Physics data booklet. First assessment 2016

Transcription

1 First assessment 206

2 Diploma Programme Published February 204 Published on behalf of the International Baccalaureate Organization, a not-for-profit educational foundation of 5 Route des Morillons, 28 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: International Baccalaureate Organization 204 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. The IB respects the principles of intellectual property and makes strenuous efforts to identify and obtain permission before publication from rights holders of all copyright material used. The IB is grateful for permissions received for material used in this publication and will be pleased to correct any errors or omissions at the earliest opportunity. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior written permission of the IB, or as expressly permitted by law or by the IB s own rules and policy. See IB merchandise and publications can be purchased through the IB store at sales@ibo.org International Baccalaureate, Baccalauréat International and Bachillerato Internacional are registered trademarks of the International Baccalaureate Organization. 4082

3 Contents Fundamental constants Metric (SI) multipliers 2 Unit conversions 3 Electrical circuit symbols 4 Equations Core 5 Equations AHL 8 Equations Options 0

4 Fundamental constants Quantity Symbol Approximate value Acceleration of free fall (Earth s surface) g 9.8 m s 2 Gravitational constant G N m 2 kg 2 Avogadro s constant N A mol Gas constant R 8.3 J K mol Boltzmann s constant k B J K Stefan Boltzmann constant σ W m 2 K 4 Coulomb constant k N m 2 C 2 Permittivity of free space ε C 2 N m 2 Permeability of free space μ 0 4π 0 7 T m A Speed of light in vacuum c m s Planck s constant h J s Elementary charge e C Electron rest mass m e kg = u = 0.5 MeV c 2 Proton rest mass m p kg = u = 938 MeV c 2 Neutron rest mass m n kg = u = 940 MeV c 2 Unified atomic mass unit u kg = 93.5 MeV c 2 Solar constant S W m 2 Fermi radius R m

5 Metric (SI) multipliers Prefix Abbreviation Value peta P 0 5 tera T 0 2 giga G 0 9 mega M 0 6 kilo k 0 3 hecto h 0 2 deca da 0 deci d 0 centi c 0 2 milli m 0 3 micro µ 0 6 nano n 0 9 pico p 0 2 femto f 0 5 2

6 Unit conversions radian (rad) 80 π Temperature (K) = temperature ( C) light year (ly) = m parsec (pc) = 3.26 ly astronomical unit (AU) =.50 0 m kilowatt-hour (kwh) = J hc = J m = ev m 3

7 Electrical circuit symbols cell battery ac supply switch voltmeter V ammeter A resistor variable resistor lamp potentiometer light-dependent resistor (LDR) thermistor transformer heating element diode capacitor 4

8 Equations Core Note: All equations relate to the magnitude of the quantities only. Vector notation has not been used. Sub-topic.2 Uncertainties and errors Sub-topic.3 Vectors and scalars If: y = a ± b then: Δy = Δa + Δb If: y = ab c then: Δy y = Δa a + Δb b + Δc c If: y = a n then: y y = n a a A H = A cos θ A V = A sin θ Sub-topic 2. Motion v = u + at s = ut + 2 at2 v 2 = u 2 + 2as (v + u)t s = 2 Sub-topic 2.3 Work, energy and power W = Fs cosθ E K = 2 mv2 E P = 2 k x2 E P = mg h power = Fv useful work out Ef iciency = total work in useful power out = total power in Sub-topic 2.2 Forces F = ma F f μ s R F f = μ d R Sub-topic 2.4 Momentum and impulse p = mv F = p t E K = p2 2m Impulse = F t = p 5

9 n = N N A Sub-topic 3. Thermal concepts Q = mc T Q = ml Sub-topic 3.2 Modelling a gas p = F A pv = nrt E K = 3 2 k BT = 3 2 R N A T Sub-topic 4. Oscillations T = f Sub-topic 4.2 Travelling waves c = fλ Sub-topic 4.3 Wave characteristics I A 2 Sub-topic 4.4 Wave behaviour n n 2 = sin θ 2 sin θ = v 2 v s = λd d Constructive interference: path difference = nλ Destructive interference: path difference = (n + 2 )λ I x 2 I = I 0 cos 2 θ Sub-topic 5. Electric fields I = q t F = k q q 2 r 2 k = 4πε 0 V = W q E = F q I = navq Sub-topic 5.3 Electric cells ε = I(R + r) Sub-topic 5.2 Heating effect of electric currents Kirchhoff s circuit laws: R = V I ΣV = 0 (loop) ΣI = 0 (junction) P = VI = I 2 R = V2 R R total = R + R 2 + = + + R total R R 2 ρ = RA L Sub-topic 5.4 Magnetic effects of electric currents F = qvb sin θ F = BIL sin θ 6

10 Sub-topic 6. Circular motion v = ωr a = v2 r = 4π2 r T 2 F = mv2 r = mω 2 r Sub-topic 6.2 Newton s law of gravitation F = G Mm r 2 g = F m g = G M r 2 Sub-topic 7. Discrete energy and radioactivity Sub-topic 7.2 Nuclear reactions E = hf λ = hc E E = m c 2 Sub-topic 7.3 The structure of matter Charge Quarks Baryon number 2 3 e u c t 3 3 e d s b 3 All quarks have a strangeness number of 0 except the strange quark that has a strangeness number of Charge Leptons e µ τ 0 υe υ µ υ τ All leptons have a lepton number of and antileptons have a lepton number of Gravitational Weak Electromagnetic Strong Particles experiencing All Quarks, leptons Charged Quarks, gluons Particles mediating Graviton W +, W, Z 0 γ Gluons Sub-topic 8. Energy sources Power = energy time Power = 2 Aρv3 Sub-topic 8.2 Thermal energy transfer P = eσat λ max (metres) = T(kelvin) I = power A total scattered power albedo = total incident power 7

