Physics Data Booklet - St Leonard's College

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Physics data bookletFirst assessment 2016

Diploma ProgrammePhysics data bookletPublished June 2014Revised edition published January 2016Published on behalf of the International Baccalaureate Organization, a not-for-profiteducational foundation of 15 Route des Morillons, 1218 Le Grand-Saconnex, Geneva,Switzerland by theInternational Baccalaureate Organization (UK) LtdPeterson House, Malthouse Avenue, Cardiff GateCardiff, Wales CF23 8GLUnited KingdomWebsite: www.ibo.org International Baccalaureate Organization 2014The International Baccalaureate Organization (known as the IB) offers four high-qualityand challenging educational programmes for a worldwide community of schools, aimingto create a better, more peaceful world. This publication is one of a range of materialsproduced to support these programmes.The IB may use a variety of sources in its work and checks information to verify accuracyand authenticity, particularly when using community-based knowledge sources such asWikipedia. The IB respects the principles of intellectual property and makes strenuousefforts to identify and obtain permission before publication from rights holders of allcopyright material used. The IB is grateful for permissions received for material usedin this publication and will be pleased to correct any errors or omissions at the earliestopportunity.All rights reserved. No part of this publication may be reproduced, stored in a retrievalsystem, or transmitted, in any form or by any means, without the prior written permissionof the IB, or as expressly permitted by law or by the IB’s own rules and policy. Seehttp://www.ibo.org/copyright.IB merchandise and publications can be purchased through the IB store athttp://store.ibo.org.Email: sales@ibo.orgInternational Baccalaureate, Baccalauréat International and Bachillerato Internacionalare registered trademarks of the International Baccalaureate Organization.4082

ContentsFundamental constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Metric (SI) multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Unit conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Electrical circuit symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Equations—Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Equations—AHL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Equations—Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Physics data booklet

Physics data booklet

Fundamental constantsQuantitySymbolApproximate valueAcceleration of free fall(Earth’s surface)g9.81m s 2Gravitational constantG6.67 10 11 Nm2 kg 2Avogadro’s constantNA6.02 1023 mol 1Gas constantR8.31JK 1 mol 1Boltzmann’s constantkB1.38 10 23 JK 1Stefan–Boltzmann constantσ5.67 10 8 W m 2 K 4Coulomb constantk8.99 109 Nm2 C 2Permittivity of free spaceε08.85 10 12 C2 N 1 m 2Permeability of free spaceµ04π 10 7 T m A 1Speed of light in vacuumc3.00 108 m s 1Planck’s constanth6.63 10 34 JsElementary chargee1.60 10 19 CElectron rest massme9.110 10 31 kg 0.000549 u 0.511MeV c 2Proton rest massmp1.673 10 27 kg 1.007276 u 938 MeV c 2Neutron rest massmn1.675 10 27 kg 1.008665 u 940 MeV c 2Unified atomic mass unitu1.661 10 27 kg 931.5 MeV c 2Solar constantS1.36 103 W m 2Fermi radiusR01.20 10 15 mPhysics data booklet1

Metric (SI) 0 –1centic10 –2millim10 –3microµ10 –6nanon10 –9picop10 –12femtof10 –15Unit conversions1 radian (rad) 180 πTemperature (K) temperature ( C) 2731 light year (ly) 9.46 1015 m1 parsec (pc) 3.26 ly1 astronomical unit (AU) 1.50 1011 m1 kilowatt-hour (kWh) 3.60 106 Jhc 1.99 10 25 Jm 1.24 10 6 eV m2Physics data booklet

Electrical circuit symbolscellbatteryac supplyswitchvoltmeterVammeterresistorvariable resistorlamppotentiometerlight-dependentresistor (LDR)thermistortransformerheating elementdiodecapacitorPhysics data bookletA3

