Help me ! One end of a nylon rope is tied to a stationary support at the top of

Question

Help me !

One end of a nylon rope is tied to a stationary support at the top of a vertical mine shaft of depth 83.0m. The rope is stretched taut by a box of mineral samples with mass 23.0kg attached at the lower end. The mass of the rope is 1.50kg. 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.) What is the wave speed at the bottom of the rope? What is the wave speed at the middle of the rope? What is the wave speed at the top of the rope?

Explanation / Answer

Apply (v = sqrt{T/mu})

At the bottom, the tension is only from the mass on the end

v = sqrt[(23)(9.8)/(1.5/83)]

v = 111.7 m/s

In the middle of the rope, we have half of the rope weight adding to the tension

v = sqrt[(23 + .75)(9.8)/(1.5/83)]

v = 113.5 m/s

At the top of the rope, all of the mass of the rop contributes to the tension

v = sqrt[(23 + 1.5)(9.8)/(1.5/83)]

v = 115.3 m/s

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