A 3000-lb wrecking ball hangs from a 40-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 40 ft in the air by drawing in the cable.
The total work done by the crane equals the potential energy gained by the wrecking ball and the cable; the potential energy gained is W = V_final = Mg L + ρ L g L/2 which is the final potential energy of the wrecking ball and the cable added together. In the case of the cable, you take the center of mass of it which is located right at the center (L/2). The result is then W = 3000*32*40 + 10 * 40 * 32 * 40 / 2 = 4096000 ft-lbf = (4096000)*(0.001285067) BTU = 5263.63 BTU
