A 0.800-kg ball is tied to the end of a string 1.60 m long and swung in a vertical circle. (a) During one complete circle, starting anywhere, calculate the total work done on the ball by (i) the tension in the string and (ii) gravity. (b) Repeat part (a) for motion along the semicircle from the lowest to the highest point on the path.

Solution 9E Introduction In all given cases, we have to identify the force and the displacement of the ball to find out the work done on the ball. Step 1 (a) (i) We know that the tension of the string in a circular motion always act towards the center, that is radially inwards, whereas the particle always move perpendicular to the radius of the path in case of circular motion. Which means, during the full circle, the tension of the string and the displacement were always perpendicular to each other. And, as we know that if the force and displacement are perpendicular, the work done is zero. Hence the work done by the tension of the string is zero. (ii) In a full circular motion, the displacement of the ball is zero. Hence, since the displacement is zero, the work done on the ball by gravity will also be zero.