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QUESTION

# If a 200 pound cable is 100 feet long and hangs vertically from the top of a tall building, how much work is required to lift the cable to the top of the building?

Since the density of the cable is

{200}/{100}=2 lb/ft,

the small piece of the cable of length dx pulls down with the force

2dx lb.

Let x be the distance of the piece of the cable from the top of the building. To lift this piece up to the top, it requires the force of

dW=2dx cdot x=2xdx ftcdotlb .

Since the cable is 100 ft long,

W=int_0^{100}2xdx=[x^2]_0^{100}=10000 ftcdotlb

I hope that this was helpful.