The rope pulls the 2.0 kg buckets vertically upwards accelerating it from rest at 2.2 m/s^2 for 3 seconds.

In 3 seconds, the distance traveled by the bucket is equal to s = u*t + (1/2)*a*t^2. Here u = 0, t = 3 and a = 2.2

This gives s...

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The rope pulls the 2.0 kg buckets vertically upwards accelerating it from rest at 2.2 m/s^2 for 3 seconds.

In 3 seconds, the distance traveled by the bucket is equal to s = u*t + (1/2)*a*t^2. Here u = 0, t = 3 and a = 2.2

This gives s = (1/2)*2.2*9 = 9.9 m

There are two forces acting on the bucket, one of them is the force accelerating it upwards at a net acceleration of 2.2 m/s^2 and the other is the gravitational force of attraction of the Earth that is equal to 9.8 m/s^2 and acts in the downward direction.

The work done by a force F that acts over a distance d is equal to W = F*d = m*a*d.

The net work done by the upward acting force applied by the rope is (9.8+2.2)*2*9.9 = 237.6 J and the work done by the force of gravity is 9.8*2*9.9 = 194.04 J