Question

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.

Answer 1

Tension in the rope at a distance 'x' from the bottom end, T_x = μxg = Mxg/L

A) v_bottom = (T₀/μ)^1/2 = 0

B) T_top = MLg/L = Mg = 1.2 * 9.8 = 11.8 m/s

C) v_top = (T_L/μ)^1/2 = (gL)^1/2 = (9.8 * 3.8)^1/2 = 37.2 m/s

D) Time required, t = L/v_avg = 3.8 / [(9.8 * 3.8)^1/2 / 2] = 1.25 s

Answer 2

the answer should be 25