AQA A-Level Physics Data and Formulas, Cheat Sheet of Physics

Download AQA A-Level Physics Data and Formulas and more Cheat Sheet Physics in PDF only on Docsity! A-level Physics data and formulae For use in exams from the June 2017 Series onwards Version 1.5 1 DATA - FUNDAMENTAL CONSTANTS AND VALUES Quantity Symbol Value Units speed of light in vacuo 𝑐 3.00 × 108 m s–1 permeability of free space 𝜇0 4π × 10–7 H m–1 permittivity of free space 𝜀0 8.85 × 10–12 F m–1 magnitude of the charge of electron 𝑒 1.60 × 10–19 C the Planck constant ℎ 6.63 × 10–34 J s gravitational constant 𝐺 6.67 × 10–11 N m2 kg–2 the Avogadro constant 𝑁A 6.02 × 1023 mol–1 molar gas constant 𝑅 8.31 J K–1 mol–1 the Boltzmann constant 𝑘 1.38 × 10–23 J K–1 the Stefan constant σ 5.67 × 10–8 W m–2 K–4 the Wien constant 𝛼 2.90 × 10–3 m K electron rest mass (equivalent to 5.5 × 10–4 u) 𝑚e 9.11 × 10–31 kg electron charge/mass ratio 𝑒 𝑚e 1.76 × 1011 C kg–1 proton rest mass (equivalent to 1.00728 u) 𝑚p 1.67(3) × 10–27 kg proton charge/mass ratio 𝑒 𝑚p 9.58 × 107 C kg–1 neutron rest mass (equivalent to 1.00867 u) 𝑚n 1.67(5) × 10–27 kg gravitational field strength 𝑔 9.81 N kg–1 acceleration due to gravity 𝑔 9.81 m s–2 atomic mass unit (1u is equivalent to 931.5 MeV) u 1.661 × 10–27 kg ALGEBRAIC EQUATION GEOMETRICAL EQUATIONS quadratic equation a acbbx 2 42 −±−= arc length = r 𝜃 circumference of circle = 2πr ASTRONOMICAL DATA area of circle = πr2 Body Mass/kg Mean radius/m curved surface area of cylinder = 2πrh Sun 1.99 × 1030 6.96 × 108 area of sphere = 4πr2 Earth 5.97 × 1024 6.37 × 106 volume of sphere = 3 4 πr3 2 Version 1.5 Particle Physics Class Name Symbol Rest energy/MeV photon photon 𝛾 0 lepton neutrino v e 0 v µ 0 electron e ± 0.510999 muon µ ± 105.659 mesons π meson π ± 139.576 π0 134.972 K meson K ± 493.821 K0 497.762 baryons proton p 938.257 neutron n 939.551 Properties of quarks antiquarks have opposite signs Type Charge Baryon number Strangeness u + 3 2 e + 3 1 0 d − 3 1 e + 3 1 0 s − 3 1 e + 3 1 − 1 Properties of Leptons Lepton number Particles: e−, νe ; µ−, νµ + 1 Antiparticles: e+, νe, µ+, νµ − 1 Photons and energy levels photon energy 𝐸 = ℎ𝑓 = ℎ𝑐 𝜆 photoelectricity ℎ𝑓 = ϕ + 𝐸k (max) energy levels ℎ𝑓 = 𝐸1 – 𝐸2 de Broglie wavelength 𝜆 = ℎ 𝑝 = ℎ 𝑚𝑚 Waves wave speed 𝑐 = 𝑓𝜆 period 𝑓 = 1 𝑇 first harmonic 𝑓 = 1 2𝑙 � 𝑇 𝜇 fringe spacing 𝑤 = 𝜆𝜆 𝑠 diffraction grating 𝑑 sin 𝜃 = 𝑛𝜆 refractive index of a substance