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## 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.