Question

A 5000-lb wrecking ball hangs from a 50-ft cable of density 10 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

The work done to lift a 5000-lb wrecking ball with a 50-ft cable weighing 10 lb/ft a height of 50 ft is 275,000 ft-lb. This is the product of the total weight lifted (including the weight of the cable) and the height.

Step-by-step explanation:

The question pertains to calculating the work done by a crane while lifting a wrecking ball. Work is defined as the force exerted on an object times the distance the object moves in the direction of the force. When a crane lifts a wrecking ball straight up, the work done is equal to the weight of the wrecking ball plus the weight of the cable multiplied by the height it is lifted. In the scenario given, the wrecking ball weighs 5000 lb and the 50-ft cable has a densisty of 10 lb/ft, meaning the cable itself weighs 500 lb. Therefore, the total weight to be lifted is 5500 lb. The work done to lift the ball and cable 50 ft is calculated as:

Work done = (weight of ball + weight of cable) × height
= (5000 lb + 500 lb) × 50 ft
= 5500 lb × 50 ft
= 275,000 ft-lb.

This calculation does not account for factors such as acceleration or the energy used to overcome air resistance and internal friction within the crane mechanisms.