A 3.8-m-long rope of mass 1.2 kg hangs from a ceiling.
part A:What is the wave speed in the rope at the bottom end?
Part B:What is the tension in the rope at the top end, where it is attached to the ceiling?
Part C:What is the wave speed in the rope at the top end?
Part D:It can be shown that the average wave speed in the rope is 1/2 sqrt(gL), where L is the length of the rope. Use the average wave speed to calculate the time required for a pulse produced at the bottom of the rope to travel to the top.
Tension in the rope at a distance 'x' from the bottom end, Tx = μxg = Mxg/L
A) vbottom = (T0/μ)1/2 = 0
B) Ttop = MLg/L = Mg = 1.2 * 9.8 = 11.8 m/s
C) vtop = (TL/μ)1/2 = (gL)1/2 = (9.8 * 3.8)1/2 = 37.2 m/s
D) Time required, t = L/vavg = 3.8 / [(9.8 * 3.8)1/2 / 2] = 1.25 s
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