s, 𝑛 = 𝑐 𝑐s for two different substances of refractive indices n1 and n2, law of refraction 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2 critical angle sin 𝜃c = 𝑛2 𝑛1 for 𝑛1 > 𝑛2 Mechanics moments moment = 𝐹𝑑 velocity and acceleration 𝑚 = ∆𝑠 ∆𝑡 𝑎 = ∆𝑚 ∆𝑡 equations of motion 𝑚 = 𝑢 + 𝑎𝑡 𝑠 = � 𝑢 + 𝑚 2 � 𝑡 𝑚2 = 𝑢2 + 2𝑎𝑠 𝑠 = 𝑢𝑡 + 𝑎𝑡2 2 force 𝐹 = 𝑚𝑎 force 𝐹 = ∆(𝑚𝑚) ∆𝑡 impulse 𝐹 Δ𝑡 = Δ(𝑚𝑚) work, energy and power 𝑊 = 𝐹 𝑠 cos𝜃 𝐸k = 1 2 𝑚 𝑚2 Δ𝐸p = 𝑚𝑔Δℎ 𝑃 = ∆𝑊 ∆𝑡 , 𝑃 = 𝐹𝑚 𝑒𝑓𝑓𝑒𝑐𝑒𝑒𝑛𝑐𝑒 = 𝑢𝑠𝑒𝑓𝑢𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑝 𝑒𝑛𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑝 Materials density 𝜌 = 𝑚 𝑉 Hooke’s law 𝐹 = 𝑘 Δ𝐿 Young modulus = 𝑡𝑡𝑛𝑡𝑡𝑡𝑡 𝑡𝑡𝑠𝑡𝑡𝑡 𝑡𝑡𝑛𝑡𝑡𝑡𝑡 𝑡𝑡𝑠𝑠𝑡𝑛 tensile stress = 𝐹 𝐴 tensile strain = ∆𝐿 𝐿 energy stored 𝐸 = 1 2 𝐹Δ𝐿 AQA A-LEVEL PHYSICS DATA AND FORMULAE Version 1.5 5 Engineering physics moment of inertia 𝐼 = Σ𝑚𝑝2 angular kinetic energy 𝐸𝑘 = 1 2 𝐼𝜔2 equations of angular motion 𝜔2 = 𝜔1 + 𝛼 𝑡 𝜔2 2 = 𝜔12 + 2𝛼𝜃 𝜃 = 𝜔1𝑡 + 𝛼𝑡2 2 𝜃 = (𝜔1 + 𝜔2) 𝑡 2 torque 𝑇 = 𝐼 𝛼 𝑇 = 𝐹 𝑝 angular momentum 𝑎𝑛𝑔𝑢𝑙𝑎𝑝 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 = 𝐼𝜔 angular impulse 𝑇Δ𝑡 = Δ(𝐼𝜔) work done 𝑊 = 𝑇𝜃 power 𝑃 = 𝑇𝜔 thermodynamics 𝑄 = Δ𝑈 + 𝑊 𝑊 = 𝑝Δ𝑉 adiabatic change 𝑝𝑉𝛾 = constant isothermal change 𝑝𝑉 = constant heat engines efficiency = 𝑊 𝑄H = 𝑄H − 𝑄C 𝑄H maximum theoretical efficiency = 𝑇H − 𝑇C 𝑇H work done per cycle = area of loop input power = calorific value × fuel flow rate indicated power = (𝑎𝑝𝑒𝑎 𝑜𝑓 𝑝 − 𝑉 𝑙𝑜𝑜𝑝) × (𝑛𝑢𝑚𝑠𝑒𝑝 𝑜𝑓 𝑐𝑒𝑐𝑙𝑒𝑠 𝑝𝑒𝑝 𝑠𝑒𝑐𝑜𝑛𝑑) × (𝑛𝑢𝑚𝑠𝑒𝑝 𝑜𝑓 𝑐𝑒𝑙𝑒𝑛𝑑𝑒𝑝𝑠) output or brake power 𝑃 = 𝑇𝜔 friction power = 𝑒𝑛𝑑𝑒𝑐𝑎𝑡𝑒𝑑 𝑝𝑜𝑤𝑒𝑝 – 𝑠𝑝𝑎𝑘𝑒 𝑝𝑜𝑤𝑒𝑝 heat pumps and refrigerators refrigerator: 𝐶𝐶𝑃ref = 𝑄C 𝑊 = 𝑄C 𝑄H− 𝑄C heat pump: 𝐶𝐶𝑃hp = 𝑄H 𝑊 = 𝑄H 𝑄H− 𝑄C Turning points in physics electrons in fields 𝐹 = 𝑒𝑉 𝑑 𝐹 = 𝐵𝑒𝑚 𝑝 = 𝑚𝑚 𝐵𝑒 ½ 𝑚𝑚2 = 𝑒𝑉 Millikan’s experiment 𝑄𝑉 𝑑 = 𝑚𝑔 𝐹 = 6𝜋𝜋𝑝𝑚 Maxwell’s formula 𝑐 = 1 �𝜇0𝜀0 𝜆 = ℎ 𝑝 = ℎ √2𝑚𝑒𝑉 special relativity 𝑡 = 𝑡0 �1− 𝑚2 𝑐2 𝑙 = 𝑙0 �1− 𝑚2 𝑐2 𝐸 = 𝑚 𝑐2 = 𝑚0𝑐2 �1− 𝑚2 𝑐2 Electronics resonant frequency 𝑓0 = 1 2𝜋 √𝐿𝐶 Q-factor 𝑄 = 𝑓0 𝑓B operational amplifiers: open loop 𝑉out = 𝑅OL(𝑉+ − 𝑉−) inverting amplifier 𝑉out 𝑉in = − 𝑅f 𝑅in non-inverting amplifier 𝑉out 𝑉in = 1 + 𝑅f 𝑅l summing amplifier 𝑉out = −𝑅f � 𝑉1 𝑅1 + 𝑉2 𝑅2 + 𝑉3 𝑅3 + ⋯� difference amplifier 𝑉out = (𝑉+ − 𝑉−) 𝑅f 𝑅l Bandwidth requirement: for AM 𝑠𝑎𝑛𝑑𝑤𝑒𝑑𝑡ℎ = 2𝑓M for FM 𝑠𝑎𝑛𝑑𝑤𝑒𝑑𝑡ℎ = 2(∆𝑓 + 𝑓M) 6 Version 1.5 AQA A-LEVEL PHYSICS DATA AND FORMULAE Version 1.5 7