Physics data booklet First assessment 2016 Diploma Programme Physics data booklet Published February 2014 Published on behalf of the International Baccalaureate Organization, a not-for-profit educational foundation of 15 Route des Morillons, 1218 Le Grand-Saconnex, Geneva, Switzerland by the International Baccalaureate Organization (UK) Ltd Peterson House, Malthouse Avenue, Cardiff Gate Cardiff, Wales CF23 8GL United Kingdom Website: www.ibo.org © International Baccalaureate Organization 2014 The International Baccalaureate Organization (known as the IB) offers four high-quality and challenging educational programmes for a worldwide community of schools, aiming to create a better, more peaceful world. This publication is one of a range of materials produced to support these programmes. The IB may use a variety of sources in its work and checks information to verify accuracy and authenticity, particularly when using community-based knowledge sources such as Wikipedia. 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Email: sales@ibo.org International Baccalaureate, Baccalauréat International and Bachillerato Internacional are registered trademarks of the International Baccalaureate Organization. 4082 Contents Fundamental constants 1 Metric (SI) multipliers 2 Unit conversions 3 Electrical circuit symbols 4 Equations—Core 5 Equations—AHL 8 Equations—Options 10 Physics data booklet Fundamental constants Quantity Acceleration of free fall (Earth’s surface) Gravitational constant Symbol g G Avogadro’s constant πA Boltzmann’s constant πB Coulomb constant k Gas constant Stefan–Boltzmann constant Permittivity of free space R σ π0 Permeability of free space π0 Planck’s constant h Electron rest mass πe Speed of light in vacuum Elementary charge Proton rest mass Neutron rest mass Unified atomic mass unit Solar constant Fermi radius Physics data booklet c e πp πn u S π 0 Approximate value 9.81 m s−2 6.67 × 10−11 N m2 kg−2 6.02 × 1023 mol−1 8.31 J K−1 mol−1 1.38 × 10−23 J K−1 5.67 × 10−8 W m−2 K−4 8.99 × 109 N m2 C−2 8.85 × 10−12 C2 N−1 m−2 4π × 10−7 T m A−1 3.00 × 108 m s−1 6.63 × 10−34 J s 1.60 × 10−19 C 9.110 × 10−31 kg = 0.000549 u = 0.511 MeV c−2 1.673 × 10−27 kg =1.007276 u = 938 MeV c−2 1.675 × 10−27 kg =1.008665 u = 940 MeV c−2 1.661 × 10−27 kg = 931.5 MeV c−2 1.36 × 103 W m−2 1.20 × 10−15 m 1 Metric (SI) multipliers Prefix Abbreviation Value peta P 1015 G 109 tera T mega M hecto h giga kilo k deca da centi c deci 1012 106 103 102 101 d 10–1 milli m 10–3 nano n micro pico femto Physics data booklet µ p f 10–2 10–6 10–9 10–12 10–15 2 Unit conversions 1 radian (rad) ≡ 180° π Temperature (K) = temperature (°C) + 273 1 light year (ly) = 9.46 × 1015 m 1 parsec (pc) = 3.26 ly 1 astronomical unit (AU) =1.50 × 1011 m 1 kilowatt-hour (kWh) = 3.60 × 106 J hc = 1.99 × 10-25 J m = 1.24 × 10–6 eV m Physics data booklet 3 Electrical circuit symbols cell battery ac supply switch voltmeter V ammeter resistor variable resistor lamp potentiometer light-dependent resistor (LDR) thermistor transformer heating element diode capacitor Physics data booklet A 4 Equations—Core Note: All equations relate to the magnitude of the