Physics 123 Equations Fall 2011 Semester. To know by heart (not an exhaustive list, I m sure)

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1 Physics 3 Equations Fall Seester To know by heart (not an exhaustive list, I sure) Fluids pressure: P F/A density: ρ /V specific gravity: SG ρ/ρ H stationary fluids: P P + ρgh (pressures at sae depths are sae) Archiedes Principle: buoyant force: ρ fluid V object g ( weight of the displaced fluid ) oving fluids, at positions and along path: VFR A v A v (Eqn of continuity, fro ass conservation, garden hose ) P + ½ρv + ρgy P + ½ρv + ρgy (ernoulli s aw, fro energy conservation) PV nrt Nk T Equipartition theore: each d.o.f. has energy k T/, for each olecule 3 transl. KEave vrs kt (can use to solve for v rs ) How to find pressure exerted by balls (atos) fro change in oentu Q cδ T; Q Wby gas PdV area under P-V curve First aw: ΔE int Q added + W on ; Q added ΔE int + W by γ C P /C V Monatoic Diatoic (~ 3K) Solids #dof E int 3/ nrt 5/ nrt 6/ nrt ΔE int 3/ nrδt 5/ nrδt 6/ nrδt C V 3/ R 5/ R 6/ R C P 5/ R 7/ R sae as C V γ 5/3 7/5 n/a Note: for onatoic, n #oles of olecules #oles of atos. For diatoic, n #oles of olecules #oles of atos. For solids, n #oles of atos. Adiabatic: P V γ γ P V How to find W, ΔE int, and Q, for isobaric, isovoluetric, isotheral, adiabatic, and cycles How to find when W, ΔE int, and Q are positive or negative for any changes Engine: Q h W + Q c ; e W /Q h (Q h Q c )/Q h Refrigerator: COP R Q c / W Heat pup: COP HP Q h / W Carnot: e ax (T h T c )/T h ; COP R,ax T c /(T h T c ); COP HP,ax T h /(T h T c ) dq Δ S T How to find ΔS for isobaric, isovoluetric, isotheral, adiabatic, free expansion, and cycles How to find expected rando fluctuations for various situations wave paraeters: x, t, A, λ, f, v, k, ω, φ i(kx ωt + φ) f Acos(kx ωt + φ) Ae speed of wave: v λ f k π/λ; ω π/t v phase ω/k

2 v group (dω/dk) kave Coplex nubers: converting polar rectangular How to add sinusoidal waves together I P/A + to d to I; +3 to d to I d: reference W Mach# v/v sound ΔP λ (constructive); ΔP ( + ½)λ (destructive) How to find standing wave resonances Result: o-o/c-c: fn nf ; n,,3,... o-c: fn nf ; n,3,5,... f fundaental frequency, v/(largest λ) f beat f f Optics aw of reflection: θ incident θ reflected aw of refraction (Snell s law): n sinθ n sinθ (θ easured fro the perpendicular) n index of refraction, speed of light c/n Condition for TIR: set θ 9 (n higher index) λ aterial λ vacuu /n Difference between linear and circular polarization Difference between s- and p-polarization Thin lens equation: /f /p + /q Difference between real and virtual iages agnification: M h i /h o (definition) q/p (useful for calculation) Sign conventions for lens/irror equation How to handle ultiple lens/irror probles f/# f/d near point & far point θ/θ How to figure out the angular agnification of a agnifying glass How to figure out the angular size of an ant, planet, or other object for which the sall angle approxiation is valid Telescope: f o /f e slit: dsinθ bright λ; dsinθ dark ( + ½)λ slit: asinθ dark λ grating: dsinθ bright λ How to cobine slit with slit forulas How to derive intensity equation for any nuber of slits When to use Approx. : θ sinθ tanθ y/ What the sinc function is OP P n ΔΟP + phase shifts λ (constructive); ( + ½)λ (destructive) How to write/interpret general 3D wave equation for arbitrary wave direction and arbitrary oscillation direction Relativity v/c; γ γ Δ Δ/γ p γv E γc KE (γ ) c E rest c

3 cons. of oentu & energy To be given on exa These equations should be exactly sae as the ones on the first page of exa as posted on the website, but with soe details issing there. For exaple, on the exa I give the equation l, but I don t say π d n that it is for the ean free path like I do below. There are any such oissions on the exa itself, so be sure to look over the first page prior to taking the exa. Fundaental constants Materials paraeters Conversion factors ( + x) n + nx b± b 4ac x a Surface area of sphere 4π r 3 Volue of sphere ( 43) π r Theral expansion: Δ α ΔT, ΔV V ΔT; 3α 3 v Maxwell-oltzann: f() v 4π v e π kt v ost probable velocity where f(v) is a axiu 8kT vavg v f() v dv π 3kT vrs v f() v dv Mean free path: l π d n Ave tie between collisions: τ l/v avg kaδt Conduction: P AΔT P ; R /k R 4 Radiation: P eσ AT e Otto ; r copression ratio V ax /V in r γ kt kt S k lnw N N! coin flips: # icrostates ; # acrostates N k k!( N k)! P ½ω A v 3

4 v v v r v R r ; T R vstring vrod vsound ; t + v v + v T μ ; μ / Y ρ ; ρ v 343 sound s stress F A Y strain Δ T 93K log I ; I I I ; I - W/ sinθ /Mach# v± vo f f v ± v s ΔxΔk ½ ; ΔxΔp / Δω ½ ; ΔE / πnx πnx f( x) a + a cos + bnsin a f( x) n n n π nx an f( x)cos π nx bn f( x)sin half step: f /f / Optics θ rewster tan - (θ /θ ) n n n r ; t n+ n n+ n f R/ ensaker s eqn: ( n ) (R pos, R neg if convex-convex) f R R n n n n Iage fro surface: + (p pos if object in front, q pos if iage in back, R pos if center of p p R curvature in back) φ πδp/λ Approx. : ΔP dsinθ E E (e iφ + e iφ + ) I ~ E π d slit: I I cos sinθ λ π asinθ slit: I Isinc λ circular aperture: Rayleigh: θ in.resolve.λ/d 4

5 R λ ave /Δλ #slits ragg: dsinθ bright λ f f ± Relativity x γ x ± γ ( ct) frae frae frae ( ct) ± γx + γ( ct) frae frae frae x γ ± γ x ct ± γ γ ct frae frae particles with ass: E ( pc) + ( c ) photons: E pc Copton shift: /p photon /p photon /( electron c) Would be given on a proble if needed (not an exhaustive list) ΔP/(ΔV/V) Otto cycle, what it looks like: adiabatic, C V, adiabatic, C V Diesel cycle, what it looks like: adiabatic, C P, adiabatic, C V γ rc ediesel γ ; r copression ratio V r γ ( rc ) ax /V in ; r c cutoff ratio V iddle /V in Musical intervals Second half-steps Minor third 3 half-steps Major third 4 half-steps Major fourth 5 half-steps Major fifth 7 half-steps Sixth 9 half-steps Minor seventh half-steps Major seventh half-steps Octave half-steps 5

Phys102 First Major-143 Zero Version Coordinator: xyz Sunday, June 28, 2015 Page: 1

Phys102 First Major-143 Zero Version Coordinator: xyz Sunday, June 28, 2015 Page: 1 Coordinator: xyz Sunday, June 28, 2015 Page: 1 Q1. A transverse sinusoidal wave propagating along a stretched string is described by the following equation: y (x,t) = 0.350 sin [1.25x + 99.6t], where x