Exam-F-equation-spring2009-phys172

Exam-F-equation-spring2009-phys172 - dp =F dt p = γ mv γ=...

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Unformatted text preview: dp =F dt p = γ mv γ= 1 v 1− c 2 v= p/m p 1+ mc 2 Fspring = k S s Fgrav = G Mm r 2 U spring = U grav k kS x 2 ω= S ω = 2π f = 2π / T 2 m Mm =G ; Near surface of Earth: Fgrav = mg U grav = mgh r K total = K trans + K tot + K vib K total 2 ptotal 1 2 (non-relativistic) = M total vcm = 2 2 M total ptotal = mtotal vcm (non-relativistic) L2 1 rot = Iω 2 2I 2 dW = F • dr K rot = r= I = mr⊥2 , for point mass distance r⊥ from axis m1r1 + m2 r2 + m3 r3 + ... ; M = m1 + m2 + m3 + ... M L = r × p = Iω τ = r×F E 2 − ( pc) 2 = (mc 2 )2 S = k ln Ω P (∆E ) = e − ∆E k BT Erest = mc 2 Ω= (q + N − 1)! q !( N − 1)! V2 V1 E = pc for massless photon 1 dS = T dEint P = nkT PV = nmoles RT R = kN A W =− Pdv ∆Ethermal = mC ∆T K trans = CV = 1 k × (deg rees _ of _ freedom) 2 vrms ≡ v 2 CP = CV + k 1 3 M v 2 = k BT 2 2 Efficiency=1 − TL / TH G = 6.7 × 10−11 N·m2/kg2 23 -1 v = 0.92vrms , for an ideal gas NA = 6×10 mol g = 9.8 N/kg c = 3 × 108 m/s k B = 1.38 × 10−23 J / K 1 atomic mass unit = 1.66 x 10−27 kg e = 1.6 x 10 −19 Coulombs ...
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