A heavy rope, 50 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 120 ft high. How much work is done in pulling the rope to the tope of the building? How much work is done in pulling half the rope to the top of the building? (W= Fd)
3 Answers

W = Fd when the force is constant, but it this case, it’s changing.
In our case, we go with an integral, W = ∫F(x) dx from 0 to 50.
F(x) = 0.5x
W = 0.5∫x dx = 0.25x^2 = (0.25)(50^2) = 2500/4 = 625ft*lbs
Work done to pull half the rope up the building would be the same integral, except evaluated from 0 to 25. That is 156.25 ft*lbs
Source(s): I hope you can do calculus, because this is the only way I know how to do this problem. 
W = Fd when the force is constant, but it this case, it’s changing.
In our case, we go with an integral, W = ∫F(x) dx from 0 to 50.
F(x) = 0.5x
W = 0.5∫x dx = 0.25x^2 = (0.25)(50^2) = 2500/4 = 625ft*lbs
Work done to pull half the rope up the building would be the same integral, except evaluated from 25 to 50. That is 468.75 ft*lbs or 1875/4 ft*lbs

50 Ft Rope
Source(s): https://shorte.im/a9IKK