Cambridge IGCSE® & 0 Level
Complete
Physics
Fourth Edition
Stephen Pople
Anna Harris
Naseemunissa Azam
Elliot Sarkodie-Addo
Helen Roff
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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
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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
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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:
□
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□
□
□
□
□
□
□
□
□
□
□
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
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