11 Equations AHL Sub-topic 9. Simple harmonic motion Sub-topic 9.2 Single-slit diffraction ω = 2π T a = ω 2 x x = x 0 sin ωt ; x = x 0 cos ωt v = ωx 0 cos ωt ; v = ωx 0 sin ωt v = ±ω (x 02 x 2 ) E K = 2 mω2 (x 2 0 x 2 ) θ = λ b Sub-topic 9.3 Interference nλ = d sin θ Constructive interference: 2dn = (m + ) λ 2 Destructive interference: 2dn = mλ E T = 2 mω2 x 0 2 Pendulum: T = 2π l g Mass spring: T = 2π m k Sub-topic 9.4 Resolution θ =.22 λ b R = λ Δλ = mn Sub-topic 9.5 Doppler effect v Moving source: f = f v ± u s Moving observer: f = f v±u 0 v f f = λ λ v c Sub-topic 0. Describing fields Sub-topic 0.2 Fields at work W = q V e W = m V g V g = GM r V e = kq r g = ΔV g Δr E = ΔV e Δr E P = mv g = GMm r E P = qv e = kq q 2 r F G = G m m 2 F r 2 E = k q q 2 r 2 v esc = 2GM r v orbit = GM r 8

12 Sub-topic. Electromagnetic induction Φ = BA cos θ ε = N Φ Δt ε = Bvl ε = BvlN Sub-topic.2 Power generation and transmission I rms = I 0 2 V rms = V 0 2 R = V 0 I 0 = V rms I rms P max = I 0 V 0 Sub-topic.3 Capacitance C = q V C parallel = C + C 2 + C series = C + C 2 + C = ε A d E = 2 CV2 τ = RC q = q 0 e t τ I = I 0 e t τ V = V 0 e t τ P = 2 I 0V 0 ε p ε s = N p N s = I s I p Sub-topic 2. The interaction of matter with radiation E = hf E max = hf Φ E = 3.6 n ev 2 mvr = nh 2π P(r) = ψ 2 ΔV ΔxΔp h 4π ΔEΔt h 4π Sub-topic 2.2 Nuclear physics R = R 0 A /3 N = N 0 e λt A = λn 0 e λt sin θ λ D 9

13 Equations Options Sub-topic A. The beginnings of relativity x = x vt u = u v Sub-topic A.3 Spacetime diagrams θ = tan v c Sub-topic A.2 Lorentz transformations γ = v2 c 2 x = γ(x vt) ; x = γ( x v t) t = γ(t vx c 2) ; t = γ( t v x u = u v uv c 2 c 2 ) t = γ t 0 Sub-topic A.4 Relativistic mechanics (HL only) E = γm 0 c 2 E 0 = m 0 c 2 E K = (γ )m 0 c 2 p = γm 0 v E 2 = p 2 c 2 + m 2 0 c 4 qv = E K L = L 0 γ (ct ) 2 (x ) 2 = (ct) 2 (x) 2 Sub-topic A.5 General relativity (HL only) f f = g h c 2 R s = 2GM c 2 t = t 0 R s r 0

14 Sub-topic B. Rigid bodies and rotational dynamics Γ = Fr sin θ I = mr 2 Γ = Iα ω = 2πf ω f = ω i + αt ω f 2 = ω i 2 + 2αθ θ = ω i t + 2 αt2 L = Iω E Krot = 2 Iω2 Sub-topic B.3 Fluids and fluid dynamics (HL only) B = ρ f V f g P = P 0 + ρ f gd Av = constant 2 ρv2 + ρgz + p = constant F D = 6πηrv R = vrρ η Sub-topic B.2 Thermodynamics Q = U + W U = 3 2 nrt S = Q T pv 5 3 = constant (for monatomic gases) W = p V useful work done η = energy input η Carnot = T cold T hot Sub-topic B.4 Forced vibrations and resonance (HL only) energy stored Q = 2π energy dissipated per cycle energy stored Q = 2π resonant frequency power loss Sub-topic C. Introduction to imaging f = v + u P = f m = h i h o = v u M = θ i θ o M near point = D f + ; M in inity = D f Sub-topic C.2 Imaging instrumentation M = f o f e Sub-topic C.3 Fibre optics n = sin c attenuation = 0 log I I 0 Sub-topic C.4 Medical imaging (HL only) L I = 0 log I I 0 I = I 0 e μx μx = ln2 2 Z = ρc

15 Sub-topic D. Stellar quantities d (parsec) = p (arc second) L = σat 4 b = L 4πd 2 Sub-topic D.3 Cosmology z = λ λ 0 v c z = R R 0 v = H 0 d Sub-topic D.2 Stellar characteristics and stellar evolution λ max T = m K L M 3.5 Sub-topic D.5 Further cosmology (HL only) v = 4πGρ 3 r ρ c = 3H2 8πG T H 0 2