd =35 m/s 1 5 a I 20 cm 1 or 1.32 x 10- ' m' b 2200 kwn1 ... 6 a o.o·o kgtn/ b (- )0.19· kgn1/ C - 0.29 1n/: 7 a con Lant pced / tenninal \ elocit) b one arro,, up ]abcllcd air re i lance/drag; one ari·ow clown label Ice.I wcight/gra,·itationa) force; two anuws the same size c accelerating, at a decreasing rale, weight is bigger lhan air re i tancc, a ·p 'cd incrca c , air r i tancc incrca e (until it reache terminal velocity) 8 a no n:suhant force, no re ultant moment b 600 Nm c 450 m d 0.6 m (from pi\'ol on right hand sic.le) 9 a 44.1 N b i l he limit of proportionalit) is where the extcn ·ion ·top being proportional to the load. ii 221 . /m or 2.2 cm. 10 a i kinetic, thermal ii che1nical b i 2.8 m/ s 2 ii 6 000 c i towards the centre of the circ1c/ cir u)ar path ii increases 2 11 a 200 000 kg/m b 402 000 12 a mca lH\! the tin1e for multiple (>5) wings; dh idc the total time b) the number of \\ ing b weight (downward ): ten ion (in ·tling, upwards) c 0.060 J 13 a r·encwable cncrg) will not run out / can be replenished (ea ·ily); non-rcne\\ able energy ,\ill run out / cannot b' rcpleni h ·d (ea ily) b i no grecnhou c ga e- C02 produced, no ulfur dioxide produced/no acid rain, large amount of enc~y 330 produced per kg offud, rcl iablc ii non-renewable, risk of leak of radioactive waste, risk of accident c renewable - biof-uel, bioma ~. tidal, wa,·", hydroelectric, geoth ,,-mal. wind non-renewable coal, oi]. ga d 0.25 (or 2-co) 14 a Milk~ way b An increa ·e in the obscrYed wa,·clcngth of the elL-cLromagnctic radiation emillL>d from ~tars and galaxie!\ mo\'ing away from Em·th. c - x 10 2 • 15 a 50 N b 765 J c 3. d 17 16 a the drawing pin will tall ofl the rod of the bc~t conductor fir ·t (a the wax on that rod will mcl l first). b copper • has free ell!Ctmn~ which gain kinetic energy when heated - free 'lcctron move through th' copper and collide\\ ith aton1 ion to n1ake them vibrate fa tcr (and energy i · transfc11'Cd (rom hotter parLS to cooler parLs). plaMic - no free •le trons - aton1 \'ibratc fa ter when heated and the e \'ibration p:l:)S [rom aton1 to atom (tran fcn~ing heat energy). c The particles arc for apart 17 T, F, F 18 a ga · n1ol x:ule collide with the wall (and e'\et1 a force per unit area) b incrca c ; molecu]c ha\'e higher a\·erage peL-d ·o collide rno1 ' frequcnch. with wall of container· ( o bigger force \ per unit area) c 1920 cm 19 a nearer - ~mall and roc"-·y; furthcsl - large and ga eous b 4 from: du ·t and gas from a nebula; pulled togeth r by gravitv; accretion di c fonned ( h·orn pinning du t and ga ); rock forrncd to make inner planets; e~t~me tempera tu re cau ec.l Iigh1er material to mo\'e away and f01m outer planets 20 a meru,u~ the time that the blo k i~ heated f01· ; calculate energy upplicd using: en rgy = power . time~ measure the ~tart and end ten1pcrattu'C calculate tcmpcr..ature rise: use: energy = m~ ~ ~pt.-cific: heal capacity x temperature change (Lo calculate the ~pccific heal capacit)) b some of the encrg) uppli ~cl 10 the iron block i~ lo l to the UITotmcLing c add in ulation around the iron block 21 a an) 3 from: ta ter/ more energetic molecule e cape; molecules escape from the ·urlacc/watcr. slower/le. s energetic molecule~ n.:main; less energy means lower lcmperaturc b 17 500 J c any 2 flum: ",·aporation - occur · nl any temperature; occurs onlv at th urfacc of the liquid; low"t the (kinetic) energy of the molecule remaining in the liquid / cause · cooling of the 1iquid. (AUow 1'C\·e~e argument for boiling occur.