At a construction site, a 63.0kg bucket of concrete hangs from a light (but stro

Question

At a construction site, a 63.0kg bucket of concrete hangs from a light (but strong) cable that passes over a light friction-free pulley and is connected to an 82.0kg 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.

A-) Suddenly a worker picks up the bag of gravel. Use energy conservation to find the speed of the bucket after it has descended 1.50m , from rest. (You can check your answer by solving this problem using Newton's laws.)

Explanation / Answer

Mc*g - T = Mc*a

for box

T - uk*(Mb)*g = (Mb)*a

Mc*g - uk*(Mb)*g = (Mc+Mb)*a

(63*9.8)-0.4*(82)*9.8 = (63+82)*a

a = 2.04 m/s^2

V^2 -u^2 = 2*a*s

V = sqrt(2*a*s) = (2*2.04*1.5)^.5 = 2.473 m/s

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