Question

A 3000-lb wrecking ball hangs from a 50-ft cable of density 5 lb/ft attached to a crane. Calculate the work done if the crane lifts the ball from ground level to 50 ft in the air by drawing in the cable.

Answer 1

Answer: 227,130 J (or 227 kJ).

How?:

When the force is in the same direction than the displacement, we can express the work of this force as: W = F x h

The force is equal to the total weight of the wrecking ball and the cable. The wrecking ball has a mass of 3000 lb. For the cable, we have to calculate the mass as:

Mc = l x p= 50ft x 7lb/ft= 350lb

The total mass is 3,350 lb.

The magnitude of the force is equal to the weight:

F= mg= 3,350lbf

The work done by this force is:

W=F x h= 3,350lbf x 50ft = 167,500lbf - ft

W= 167,500lbf - ft x 1.356J/1lbf - ft = 227,130 J (or 227 kJ).