At a construction site, a 28.0 k g bucket of concrete is connected over a very l

Question

At a construction site, a 28.0kg  bucket of concrete is connected over a very light frictionless pulley to a 380N   box on the roof of a building. (See the figure.) There is no appreciable friction on the box, since it is on roller bearings. The box starts from rest.(Figure 1)

At a construction site, a 28.0kg bucket of concrete is connected over a very light frictionless pulley to a 380N box on the roof of a building. (See the figure.) There is no appreciable friction on the box, since it is on roller bearings. The box starts from rest. Find the acceleration of the bucket. How fast is the bucket moving after it has fallen 1.50 m (assuming that the box has not yet reached the edge of the roof)?

Explanation / Answer

A) net force on bucket, Fnet = m1*g - T

m*a = m*g - T

T = m1*g - m1*a --(1)

m2 = 380/9.8 = 38.78 kg

net force on block

Fnet = T

m2*a = T ---(2)

from euations 1 and 2

m2*a = m1*g - m1*a

a = m1*g/(m1+m2) = 4.1 m/s^2

B) v^2 - u^2 = 2*a*s

v = sqrt(2*a*s) = sqrt(2*4.1*1.5) = 3.507 m/s

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