Question

A 30-m-long chain hangs vertically from a cylinder attached to a winch. Assume there is no friction in the system and the chain has a density of 5 kg/m.

How much work is required to wind the entire chain onto the cylinder using the winch?

Solution

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Answered 1 year ago
Answered 1 year ago
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a.

Use formula

abF(y)dy\int_{a}^{b}F(y)dy

with 0y300 \leq y \leq 30 and

F(y)=(30y)gpF(y)=(30-y)gp

where 30-y is length of chain that has to be lifted

W1=030pg(30y)dy=pg450=22050JW_1=\int_{0}^{30}pg(30-y)\,dy=pg\cdot 450=22050 \,J

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