Work-Energy Theorem EX 4

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The diagram below shows our understanding of the situation. There are two forces acting on a bucket of water: and . The tension in the rope lifts the water up. Therefore, the question in this problem is to find the work done by the tension. We choose the x-axis parallel to the displacement and thus the x-component of the displacement is .

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We can determine the net work because we know the acceleration, which is related to the net force:



Consequently, the net work is



Since the net work is the sum of the work done by gravity and by the tension () we can find the work done by tension by first finding the work done by gravity. The x-component of the gravitational force is :



From the net work and the work done by gravity, we find