Question

The figure shows a ball with mass m = 0.295 kg attached to the end of a thin rod with length L = 0.306 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. The rod is held horizontally as shown and then given enough of a downward push to cause the ball to swing down and around and just reach the vertically upward position, with zero speed there. How much work is done on the ball by the gravitational force from the initial point to (a) the lowest point, (b) the highest point, and (c) the point on the right level with the initial point? If the gravitational potential energy of the ball-Earth system is taken to be zero at the initial point, what is it when the ball reaches (d) the lowest point, (e) the highest point, and (f) the point on the right level with the initial point?

Answer 1

The ball has moved vertically down through a distance
=0.306 /2 = 0.153m

Work done by gravity = 0.295*9.8*0.153 = 0.442 J.
When it is again horizontal this energy will be lost and to go up it must have and additional energy of 0.442 J
Initially it had an energy of 0.442 J
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a} + 0.442 J.
b) - 0.442 J
c) Zero.
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(d) the lowest point = -0.442 J
(e) the highest point = +0.442 J
(f) the point on the right level with the initial point = Zero.