1 PHYSICS 2210 Equation Sheet #4 1. x – x0 = v0x + vx 2 t – 0 = !0 + ! 2 t vx = v0x + axt ! = !0 + t x – x0 = v0xt + 12axt2 = 0 + !0t + 12t2 v2x = v20x + 2ax(x – x0) !2 = !20 + 2(- 0) 2. ~Fnet =X~F = m~a = d~p dt ~net =X~= I~= d~L dt ~p = m~v L = I! = mvr sin = rF sin 3. K = 12mv2 = p2 2m K = 12I!2 = L2 2I 4. W = Fs cos = ~F · ~s (constant F) W = (- 0) (constant ) 5. Wnet = Kf -Ki P = dWdt = Fv cos = ~F · ~v P = ! 6. s = rvt = r! at = rxcm = Pmixi Pmi ac = v2 r = !2r T = 2r v g = 9.8 m/s2 7. I = Pmir2i I = Icm +Md2 I = Mr2 (point mass) Icm = 25MR2 (solid sphere) Icm = 23MR2 (hollow sphere) Icm = 12MR2 (disk) Icm = MR2 (hoop) Icm = 1 12ML2 (rod) 8. Ug = mgy W = mg Uel = 12kx2 ~Fel = -k~x 9. = mV p = F? A p = p0 + gh p = F1 A1 = F2 A2 10. FB = V g 1 atm = 1.013 × 105 Pa dV dt = vA v1A1 = v2A2 p1 + 12v21 + gy1 = p2 + 12v22 + gy2 11. Fg = Gm1m2 r2 Ug = -Gm1m2 r MSun = 1.99 × 1030 kg RSun = 6.96 × 108 m MEarth = 5.98 × 1024 kg REarth = 6.37 × 106 m
Equation Sheet #3 2 12. x = Acos(!t + ) v = -!Asin(!t + ) a = -!2Acos(!t + ) = -!2x E = 12mv2x + 12kx2 = 12kA2 T = 1f = 2! ! = s km ! = rgL ! = smgd I 13. v = f= !k ! = 2f k = 2/v = sTµ µ = m/L Pav = 12µ!2A2v I = P 4r2 n = 2L n fn = nv 2L 14. v = sBv = rp v = sRT M M = NAm = 1.4 (air) 15. = (10 dB) logI I0I0 = 10-12 W/m2 fL = v ± vL v vS fS sin= v vS fn = nv 2L (m = 1, 2, 3, . . .) (open) fn = nv 4L (n = 1, 3, 5 . . .) (stopped) v = 344 m/s (air) 16. L = L0(Tf – Ti) V = V0(Tf – Ti) = 317. Solids and liquids: Q = 0 Q = mc(Tf-Ti) Q = ±mL Q = nC(Tf-Ti) C = Mc 18. H = dQ dt = kATH – TC L H = Ae(T4 – T4 s ) = 5.67 × 10-8 W/m2·K4 19. pV = nRT = NkBT n = N NA TK = TC + 273 NA = 6.02 × 1023 1/mol R = 8.31 J/mol·K kB = 1.38 × 10-23 J/K 20. Ktr = 32nRT = 32NkBT vrms = s3kBT m = s3RT M Q = nCV (Tf – Ti) (constant V) 21. CV = 32R (monatomic) CV = 52R (diatomic with rotation) 22. Mean free path: = 1 4p2(N/V )r2 23. g = 9.8 m/s2 c = 3.00 × 108 m/s MSun = 1.99 × 1030 kg RSun = 6.96 × 108 m MEarth = 5.98 × 1024 kg REarth = 6.37 × 106 m 24….