Exercise 15.18: Weighty Rope One end of a nylon rope is tied to a stationary sup

Question

Exercise 15.18: Weighty Rope

One end of a nylon rope is tied to a stationary support at the top of a vertical mine shaft of depth 83.0 m . The rope is stretched taut by a box of mineral samples with mass 16.0 kg attached at the lower end. The mass of the rope is 1.50 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.)

Part A

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

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Part B

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

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Part C

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

Exercise 15.18: Weighty Rope

One end of a nylon rope is tied to a stationary support at the top of a vertical mine shaft of depth 83.0 m . The rope is stretched taut by a box of mineral samples with mass 16.0 kg attached at the lower end. The mass of the rope is 1.50 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.)

Part A

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

v = m/s

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Part B

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

v =   m/s

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Part C

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

v =   m/s

Explanation / Answer

Part A) Use equation,

v = sqrt(m1gh/m2) = sqrt(16*9.8*80/1.5) = 91.45 m/s

Part B) Use equation,

v = sqrt[(m1+m2/2)gh)/m2) = sqrt[(16+1.5/2)*9.8*80)/1.5)  = 93.57 m/s

Part A) Use equation,

v = sqrt[(m1+m2)gh)/m2) = sqrt[(16+1.5)*9.8*80)/1.5)  = 95.63 m/s

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