Equations—CoreNote: All equations relate to the magnitude of the quantities only. Vector notation hasnot been used.Sub-topic 1.2 – Uncertainties and errorsIf: y a bthen: y a bIf: y then:AAVabc yy a b c abc yyθ n aaA V A sin θSub-topic 2.1 – Motion1 2at2v 2 u 2 2ass Sub-topic 2.2 – ForcesF mav u ats ut Ff µsRFf µdR(v u ) t2Sub-topic 2.3 – Work, energyand powerW Fs cos θSub-topic 2.4 – Momentumand impulsep mvEK 1mv 22F Ep 1k x22EK Ep mg hpower Fvefficiency 4AHAH A cos θIf: y a nthen:Sub-topic 1.3 – Vectors and scalars p tp22mimpulse F t puseful work outtotal work inuseful power outtotal power inPhysics data booklet

Sub-topic 3.1 – Thermal conceptsQ mc TSub-topic 3.2 – Modelling a gasp FAn NNAQ mLpV nRT EKSub-topic 4.1 – OscillationsT 1fSub-topic 4.2 – Travelling wavesc fλSub-topic 4.3 – Wave characteristicsI A2I x 2I I 0 cos2 θPhysics data booklet33 R kBTT22 NASub-topic 4.4 – Wave behaviourn1 sin θ 2 v 2 n2 sin θ1 v1s λDdConstructive interference:path difference nλDestructive interference: 1 path difference n λ2 5

Sub-topic 5.2 – Heating effect ofelectric currentsSub-topic 5.1 – Electric fieldsI q tq1q2r2F kk 14 ε 0Kirchhoff’s circuit laws:ΣV 0 (loop)ΣI 0 (junction)R VIV Wq P V I I 2R E FqRtotal R1 R2 .I nAvq1Rtotalρ Sub-topic 5.3 – Electric cellsε I (R r ) V2R11 .R1 R2RALSub-topic 5.4 – Magnetic effects ofelectric currentsF qvB sin θF B IL sin θSub-topic 6.2 – Newton’s law ofgravitationSub-topic 6.1 – Circular motionv ωr6F Ga v 2 4 π2 r 2rTg F mv 2 mω 2 rrg GMmr2FmMr2Physics data booklet

Sub-topic 7.1 – Discrete energy andradioactivityE hfλ Sub-topic 7.2 – Nuclear reactions E mc 2hcESub-topic 7.3 – The structure of matterCharge2e31 τ0νeνµντAll leptons have a lepton numberof 1 and antileptons have a leptonnumber of –1All quarks have a strangeness numberof 0 except the strange quark that hasa strangeness number of argedQuarks,gluonsGravitonW , W , Z0γGluonsSub-topic 8.2 – Thermal energytransferSub-topic 8.1 – Energy sourcespower energytimeP eσ AT 4power 1Aρv 32λmax (metres) I powerAalbedo Physics data booklet2.90 10 3T (kelvin)total scattered powertotal incident power7

Equations—AHLSub-topic 9.1 – Simple harmonicmotionω 2πTSub-topic 9.2 – Single-slit diffractionθ λba ω 2 xSub-topic 9.3 – Interferencex x0 sin ω t ; x x0 cos ω tnλ d sin θv ω x0 cos ω t ; v ω x0 sin ω t1 Constructive interference: 2dn m λ2 v ω ( x0 2 x 2 )Destructive interference: 2dn mλEK 1mω 2 ( x0 2 x 2 )2ET 1mω 2 x0 22pendulum: T 2πlgmass-spring:T 2πmkSub-topic 9.4 – Resolutionθ 1.22R λbλ mN λSub-topic 9.5 – Doppler effect v Moving source: f ′ f v us v uo Moving observer: f ′ f v ff8 λλ vcPhysics data booklet

Sub-topic 10.1 – Describing fieldsW q VeW m VgSub-topic 10.2 – Fields at workGMrVe Vg rE Vg g Ep mVg Fg Physics data bookletGMmr2v esc 2GMrv orbit GMrkQr Ve rGMmkQq Ep qV errFe kQqr29