quantities only. Vector notation has not been used. Sub-topic 1.2 – Uncertainties and errors Sub-topic 1.3 – Vectors and scalars If: π¦ = π ± π then: π₯π¦ = π₯π + π₯π ππ π π₯π¦ π₯π π₯π π₯π then: = + + π¦ π π π If: π¦ = If: π¦ = ππ then: βπ¦ βπ = οΏ½π οΏ½ π¦ π Sub-topic 2.1 – Motion π΄H = π΄ cos π π΄V = π΄ sin π Sub-topic 2.2 – Forces π£ = π’ + ππ‘ πΉ = ππ π£ 2 = π’2 + 2ππ πΉf = πd π 1 2 π = π’π‘ + ππ‘ 2 π = (π£ + π’)π‘ 2 πΉf ≤ πs π Sub-topic 2.3 – Work, energy and power Sub-topic 2.4 – Momentum and impulse π = πΉπ πππ π π = ππ£ 1 πΈK = 2 ππ£ 2 1 πΈP = 2 πβπ₯ 2 βπΈP = ππββ power = πΉπ£ useful work out total work in useful power out = total power in EfοΏ½iciency = Physics data booklet πΉ= βπ βπ‘ πΈK = π2 2π Impulse = πΉβπ‘ = βπ 5 Sub-topic 3.1 – Thermal concepts π = ππβπ π = ππΏ Sub-topic 3.2 – Modelling a gas πΉ π΄ π π= πA π= ππ = ππ π 3 3 πΈοΏ½K = 2 πB π = 2 Sub-topic 4.1 – Oscillations π= 1 π Sub-topic 4.2 – Travelling waves π = ππ Sub-topic 4.3 – Wave characteristics πΌ ∝ π΄2 πΌ ∝ π₯ −2 πΌ = πΌ0 πππ 2 π π π πA Sub-topic 4.4 – Wave behaviour π1 sin π2 π£2 = = π2 sin π1 π£1 π = ππ· π Constructive interference: path difference = ππ Destructive interference: 1 path difference = (π + 2)π Sub-topic 5.1 – Electric fields Sub-topic 5.2 – Heating effect of electric currents βπ βπ‘ π1 π2 πΉ=π 2 π 1 π= 4ππ0 Kirchhoff’s circuit laws: πΌ= π= πΈ= π π πΉ π πΌ = ππ΄π£π Σπ = 0 (loop) π = ΣπΌ = 0 (junction) π πΌ π = ππΌ = πΌ 2 π = π total = π 1 + π 2 + β― 1 π total = π π΄ πΏ 1 1 + +β― π 1 π 2 Sub-topic 5.3 – Electric cells π= π = πΌ(π + π) πΉ = ππ£π΅ sin π Physics data booklet π2 π Sub-topic 5.4 – Magnetic effects of electric currents πΉ = π΅πΌπΏ sin π 6 Sub-topic 6.1 – Circular motion Sub-topic 6.2 – Newton’s law of gravitation π£ = ππ π= πΉ= π£ 2 4π 2 π = 2 π π πΉ=πΊ ππ π2 π=πΊ π π2 π= ππ£ 2 = ππ2 π π πΉ π Sub-topic 7.1 – Discrete energy and radioactivity Sub-topic 7.2 – Nuclear reactions πΈ = βπ βπΈ = βπ π 2 π= βπ πΈ Sub-topic 7.3 – The structure of matter Charge 2 π 3 Quarks u 1 − π 3 d c s Baryon number t b Charge –1 1 3 0 1 3 Particles mediating e υe µ τ υµ υτ All leptons have a lepton number of 1 and antileptons have a lepton number of –1 All quarks have a strangeness number of 0 except the strange quark that has a strangeness number of –1 Particles experiencing Leptons Gravitational Weak Electromagnetic Strong All Quarks, leptons Charged Quarks, gluons Graviton W+, W–, Z0 γ Sub-topic 8.1 – Energy sources Sub-topic 8.2 – Thermal energy transfer energy Power = time π = πππ΄π 4 1 Power = 2 π΄ππ£ 3 Physics data booklet πmax (metres) = Gluons 2.90 × 10−3 π(kelvin) power π΄ total scattered power albedo = total incident power πΌ= 7 Equations—AHL Sub-topic 9.1 – Simple harmonic motion π= 2π π Sub-topic 9.2 – Single-slit diffraction π= π = −π2 π₯ π π Sub-topic 9.3 – Interference π₯ = π₯0 sin ππ‘ ; π₯ = π₯0 cos ππ‘ ππ = π sin π π£ = ±ποΏ½(π₯0 2 − π₯ 2 ) Destructive interference: π£ = ππ₯0 cos ππ‘ ; π£ = −ππ₯0 sin ππ‘ πΈK = 1 2 1 ππ2 (π₯0 2 πΈT = 2 ππ2 π₯0 2 −π₯ 2) 1 Constructive interference: 2ππ = (π + 2) π 2ππ = ππ π Pendulum: π = 2ποΏ½ π π Mass–spring: π = 2ποΏ½ π Sub-topic 9.4 – Resolution π = 1.22 π = π π π = ππ Δπ Sub-topic 