-. onl~ al one temperature / boiling A SW RS poinL; occurs throughout the liquid; docs not lower (kinetic) energy of the molecules in the liquid / cause cooling~ hu bblc- · o cUt-) 22 a ound wav i rcncctcd b tran vcr wa\·e ha o cilla1ion at right angle to the direction of tra\'el/cncrg~ tran kt~ longitudinal wa\'c has oscillations parallel to the direction or tr..l\'cl/encrgy trnnsfor c 4 12.5 Hz 23 a a nd b ·cc diagram below Path of ray X atter t reaches them r,or c any L\\"O rrom: same size as the object; upright; 0° 24 a ranu i further fron1 th ~ un b Jupiter; large t gravitational field trength c 4.9 x 1O12 m d 2.3 25 a normal b angle of reflection c thcv arc equal d total in Lem a l reflect ion shown i~sidc the optical fihre with a maximum or 4 rc0cctions in total; angl ' of incidence - angle of reflection e 42° 26 a ( tudcnt B ) nlca ure the time u ing the topwatch between hearing the clap and hearing the echo: uses sp(.-cd = distance/time; where cl = -oo m. b (student A is incon"'l!cl) wa\'c X has a lower pitch as i t has a lo\\er frequenc~; (student A i correct) wa\'e X i louder a it ha a larger an1plitudc. 27 a Q - microwave : R - gamma ray ~ b infrarcd c ultr.l\ iolet 28 a C b \ ir1ual / magnified / erect / same side of lens as ohjcct c the image of a disLnnt objecl is formed in front or th .. 1~"tina; a dh·crging lens dh·erg~ prcads out the light ray ; o the 1-a, · will focu on the retina 29 a and b ec diagran1 la1eraJly in\ ·eracd; same distance away from the min'Or a t h ' obiect d h' ' d iagran1) C'\t •nd both ray!-. behind the mirror; ray · me 't at a point; label image I 30 a con-cct ymbol ·; ammet 'r. cell and fi-.;cd re i tor in eric ; \'oltmctcr in parallel b 100 n c arrow ·howing cun-~nt lrom po ili\'e terminal to negative terminal d 14 s 31 a \'ariahlc r\!sistor b i (filament) lamp b ii a..., the pol >ntial di ffcrencc incrt.:ascs, the current increa e at a decrca ·ingrate; a th, CUTT "nt incrca c , the temperature increa e ; " the tcmpcratu1~ increa e , the re i tancc of the larnp increases. 32 a a n:gion \\ hen! an electric charge reds a force b + - - - . - + + + - - + + . + + - - - ....- c 0.0020 A d 0.010 A 33 a any 3 h·om: place plotting comp~ · on the cardboard/near to the\\ ire (and ·witch on current); draw a dot al the head of the compass arrow; mo, e the an-ow and draw anolhcr dot at the head (id .. a of top-to-tail); repeat at different di lance from the wire b circular n1agnctic field line (getting (urther apart); anticlock\\ i c direction c re,·crses direction or magnetic field 34 a iron core b a ltc1-nating cun1.:nt in the primary coi l; cau~es a changing magnetic field in the iron core; induce alternating p.d./current in ccondarv coil c B: C d i 500 V ii J 2.5A n1 to 1 duce the current; to reduce hcat/energ) lo to Lhc u,,·ounding 35 a magnetic ficlc..l (lines) are cut / there is a changing magnetic field~ current/pd induc,.-cl; b one from: inc1 •a . .. magnetic field tn:ngth, increase number of tlllTI on coil of \\ire, incrc~c pccd of mo\'cment of magnet c one lt'Onl: change direction 331 A SV.J RS of n1agnelic field, change din.'"Ction of mo\' --ment of magnet d Pt "pcl oppo c outh pole of magnet 36 a ratio ol pecd at which a gala.