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

Question

At a construction site, a 65.0kg bucket of concrete hangs from a light (but strong) cable that passes over a light friction-free pulley and is connected to an 85.0kg box on a horizontal roof (see the figure (Figure 1) ). The cable pulls horizontally on the box, and a 47.0kg 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.

Part C

Suddenly a worker picks up the bag of gravel. Use energy conservation to find the speed of the bucket after it has descended 1.90m , from rest. (You can check your answer by solving this problem using Newton's laws.)

Explanation / Answer

m = 65kg
M = 85kg
b = 47kg
us = 0.7
uk = 0.4
h = 1.9m
1) since it doesn't mention a coefficient of friction for the gravel on the box I would assume it was zero so the friction force
F = ubg = 0*bg = 0
2) F = (us)(b+M)g = 906.44N
notice that this is bigger than mg so the system will stay still while the gravel is there
3)
potential energy of bucket converts to kinetic energy of box & bucket plus friction on bucket
mgh =

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