Question

How much work is done lifting a 10 pound object from the ground to the top of a 40 foot building if the cable used weighs 2.5 pounds per foot?

Answer 1

2,400 foot-pounds

Explanation:

Say at any instant x is length of Rope

Work done in lifting rope by dx amount will be:

dw = -(2.5x + 10)dx

w = -(40)∫(2.5x+10)dx

w = (2.5(40)^2) / 2 + 10(40)

w = 2000 + 400

w = 2,400 foot-pounds