·9 i moYing awa\' fro1n Earth to its di lance from Earth b 7.3 x 10 22• m c grL1dienl of graph; \'aluc wiLhin 5 km/s/Mpc 37 a i circuit A a ii circuit B a iii 4000 a iv 750 b 9V 38 a i 226 a ii a iii 13 b (form of an clement with) ame atomic nun1ber/nun1bcr of proton; different m~ · number/number of neutrons 39 a i time taken for Lhe acLi\'iLy to halve/ half of the radioacti\'c nuclei 10 decay a ii minutes b ~mooth Clff\'e ·tarting at 400 count, min; aho\·e the otigina] curve c 350 - 30 = 320: 50 - 30 = 20; 4 halt-liv~; half-life = 2015=5 da\' 40 a i alpha a ii alpha bi radiation that i · all around us b ii any Lwo from: radon gas, rocks/ buildings, food/drink; cosmic rays c cur\'ed path: out of pap r; at right angle to th > magnetic field 41 a 2 ~l in p; b a-particles cause air particles to ionise so a small current flows; smoke particles ab orb the <X-paniclc ·; ·o le s air particle are ioni cd; the cun·cnt i reduced ( o the alarm 1ing ) c curve up\\ ards 42 a 10 million yea1 b 2 yea a c i proto tar ii red giant ill while dwarf iv red upergiant v neutron star vi black hoJc AJternative-to-practical paper questions 1 a vertical ruler drawn S 0. 0cm from th .. ·pring b colun1n 2: I or length of pring / mn1; c or cxtcn ion / mn1 c (in order) 3.0, 5.0, 9.0, 12.0, 15.0 (mtn) d a..,es Lhc com.-cl \\ay round and labelled"' ith the quanLity and unit; linear ~ales and not awk\\ ard number~; poinr.s (small do1s or cro~scs) plolled accurately (to the nearest 'Ii square); straight line of be t fit drawn e (y ) traight line through the 01igin f con\.~t \'aJuc read fron1 graph e .g. 6.9 n1n1 2 a look pcrpendiculai· to the n.1.lcr when reading Lhe scale b i 26.36 s ii I .32 s c i 1. 7 s 2 ii l 0 m/s 2 d an, 1wo f mm: n.-pcaL using different length( ·) a;,d calculate the mean; repeat the timing and calculate the mean; u c inc1 ~a ·d number or o dilation ·; u ea fiducial n1arkcr 3 a ([rom top) 50, 75, 100 b i (all rcacLings) 0.35 ii 1.4 c i JK 2.7 JL 4.0 Jl\1 5.4 ii n (ohm) d .0 (or . t) n 4 circuit diagnm1 "" ith correct ·ymbol for power upplv, ammeter~ \·oh meter and re i Lance \\ h\! and component correctly connected with ammeter in sc1ies and \'oltmctcr in parallel with Lhe resistance win.- (variabJe n:sisLor is optional); measure Lhe potential dift~rcnce and currenl for each metal wire; calculate the resistance for each metal wir "'; repeat (with different p.d.) and calculate 332 the mean; JcngLh, diameter~ temperature (of win:); tahlc wi1h columns including correct units for type of wire, \'Oltage, cu1Tcnt and n.-"Sistance 5 a 4001n b trundl' wheel, mca urjng tape c 346 ml d too man~ ignificant figure u ed / two · ignificant figure arc morx: appropriate 6 a 6°C b i °C ii I 0°C iii 5° iv Lhe (~tarting) temperature is closer to room temperature c two from: ren10\·e lid, n:mo\·e in ulation, incrca c tarting tcn1perature of water Check-up on practical papers (page 291) 1 a co1Tcct L\'aluc · (or c\·cry 30 · up to 210 ; temperature~ decreasing for beaker~ A and B : lca.-,1 d<.."Cn:asc in beaker A. b °C in both columns c i ax<.>s corrcctl) labelled and right way round; uitabl' ca]c (not awkward nrnnb 'r ); point plotted con·cctly to +/- half a quarc: mooth curve ol be t fit ii point · plotted correct]) to /. half a square; ~mooth curve of be LfiL d adding insulation decnmscs the rate 0£ cooling of the water; refen!nce to readings showing th • tempcratur .. difference for beaker and beaker B. e anv Lwo fron1: anlc \'olumc ol water; amc ·tarting ten1pcraturc, an1e rnate1iaU ·ize o( beaker~ bolh beakers must ha\C no lid, same tcmpcr.Hure of the surrounding~ f any one from : (avoid parc1l1ax error hy) reading the thermometer p •111 •ndicular to th' calc, th rmomct 'r n1u l have ·topped 1i ing before fit L reading taken, thermometer hould not touch the beaker, ·tir the \\~Her 2 a normal al the centre of AB and CD and EX al 30° 10 1he nonnal; P 1 and P 2 at lt:ast 5 cm apar1; Line through P 3 and P 4 to meet normal at Z; b (their) u n1ea urcd COIT x:tly to ± 2o; I mca urcd c01Tccd~ to ±2 (mn1) c u n1ca!,urcmcnt ol 2 - 32°; unit of I i~ 1nn1 d ~tatcment agl'ee!) with reading~ (Yes or I o); Yes - idea of\\ ithin the limits of exper·imenLal accunic) or No • idea of outsidl· the limit ~of e"periniental accuracy e any one from: pin cparation · hould be large, \'icw the ba c or the pin , make urc pin arc \'ertical, u e thin pins/pencil line · numhc,· i.., gin~n in buld, ,ou ,hould 11101.: 1lu, up Iii ,t. 11 a f).\gl' •1b,oh1h: ,en, 10.l eh. nging to J .c:. ISS L'm.•1-atu1~ 2 l-4- 2 l5 mam, ,uppl, l 92 ,ohagl' 176. 192. 21-4 .u:Cdl'hlllon 29- 37. -40-41 uf fr .,.. f. 11. g '-'-3 unifo, ,n ,me.I llClll•llllifonn 3~17 .11.:crclirm d,-.'- 2·9 '-l..'1111iax·1.J (..and '°'·'1ll1ifug:,I ) fore(.· 54_::;- ..:h.1i11 n.·., tltlll 116-1l7 1.:h.lrg1,.• It, '-171 on ckd1tH1.., .111d prnlons lb8. 220 imlu nl 170 1 ,h.: li\'it, 1.'4- 2.'5 .,~1io11 .111d 1\',1t..:1ion 46 7 ,lii lt.•-.i..,l,IUC\.' 38, 39, 4., .,lph., d'-'<'•" 2 J2 .,lph., p.111kh.·, 22 • 229 altcm:itmg nu •~·nt ' t'l ' ., c:. .,ltcrn.,trJI"- 214-215 ,Ul\lll1.'ll'I 174 .,rnp ' I'(', unh c 111 '111 174- 175 .,mphtuc.h.· 12·. 1.n ,uMloJ;Ul' ,,g n.,1, I b2 or .,. .,..,.ru,d, 252. 2 4 atmosplw,k prt.••,M11~· 72- 7.'i ,11omk number 226 , ~:?O ,IIOSll', 100, lb , 226 227 motl1.•I.., ol 226. 2~2- 24 ~. 271 b ..,l-111 ...x-. fo, ,wi~hing 14, 22. bal.111C'<', ,tah.· ol ti0-61 h. mmch.: 1 7"\ l>.'llh.'" I 74 , 176 bc~quc1-cl. umt ol act1n1, 2 4 bt:-la dL 1,.:i, 233 . 24· tx.·1., J),1r1idc, 22 ' - 229 Big B.ing th..:,,., 262- 263. 27 bm,1.·1.11 ,trip I o· hin, n c<J<.h.· 162 bmluds 93. 94 blad: hole .2o I 0 blu'-·1on1h I t,3 Bolt,. , ,d, 2-13, 271. 27tt boihn • 114 boiling point ol \\,alcr 102 B°'h.·'s l..m 74- 75 bulb-.. lila111c111 17,', I; I Browni.rn motion I 01 1.:amcra l;b 1.:dl, Cch:diic) Ii-I in '-t.'I il'-. amJ in r>.i• .Jld l 7o. I ' S Ct.•bills all.' 102 103 L(.'111 IC uf gr.1\ ii\ 62 6:l, ~ \.(.'n11-: of m,,._.. 62. 6- link,,i1hn111cnt ns unil of Ii I ..:1n:u11 hn.·.1k..·1~ 192, 19J, 20S 1.:i1cuil '"nbnls 174. 321 1.: in::ui1-. I 7-t- 177. 184- 189 rn.,in, 192- 193 1,.' il"\' t1lar m111io,1 5-'- SS douc..l c:hamlx.-r 231 i;.:oil. m,lfllCIIC held :ituund 202- 203 i;.:olou, a.it . l-'7 1.:0111~·· .. 255- 2 6 c:ornnm1a1or 20' l:Olll p.1,, 200 1.:omponcnt-. of., H"Ctor 3.' 1.:0111 prc.....1011' (\,-a"-"') 124 1.:0111.:.,,t.· lcn,c-. 152. I comJcn,,1ti1111 111,onduction (dc1.:11 k,rl) 169 c:ondu1. lion (th.:1111,11 ) I O '- 109 1.:011dud111~ lckct1 ,~an lo9 1.:ondudrJ1~ (lhcnnal) 10. - 109 l:Olls<'r\, lion 1111.•ll('I ., S2 '-o"''-'l\atio11 ol mcm11,.•n1u1rr SO-· I 1.:onh"Cllon 1 I0 - 111 1,om-cnt ronal Ul'1"\'lll du .:... 11on 175 1.:omc1-g ing ten-. 152 1.:omc, kn''-'" 152- 1·7 CMBR (mic:111,,~w b,..:kg,ounJ) 2t.2 1.:ouluanb. unit ol 1.: h.u-gc 171 \.litic.11 :mglc.• 1"8. I• 1 1.:unl..'nl, t-•lc.-c1rri;.: 174--17ui1\.'diou 17S m..,gr1'-·ti dh: 1 202- 20.5 m.,gnctk lurn• un 206-209 <ligit,11 sigri.,b lt,2- 163 Jio<lc:-. 179, I , I, I ' S Ji11.• tc.:un.:nt -.eeJ.c . <l1,pl,1ccm\.'11t 1.:..m 20 Ji-.