A cable weighing 2 pounds per foot of length (and so having a mass of 2 pounds per foot) is suspended from the top of a well 200 feet deep and extends to the bottom. Find the work done in raising the cable to the surface. Over the distance of 200 feet you may use 32m as the constant weight of a mass 'm'.
3. attempt at a solution
dW/dr = F
dW/dr = 32m
dW/dr = 32(2r)
dW/dr = 64r
W = 32r^2 + C = 32(200)^2 = 1280000
The fact that 'r' is measuring cable length (instead of distance between two objects which was used to derive the original equation) is screwing with me. I need someone to help me get my head around it.