At a construction site, a 67.0 kg bucket of concrete hangs from a light (but str

Question

At a construction site, a 67.0 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 2.20N , from rest.

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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