Question

Consider a 40-foot chain that weighs 4 pounds per foot hanging from a winch 40 feet...

Consider a 40-foot chain that weighs 4 pounds per foot hanging from a winch 40 feet above ground level. Find the work done by the winch in winding up the entire chain.
Math   Calculus   
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Answer #1

Answer: The force required to lift an object is equal to the weight of the object. If the

bottom of the chain is y feet above the ground, then the length of the chain hanging

from the winch is (40 − y). Therefore, the weight of the chain is 4(40 − y) = 160− 4y

In other words, the force that the winch needs to apply to the chain when the end of the

chain is y feet above the ground is

F(y) = 160− 4y.

Therefore, winding up the chain requires

foot-pounds of work.

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