(X'I ,JC>II 147 c.liw1 •irig lcn, I s2 Juuhk· ins11fo1io11 192 dra • 4 Earth l'ot.tlion and or bit 250 pl.111ct..u, d.,,., 2 J (.',tr11hin • 170, 192 cd101.:, 131 c.:dto-,(Jlmding DI. 13~13S L'dd, cmn.·nb, 213 . 219 I lubhlc, Ed,, in 275 . 276 Ein-.11.·in. Alhc11 237. 26.'. 270. 276 ..,-ffid ·n , ., 6 of f)(>\\1,,' I ,1.,1 ior1' S9 d •.-.t11.: ltnut oo-67 dL'Clrtc cdl, '>t"t' u•II, de II i...· ch.11--gc ,·,: d1.1rgc de t1icl:i1 uits ~t·e d11,.ui1-. dc; t ric cu 11"\'n1 :o.tt• 1.: u1·1en 1 di;; 11 ic field, 171- 17.l ek-c11 ic mritm .20,' -209 d ...-ctm:.,I cn\.'1 g, SI ,._n,L ol 191 '-"c.\U,11ion f"'· 191 d1.: t 1 1c .,I f)O\\.: r ,,t• pu\\ •r \.'(ttl.ltion fur 190, 22 ~ d..: llic.:il, i;.:c ,t ol 191 1.•~uh iJ1.•,,, 272- 273 cl...-c1rom~g11('1i inJuc:1ion 21 O 219 d1.: tromagnt•tH.' \\a,c, 122. 158- lhl -.pcl..'d ol I • ' ell' t1-.:mrng11e1, 204 -20d..: 11·o moli\l' for u• 176 di;; 110n ,hdl, 227 d1.· tror" J:.,.-k matte, .,n<l \.'llCI" ,, 2h3 , 2r tl.l\ and night 250 d.c. 192 ,i, '-' d..: ·"· ••,Jk~K 22 ". 232- 2.l5 . 2-'5 d.: dcr. 1inn 29 d.:rn, •n1.•1i,ing m.,gnc1, 103, 20c..lcn-.il, 18- 21 , 23 "•'''-'I' change-,. in 105 ,11lc.l 1l,i.,1ing 23 lll\.",l'l•-111 ing 20-2 J of pl.mct:-. 2 ·, and r• .....,tu c 7 ~ diffr ..u.: ti1111 i11 J 1ppl1.• l.lllk 127 of 1,1dio "•'\'-' " I ~O in .,tmn-. lt> ', 226- .2.27 in drcuii.. 174 di~o,e1, ol 2-'2 . 271 in ckdrk.J 011ducto1, 169 in ,h1.·rm.,I conuuc.:tm~ 109 11.111,for h, mbhmg lti - 169 dl."CI I C)',U>pl.' Ih .. t.•k-c1n,,1at11.: cha, •t.• 16h, 1o9 d1.-..· aro,1.11k· i·11('1'8) " 1 ck 110,1.uk fo1H· ·1 dcmcnt-. 2 2, 24 e.m.f. 174 ('fl('I g) ('0-95 d1c1111caJ SI 1,on,1,,'I\•'' ion l,I\\ 2 333 \.'al'h- idc,1., 26 •269 da .. tk(~u,,in) 81 elcctrkal I, 191 clcc110,1ati 8l ~l'olhcrn,al 93, 95 gr..\\ itational potcnlial 81. h,drodc.: tri.: 91 , 92, 9intcmal IOI. 116,269 kinetic 81, 84 5 m .1gnc1k I an<l m.., , 237 non-, l!lll'\Htblc ~ ...ounc, 92 nuch:ar 'I, ' , 9i;, 236 23 po1cntial 'I, 84 5 n:nc\\ablc rc,;ourcc, 92- 93 rcsoun::t.'" 92- 9. ,ol:.u· 93, 94 "P• l!ading 9 from un 92, 93, 94-95 thermal :o.ee 1hcrm.1I ,mc1 ,, tidal 91 , 9.'\, 95 lran.,for.. 82- 3 ,,ind 90- 91. 93,9ent.'l'g) ,1orc-. 'I cquilibtium 61, 63 c,-..por.uion 114-11c:\p:.msion (thermal) or gase, 107 ol ic..- .md \\,11c,· 105 ol ,oliJqind liquid, 104- 105 c,tcnsicm or :-.pring 66 c,c, hum.111 150- 1·7 ,hu1 l a,,c.J loug ..,jght I -7 foir t1.~t 2 1 F.u .1d,,,\ law or elect, om:.1gne11c induction 210 fibc '-'"• <,Pli1..-aJ 149, 163 fi.....,ion, 11ud1..•a1 8. 92, 236-237, 239 fiwd point, (tcmpcr.,turc) 106 F1cming-... lclt•h,rnJ ndc 206 Ffoming's right-hand rule 212- 213 floating and demit · 23 flttot'C, Clll"C 161 ,l length 152, , -for cc 38- 5 l , 56-t) ,md ,u; cl ·1.,1ion .;0-41 '-='-'nlript.•tal t:;,4 c;5 gr..l\ italicm.t.l -14 ,md momentum 48 and p, ,,,u 1'-' 68 69 and \\ork 0 tumin • dtl."'Ct of 60 fossil fuels 92, 94 r~qucnc · 12:; ol ,1.1.. rn.,in, 192 ollight,,.wc, 141 or radio \\.l\"C'> 163 o I sound \\ ah''- I 32 134 roc. 334 r, ic:1ion 42 3 fod, 90. 92- 94 nuclc.11" 92, 236-237, 239 fundamental p.u-t icJc., 2-1-1 foscs 192-193 fo,ion. latent heal or 118 fo,ion, nu h.•ar 92, 94, 238- 239 in """' ( un) 259- 260 g (.u: dcr..,tion or free r.,11) 34-35, 45 t-: (&u th', g1~l\ itational fo:ld -.t1 ,.:ngah) 44-4c; gal:-txic, 258, 262- 263, 275 ~arnma 1 , , , , in dl.' lmmagnctic spt.'Ctrum 159, 161 111-.~11ic :.m<lcff\.-,,., 22 229, 23.~ 1.LWS 240-241 inc,1i.:a 40 inftar\.'J 112, 159 160, 163 insulators (de trii.al) 169 in..ulators (1hc1 m.,I) 10 - 109 i nlt.