10.1 – Describing fields Sub-topic 9.5 – Doppler effect π£ Moving source: π ′ = π οΏ½ οΏ½ π£ ± π’s Moving observer: π ′ = π οΏ½ βπ βπ π£ = ≈ π π π π£±π’0 π£ οΏ½ Sub-topic 10.2 – Fields at work π = πβππ π = πβππ ππ = − π=− πΊπ π Δππ Δπ πΈP = πππ = − πΉG = πΊ π£esc = οΏ½ 2πΊπ π πΊππ π π1 π2 π2 ππ = ππ π πΈ=− Δππ Δπ πΈP = ππe = πΉE = π ππ1 π2 π π1 π2 π2 πΊπ π£orbit = οΏ½ π Physics data booklet 8 Sub-topic 11.1 – Electromagnetic induction Sub-topic 11.3 – Capacitance π· = π΅π΄ cos π πΆ= π = −π π = π΅π£π βπ· Δπ‘ π = π΅π£ππ Sub-topic 11.2 transmission πΌrms = πrms = πΆparallel = πΆ1 + πΆ2 + β― 1 – Power generation and πΌ0 √2 π0 √2 π0 πrms π = = πΌ0 πΌrms πmax = πΌ0 π0 1 ποΏ½ = 2 πΌ0 π0 πp πp πΌs = = πs πs πΌp π π πΆseries πΆ=π πΈ = = π΄ π 1 1 + +β― πΆ1 πΆ2 1 πΆπ 2 2 π = π πΆ π‘ π = π0 π −π π‘ πΌ = πΌ0 π −π π‘ π = π0 π −π Sub-topic 12.1 – The interaction of matter with radiation Sub-topic 12.2 – Nuclear physics πΈ = βπ π = π 0 π΄1/3 13.6 ππ π2 πβ ππ£π = 2π π΄ = ππ0 π −ππ‘ πΈmax = βπ − π· πΈ=− π(π) = |ψ|2 Δπ π = π0 π −ππ‘ sin π ≈ π π· β 4π β ΔπΈΔπ‘ ≥ 4π Δπ₯Δπ ≥ Physics data booklet 9 Equations—Options Sub-topic A.1 – The beginnings of relativity ′ π₯ = π₯ − π£π‘ ′ π’ =π’−π£ Sub-topic A.3 – Spacetime diagrams π£ π = tan−1 οΏ½ οΏ½ π Sub-topic A.2 – Lorentz transformations πΎ= 1 2 οΏ½1 − π£2 π π₯ ′ = πΎ(π₯ − π£π‘) ; βπ₯ ′ = πΎ(βπ₯ − π£βπ‘) π‘ ′ = πΎ(π‘ − π’′ = π£π₯ π2 π’−π£ π’π£ 1− 2 π ) ; βπ‘ ′ = πΎ(βπ‘ − π£βπ₯ π2 ) βπ‘ = πΎβπ‘0 πΏ= Sub-topic A.4 – Relativistic mechanics (HL only) πΈ = πΎπ0 π 2 πΈ0 = π0 π 2 πΈK = (πΎ − 1)π0 π 2 π = πΎπ0 π£ πΈ 2 = π2 π 2 + π0 2 π 4 ππ = βπΈK Physics data booklet πΏ0 πΎ (ππ‘ ′ )2 − (π₯ ′ )2 = (ππ‘)2 − (π₯)2 Sub-topic A.5 – General relativity (HL only) βπ πββ = 2 π π π s = βπ‘ = 2πΊπ π2 βπ‘0 οΏ½1 − π s π 10 Sub-topic dynamics B.1 – Rigid bodies and rotational π€ = πΉπ sin π π = βπ + π 3 πΌ = ∑ππ 2 π = 2 ππ π π€ = πΌπΌ βπ = π = 2ππ πf = π i + πΌπ‘ πf2 = πi2 + 2πΌπ 1 2 π = πi π‘ + πΌπ‘ πΏ = πΌπ 2 1 πΈKrot = 2 πΌπ2 Sub-topic B.3 – Fluids and fluid dynamics (HL only) π΅ = πf πf π π = π0 + πf ππ π΄π£ = constant 1 2 Sub-topic B.2 – Thermodynamics ππ£ 2 + πππ§ + π = constant πΉD = 6ππππ£ π£ππ π = π 5 βπ π ππ 3 = constant (for monatomic gases) π = πβπ π= useful work done energy input πCarnot = 1 − πcold πhot Sub-topic B.4 – Forced vibrations and resonance (HL only) π = 2π energy stored energy dissipated per cycle π = 2π × resonant frequency × energy stored power loss Sub-topic C.1 – Introduction to imaging Sub-topic C.2 – Imaging instrumentation 1 1 1 = + π π£ π’ π= π= 1 π Sub-topic C.3 – Fibre optics βi π£ π= =− βo π’ π= πi πo πnear point πo πe π= 1 sin π attenuation = 10 log πΌ πΌ0 Sub-topic C.4 – Medical imaging (HL only) π· π· = + 1 ; πinοΏ½inity = π π πΏI = 10 log πΌ = πΌ0 π −ππ₯ πΌ1 πΌ0 ππ₯1 = ln2 2 π = ππ Physics data booklet 11 Sub-topic D.1 – Stellar quantities π (parsec) = πΏ = ππ΄π π= 4 1 π (arc–second) πΏ 4ππ 2 Sub-topic D.3 – Cosmology π§= βπ π£ ≈ π0 π π§= π −1 π 0 π≈ 1 π»0 π£ = π»0 π Physics data booklet Sub-topic D.2 – Stellar characteristics and stellar evolution πmax π = 2.9 × 10−3 m K πΏ ∝ π3.5 Sub-topic D.5 – Further cosmology (HL only) 4ππΊπ π£=οΏ½ π 3 πc = 3π» 2 8ππΊ 12
