One end of a nylon rope is tied to a stationary support at the top of a vertical

Question

One end of a nylon rope is tied to a stationary support at the top of a vertical mine shaft of depth 75.0 m . The rope is stretched taut by a box of mineral samples with mass 23.0 kg attached at the lower end. The mass of the rope is 1.80 kg . The geologist at the bottom of the mine signals to his colleague at the top by jerking the rope sideways. (Do not neglect the weight of the rope.)

A What is the wave speed at the bottom of the rope?

B What is the wave speed at the middle of the rope?

C What is the wave speed at the top of the rope?

Explanation / Answer

here,

length of rod , l = 75 m

mass of box , M = 23 kg

mass of rope , m = 1.8 kg

A)

for the bottom of rope,

u = m/L = 0.024kg/m

T = M * g

T = 225.4 N

speed of wave , v = sqrt( T/u)

v = sqrt(225.4/0.024)

v = 96.91 m/s

(b)

for the middle of rope,

u = (m/2)/(L/2) = 0.024kg/m

T = (M + m/2) * g

T = 234.22 N

speed of wave , v = sqrt( T/u)

v = sqrt(234.22/0.024)

v = 98.79 m/s

(c)

for the middle of rope,

u = (m)/(L) = 0.024 kg/m

T = (M + m) * g

T = 243.04 N

speed of wave , v = sqrt( T/u)

v = sqrt(243.04/0.024)

v = 100.63 m/s

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