•rnal en erg, IOI. 21 . 269 ioni1a1ion 17.3, 22 229 ion .. in ,1ir 17 i-.om,~, 226-227 jcl cngin\." -17 jouk uni1 ur wo1 k an<l enc~· 80 Kd,in:-.i.:alc 103 l.1logi am, unit ol m.,,, 14 kilo,, au 80. 190 J.:ilo\\all hom· (kWh) 191 kineaic l.'l\crg, 'I l:akulating 84 kincai thc:or. 100 la~r. light fn,m ~ 41 laser diode 16., latcnl heat 1 I - 119 LOR, 179, I '9 LEO, 163. 189 length 15 16 lcn,c:-. 152- 157 Len,'s km 212- 213 lighl 140- 160 earl, iJca, 270 fmm .m atolll 2-'4 in .:lcctromagnctk "Jlt.'Ctn.1m 1-9- 160 ,1)('1..-<l of 141. ISO. 15 ' \\a\ •s 1-11 r. '-':\f>" n,ion of I07 heating 106-107 particll.·s in 100 111'C~-.urc 74 -r. 106- 107 J)1-c ..,ure•,olum1..• la,, 74 -r Gciscr-.\ H1llcr tube 230- 231 gcncr~101, 214-215 gco,tationa1') orbit 2c;7 gcothcnn:.,I t.•nc"K' 93. 95 global,,, rming 90, 113 gradicmt or._, gr .. ph 30 gr•" itation.,I licld -.u~ngth 44--15 on pl;mct, r 3 gr-a, iamim,al 101 l.l' 44, c;c; gt'a\ ih 4-4-45 c:cm re of 62 63, 65 and orb1h 2S6 G1id (ell.' tr icit ·) 220 hall-life 234- 235 heal ~u thcnnal cncr-g, hertz 125, 1 2 llooki:-... l,t\\ 6 7 ll ubble c.:on">tant 263 ll ubblc, E<l\\ in 275, 276 h,d1odc 11ic pc>\\'l'I' 91 , 92, 95 h,d,ogcn .,tom :;:;, 227 in the: un 239, 260 h~dmrnl.'lu 21 light w.-ir 25' light-Jc~ndcn1 ,c,i,101 179, I '9 lighl-cmittin T dioc.ll.', 163, 189 limit of prnportion.,lit, 60 liquids np~uhion or 104- 105 p.'lrtick~ in 100 P"-'''Ul • in 70 -71 long ,ight l :;7 longitudin.tl \\c.l\t.':o. 124 loudnc.:,, I 33 loudsf)(',lkl!r' 207 im..,g1..· fo1111,11ion b, pl:.mc min 01 :-. 142- 145 h, lcn:-.~ 152-1 S7 irnagc,. 1~..11 and , it tual 142, 152, I 'i-' impube 4~ rn;-i •nc:tic cft~-ct of .l CUlTCnl 202- 205 magnctic.: lidc.J 200-203 E.a11hs 20l rn;1gnctic m,11cri,1I, 199 magnetic: pol1.•, 198- 201, 203 m.1gnctic :-.tora ''-" 20S m.1 Tnc:ti-.m, c.uh idc," 272 magnets 19 201 making and dt.•magnl!ti1:ing indu~cJ charge 170 indU1:cd n1.1g11e1i,m 198 mduu.-d ,ohagc and l.UfTl.'nl 2 l0 -219 di,.: lionorcuncnt 212- 213 rn;1gni" ing gla:')-. 1-4 m.,ins d~-ctricit, 192- 193 suppl, '):-.lcm 220-221 iJc,,I ga, 75 199,203 manometer 7 nl.l,._ 14 ,m<l .u:cdcmtion 40-11 ccrurc ol 62-63 ~m<l de n">il\ I - 19 an<l energy 237 rnc,1,mi11g h, ornp..,r;ng 22 ,,nd ,,eight 44 5 m.L...... numb ·r 227 medium (Ii •Ill) 146 m~-dium hound) 128 mching 118 melting point or \\ate, 102 lllCtc.:or... .inJ nlCh,.'01 itc, 25lUCtl\.1, unil of lcn~lh 1m icru\\ a\l's 13 J. 159 160 from '.',P• .:c 262 Milkv W.,, 25 mirrors 142- 143 molccub, l 00 moments 60-61, 64-65 piinl·ipl~ of 60 mo,nl·ntum 48- -1 con~n.llion of 0-51 monochrnm.11if: light 141 Moon 250-2 1 phast.•s ol 251 moon'.', around planet'.', 2·3 motion 2 - 3 7. 'w SS cir uJ:.11 'i-4 5 l.'ar I~ 1<ll'J'."I 268 graph, 30 l 1. 35-37 e" ton.._ h1 ,1 I,"' ol 3 • 'c\\ ton's '>l-'Cond la\\ ol 40 • C\\ ton's third la\\ of 47 moto~. dl-'Ctrk 20 209 mutual induction 216-219 nchul., 2 ll- 2 59 neutron ,tar 261 rn.•utron, 16 , 226 in h'.'.'lon 236-237, 2P ,1n1e.:tun: of 244- 245 ne\\ ton. unit of fo l.' 3 • 41 c,,ton. krnc 26,. 270. 274. 276 la,,'.'. of motion ~et• motion nudc,1r eOCl;r\' 'I,..: ,9-, 23 239 li'."l,ion • 92. 236- 237 fuel 92. 236-237 fusion 92. 94. 23 239, 260 l)O\\e1· -.1ations 88. 236-237. 2]9 r.1dia1ion 22~ -231 I\.'~ tor~ 23 239 nucleon numbcl' 227 nucleon, 226 nucleus 1btt 226 ch;rngc:-. durin dt.-1..l\ 232- 233 c, 1d'-·nn.• lor 242. 271 nuclide 227. 