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hw2_solution - Physics 3C Webassign Homework 2 Solutions a...

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Physics 3C Webassign Homework 2 Solutions:
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a. v_y = dy/dt, so v_y(x,t) = (0.100 m)(5 π )cos( π x/8 + 5 π t) v_y(1.7,0.27) = (0.1m)(5 π )cos(1.7 π /8 + 5 π (0.270) ) = 0.306 a_y = dv_y/dt = -(0.1m)(5 π ) 2 sin(1.7 π /8 + 5 π (0.270) ) = 24.2 b. λ = 2 π /k = 2 π /( π /8) = 16m T = 1/f and f = ω /2 π so T = 2 π / ω = 2 π /(5 π ) = 2/5 s = 0.4s v = f λ = π /T = 16m/0.4s = 40 m/s v = 8(4.25m)/(0.865 s) = 39.3 m/s v = [T/ μ ] 1/2 T = μ v 2 = (.18kg/4.25m) (39.3 m/s) 2 = 65.4N v 1 = [T 1 / μ ] 1/2 v 2 = [T 2 / μ ] 1/2 (v 1 / v 2 ) 2 = [T 1 /T 2 ] => (25/33) 2 = [6.2N/T 2 ] => T 2 = 6.2N(33/25) 2 = 10.8 N
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Start by assuming that the speed of sound is infinite. In this case the distance to the lightning stroke is just given by the time it takes to hear the sound after seeing it: D = vt = 343m/s(14.5s) = 4,973.5m = 4.97km. Check to see if the time it takes light to travel this distance is small compared to 14.5 seconds: T = D/v = 4973m/(3.e8m/s) = 0.000016 s << 14.5 s, so our approximation is fine.
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