A 3000-lb wrecking ball hangs from a 10-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 10 ft in the air by drawing in the cable.

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  30,500 ft·lb

Step-by-step explanation:

The 3000 lb ball is raised 10 ft, so (3000 lb)·(10 ft) = 30,000 ft·lb is the work done on it.

The weight of the cable is (10 ft)·(10 lb/ft) = 100 lb. Its center of mass is at its midpoint, 5 ft above the ground. When all of the cable is raised to a height of 10 ft above the ground, that center of mass is elevated 5 ft. The work done on the cable is ...

  (100 lb)·(5 ft) = 500 ft·lb

The total work done on the ball and cable is ...

  30,000 ft·lb +500 ft·lb = 30,500 ft·lb