2.U 11 octa,c, 132 ohm. unit or resistance 17 Ohm\la" 181 optical librc, 149. 163 in cable-. 16., orbital speed 251 urbh:-. SS. 274 or Earth .m<l Moon 250- 25 I of pl.mcl'.', 252- 253. 256. 274 of ,.ltdlitc, i-1 oscillo:-,('.O~ <li,pla\'ingsound-.on 129. 132- 133 ·s. P (J)lilll,11\) \\3\1.', 124 parallel circuit, I 4-187 p.ir, lldo n ,m1 mlc ror we tor:-. S2 par&ide a l'.dl.'1 ators 244 par&idc-. in atoms 226 227, 244- 245 lun<l.11ncn1.,J 2-U- 2-15 in ..c,lids. liquid'.'., g,L,~, 100- 101 p.1,cal, unit of prc,su,-c 68 p.t.l. 17b drcuit nrlcs 177, 185 dk-c1oncu1n:nt 1 0-181 pendulum. period or 17 pcne111.11ion (r,,diation) 229 period of orbil -s. 2'i6 of o,cillation 17. 1r P,: I i,1.0P,: 14 photo<liode 163 photons 141. 244. 271 pitch 1.32 pl,lll('h 252- i- - <la1a on 253 rom1,l1ion of 259 orbi,, or 253, 274 plug.'), ek II i 192- 193 poll's, magnetic 198- 201. 203 pollution 90 ('lOll.'nlial diffcr~nlc .)(e pd. potential dh idl'1 I 9 potential eneq;, l g, ,I\ hation,11 I, 8 85 p)\\1,.•1 86. 190 clc tr ical 190- 191 suppl, '."I\ ,tcm 220-221 pc>\\crlos, in .l c.1blc 221 pmc1 l'ating ol applia1\Cl.'-. 190 po,,e, ,1 ..1tions ~ ~ 91 1 ~a IOI in 2 6-239 pe,,u, • 68 .,,mc~phc,·ic 72- 73 or g.,s 74 -r . 106-107 in Jiqui<l, 70-71 ,nc.,.._.uing 7J pa c'."l,u oluml I.a\\ for g;t'."le'> 74- 75 pa·incipal focus 152 n:-, pri,m., 147, 14 l ,,,n,por tinn. direct and imct,l' 29pn,1011 1\umlx-1 226 ('lfUIOO'.', 16 , 226 ,tn1 tun.- o( 244- 24 J)ffllO', \,lf 2 9 pUmP\.-d StOl .age 9 l qualit, (,oun<l) 133 quaruurn thl"Of)' 243. 244, 271 quark., 244-245. 271. 276 I aJ,,r 131 , 159 radi.11ion background 230-231. 235 dangers 230 cb.: tr"Umagnctit.· 15 ' - 161 nm:lcar 22' 231 thermal (treat) 112- 1I.' radio"•" •s I 59 160. 163 radio,, the d ,,, 22 , 232-23-. 245 , adio.1ctiw ";:t\ll-' 23 7 , .ldio.1cth ii\ 22 ' 237. 240-241 u-.c, of 240-24 I 1adioi,otopes (r-a<lionuclide,) 240 , adi 01 he I ap, 240 ,ard.ction~(\\,\1;,) 124, 12' RCD (1~,idm,I cu11 cnt de\ i I.') 193 , ..Ktors. nudl.',U' 236- 239 real im.tgc I 52 1--ccm·ding 201 \.Ctifil'I' l88.2JS , "-<l grants and supcrgiants 260-261 ri.J ,hilt 262 r"e<.·c.l "' itch .,nd 1 •l.1 I 9 re flee I ion 1.m-. or 142 h, pfoni: mino" 142- 145 in prisms 148 in ripple tank 126 of..c,unJ 131. U-l - 135 tot~I illll'ln,,J 148- 149. 151 1>cf1._1~1ion of Ii ~h, 146- 147. I -0-151 inlippli:t,mk 126 ofsound 131 l'cfracti\C i ndl':\ l 37, 150-l • 1 rdrigc1 .,tor 111, 115 I •1.w magnetic 204 1':t:<l 189 , ~~lance 178- 7 l.1ctm s .,IT~"Ct ing (fof\i.ir •) 17 , l 2- 1 3 I 'Cs.i SI i\'il, I 87 r'C~hlors 179 in ,l.'rit:, and p..11-..,llcl 18-- 187 , • 1i,1hk 179 335 1 \:~h.ult 40. 2 rct;,rdation 29 RF I O 163 11gh1•han<l glip I ull".., 202. 203 1 ippll" tank 126-127 1 odc.>t engine 47 ( :-.cconda" ) \\ a, c~ 12 4 ....,fr,, i.:k·cllkal 193 in ah'-' labor,1to1 231. 278- 279 nud.:.tr 231, 236 :-.atcllitc ,ind mohill.' phone, 163 satcllitc:s (ai tilicial) orbit... ol ••• 256 257 l1't:' 2'i7 seal.us 52. 8'i :-.dcntific notation 13 :-."a,011' 250 SL'Ccmd, unit ol timt.• Ic; sl."1smk ,,a,c, 124 ,cmil.'011ducto1~ 169 ,c,it."-. d1 cuh, l '4- 1 '7 ,hort si •hi 157 I unib 1-1-1 • table or 320 signals. analogue: and digital 162- 163 :-.lip ling., 214 11'.•11', law 150 solar· 1."Clls 93, 94 ertef'g\ 93. 94 panel 93, 94. 113 obr ,,h:m 2 2- 255 :-.oleno1d 202 solidi licat aon I 15 solid, p._'U t ich: s in I00 i.: p.ubiorl of l<M- 105 :-.otind ch,,r.11.:tcri,ti ,of 1.32- 133 spc<.