Sub-topic 11.1 – ElectromagneticinductionΦ BA cos θ Φ tε Nε Bv lSub-topic 11.3 – CapacitanceC qVCparallel C1 C2 .1Cseriesε Bv l N11 .C1 C2 ASub-topic 11.2 – Power generation andC εtransmissiondI0Irms E 2V0Vrms 1CV 22τ RC2V0VR rmsI 0 Irmsq q0 ePmax I 0V0I I0e1I 0V02V V0 eP tτtτ tτε p Np I s ε s Ns I pSub-topic 12.1 – The interaction ofmatter with radiationSub-topic 12.2 – Nuclear physics1E hfR R0 A 3Emax h f ΦN N0 e λ tE 13.6eVn2mvr nh2πA λ N0 e λ tsin θ λD2P (r ) ψ V x p h4π E t h4π10Physics data booklet

Equations—OptionsSub-topic A.1 – The beginnings ofrelativityx′ x v tSub-topic A.2 – Lorentztransformations1γ 1 u′ u vSub-topic A.3 – Spacetime diagrams v θ tan 1 c v2c2x′ γ ( x vt ); x′ γ ( x v t )vx ; t ′ γc 2 t′ γ t v x t c 2 u vuv1 2cu′ t γ t0L L0γ(ct ′)2 ( x′)2 (ct )2 ( x )2Sub-topic A.4 – Relativistic mechanics(HL only)E γ m0 c 2E0 m0 c 2EK (γ 1) m0 c 2p γ m0vE 2 p 2c 2 m0 2c 4Sub-topic A.5 – General relativity(HL only) f g hc2Rs 2GMc2f t t01 RsrqV EKPhysics data booklet11

Sub-topic B.1 – Rigid bodiesand rotational dynamicsΓ Fr sin θI mr 2Γ Iαω 2πfωf ωi α tω f2 ω 2i 2αθ1θ ωi t α t 22L IωEKrot 1 2Iω2Sub-topic B.3 – Fluids and fluiddynamics (HL only)Sub-topic B.2 – ThermodynamicsQ U W3nRT2U S QT5pV 3 constant (for monatomic gases)W p Vη useful work doneenergy inputηCarnot 1 TcoldThotSub-topic B.4 – Forced vibrations andresonance (HL only)energy storedenergy dissipated per cycleB ρ fVf gQ 2πP P0 ρ f gdQ 2π resonant frequency energy storedpower lossAv constant1 2ρv ρ gz p constant2FD 6πη rvR 12vr ρηPhysics data booklet

Sub-topic C.1 – Introduction toimaging1f 1 1 v uSub-topic C.2 – ImaginginstrumentationfofeM 1P Sub-topic C.3 – Fibre opticsfn hvm i houM attenuation 10 logθiθoMnear point 1sin cDf 1; Minfinity Sub-topic C.4 – Medical imaging(HL only)DfII0LI 10 logI1I0I I0e µ xµ x 1 In22Z ρcSub-topic D.1 – Stellar quantitiesd (parsec) 1p (arc-second)L σ AT 4b Sub-topic D.2 – Stellar characteristicsand stellar evolutionλmaxT 2.9 10 3 mKL M 3 .5L4πd 2Sub-topic D.3 – CosmologySub-topic D.5 – Further cosmology(HL only)z λ v λ0 cv 4πG ρr3z R 1R0ρc 3H 28πGv H0 dT 1H0Physics data booklet13

Fundamental constants Quantity Symbol Approximate value Acceleration of free fall (Earth’s surface) g 98.m1 s 2 Gravitational constant G 66. 71 0 11Nm22kg Avogadro’s constant N A 60. 21 023 mol 1 Gas constant R 83.J1 Km 11 ol Boltzmann’s constant k B 13. 81 0 23 JK 1 Stefan–Boltzmann constant σ

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