Question

A 3000-lb wrecking ball hangs from a 50-ft cable of density 7 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:

The work done is 227,130 J (or 227 kJ).

Step-by-step explanation:

When the force is in the same direction than the displacement, we can express the work of this force as:

$W=F\cdot h$

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:

$M_c=l\cdot \rho=50\, ft\cdot 7\,lb/ft=350\,lb$

The total mass is 3,350 lb.

The magnitude of the force is equal to the weight:

$F=mg=3,350\,lbf$

The work done by this force is:

$W=F\cdot h=3,350\,lbf\cdot 50\,ft= 167,500\,lbf-ft\\\\W=167,500\,lbf-ft*\frac{1.356\,J}{1\,lbf-ft}= 227,130\,J$