-d of IJO \\3\"CS 12 IJ5 ,pccifk heat caJl,1dt, 116- l 17 sf)Ccilk fotl."nt he.it of fusion l I of ,-apori:1.11iun 119 spt:ctral line:-. 243 :-.pc:ctnun clcct1'<>m,1l;nc1ic 15 ' - 161 light 147,243 ,pccd-timt." g,~ph, 31. 36 -37 spring b."11.mcc 38 ,prin COJ1't.mt 67 spri11g, :o.t1i.:tching 66-67 stabilil\· ol balancL-d ubje h 63 :-.tabilit, or nudi.>ti-. 235 'l'"ll~ 2 26 I :-.latL•, changt.·, or l Is. I 18 ,tr.,in (cla:o.tk) cncr !\ I UH birth ol r9 cJcath of 260 c.>ncrg, from 9-' 9-; ru-.aon m 92. 94. 238- 239, 260 and planet:-. r 2 ,u pi.:, nm .., 261 S'\\\.':.lli"g J , :-.,\itch·, 1ti4, 192 m;:1grn.•1ic (rcl;:1,) 20 r't'-'d(lcla ·) 1,9 !'.'\ mbols. cm:u1t 174, 321 \\ate,· 20S tck:,coJk I tl.'mJ)l'r.lturc J 02 103. 269 tcm1in. I ,..:101.il\ 39 tht.•nnal capacit · 116 thermal cncr · 81, 101 c,1paci1, and ,toring 116- 117 and l~h.•nt hc-M 114- 1I thermal rncliation 112 113 thcnni,tor-. 102, 179 tht.•nnornctcr:-, I0 2 tht.•nnos tat I 05 tick~·r-iapc c,pcr imcn1, 32- 33 tidr,1 pc,,,cr 91 . 93. 95 time 15 mt:.L,tuing small in ten aJ:o. 17 101 ..,l i111crnal ,~tlc-ction 148- 149, 1· 1 t1.acc:1 (I ..1c.lioac1i\ •) 240 tmn,for mi.:r:-. 217- 220 ,tcJNIJl and ,tcr>-c.lo,, n 21 ll'a n.-.\ I." r.oiC \\a\ L"S 124 uh r.1,on k soun<ls 134 uh1~1..,ound U4 135 uhrj\ iolct 159, 161 un1;crtaintic, (in mi.:.t,ur'-'nlCnt,) 2S2 unih 12 1$ I 14-1 c;, 320 nl\~r::-.t.• 2 8. 274- 275 age of 262- 263 '-"'~ ndin~ 262- 26 :"IJX,'L-<l 28 oflight 141 , 1·0. 158 of soun<l U0 336 \hllt."1· 114- J l \ .ui .1blcs 280 2 81 \i.: tor.- 28. 52- =i' ,docity 28 tcm1in~,1 39 ,doci1,-1inic gmph, , i11ual i m,,gc 142 in lt.•n:-.c, 154, 1•• in pi.me minor 142 ,oh. unit or p.J. al\d '-',in.I 176 ,t>ltagc 176. 214 -.c-e al"-<> pd. and c.mJ rn,,i11, 192. 220 ,oltmctcr 176 ,olurnl.' I - 20 , ,lf)Olll', ,. cuum 73 ,apori,ation. latcllt hi.:al ol 119 <lcn,it\ of 18. 19 and kc IOS melting and boiling poinl'i. ol 102 'JX"<'ifk h\.',lt 1.-apacit, of 116 .... ~ilk l..lh.:nt he.ll~ or 11 ' - 119 \\.111.'r J)O\\.l.'I" 90 91 , 93. 9• "•'tL-r,.,pour I 1-i--11 • unit ol po,,cr 86, 190 \\aw en~•~' 93. 95 \\a, • cqu,llion 125. I 33 ,,,l\dcngth 12or ck lmmagnctu.: \\,1\1.'S 159 or Ii •ht 141 ol sc>llnd l28 \\atl. eh: 1mm,,gnc1i ~ 1- - 161 light 141 longituclinJI 124 ,~dio 159. 160. 163 in 1ipplc t ..1n'- J 26- 127 soun<l 12 1311.in,,cr-sc 12-1 ,,~ighl 22, 44-4 5 "hitc d,,arf 260 \\ ind po\\ cl" 90-9 l. 9 3. 95 \\OJ k 80, 3 X-r,1\:-. 159, 161 :,er o t."n or 17 Cambridge IGCSE & 0 Level Complete Physics d1rec-tly matches the latest Cambridge Physics IGCSE (0625) and 0 Level (5054) sytlabuses, supporting comprehension of Empowering every learner to succeed and progress complex ideas and independent learning. A stretching, Complete Cambridge syllabus match skills-based approach w1th a light touch ensures ;t is Comprehensive exam preparation engaging, progressively strengthens student ability, Embedded critical thinking skills and enables confident exam performance. Progression to the next educational stage • FuUy prepare for exams - assessment-focused support improves students· performance ./ Reviewed by international subject specialists • Q Develop advanced skills - a rigorous step-by-step approach increases students' confidence Progress to the next stage - differenhated extens10n material eases the transit1on to 16-18 study Answers available on the accompanying support site: www.oxfords«ondary.com/ complttt-1~nct Also available 978 1382 00593 7 978 1382 00598 2 978 1382 00601 9 ISBN 978•1•382 00594 4 9 lll~lllllll