Question

Bob has a tree house at a height of 20 ft. When he's feeling adventurous he uses a rope to climb the tree house instead of the ladder. If the weight of the rope is 32 lb, then how much work must Bob do to pull the rope up once he has entered the house?

Answer 1

This is an integration problem. As you lift the rope each foot it gets lighter from the 20 foot position being maximum mass to the zero foot position having no mass.

The rope is 32 lbs /20 ft = 1.6 lbs per foot

So each foot you lift the rope, the weight decreases by 1.6 lbs. The integral will be :

integrate 1.6(20-x) dx from 0 to 20

work = 320 ft-lbs of work