At a construction site, a 65.0 kg bucket of concrete hangs from a light (but str

Question

At a construction site, a 65.0 kg bucket of concrete hangs from a light (but strong) cable that passes over a light friction-free pulley and is connected to an 85.0 kg box on a horizontal roof (see the figure ). The cable pulls horizontally on the box, and a 50.0 kg bag of gravel rests on top of the box. The coefficients of friction between the box and roof are shown. The system is not moving.

Suddenly a worker picks up the bag of gravel. Use energy conservation to find the speed of the bucket after it has descended 2.00 m, from rest. (You can check your answer by solving this problem using Newton's laws.)

Explanation / Answer

The frictional force on the gravel is 0 because it's not on the ground. For the box it's (130 kg)(9.8 m/s2)(0.7) = 891.8N. Initial kinetic energy: 0 Initial gravitation potential energy: (65 kg)(9.8 m/s2)(2.0 m) = 1274 J Dissipative work: (80.0 kg)(9.8 m/s2)(0.4)(2.0 m) = 627.7 J Final kinetic energy: ? Final gravitational potential energy: 0 Ki + Ui = Kf + Uf + Wdissipative 0 + 1274J = Kf + 0 + 627.7J Kf = 646.3J 646.3J = (145 kg*v2)/2 ==> v = 2.99 m/s

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