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?

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Answer 1 · 2014-10-29T18:25:58

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# ft#cdot#lb .

Since the cable is #100# ft long,

#W=int_0^{100}2xdx=[x^2]_0^{100}=10000# ft#cdot#lb

I hope that this was helpful.