calculating force(show me how so i can solve myself answer so i can check

Question

How much work is done lifting a 30 pound object from the ground to the top of a 50 foot building if the cable used weighs 2 pounds per foot?

Answer 1

Assuming the object was lifted at almost 0 speed ie maintaining equilibrium,

let the length of the cable at any time be x.

In the beginning, x = 50 ft.

In the end, x = 0 ft.

Force due to the object = 30 lb

Force due to the cable at length x = 2x lb

total force at any given point while lifting the object = (30 + 2x) lb

Work done = Integral (F.dx) over the length of the entire distance of 50 ft.

Integrate this and you will get the following results...

Work done = Integral of (30 + 2x)dx

The final work done comes out to be = -30x - x^2. Apply the limits from 50 to 0.

You will receive the work done = - (-1500 - 2500) = 4000 lb.ft