The figure below shows a ball with mass m = 0.300 kg attached to the end of a th

Question

The figure below shows a ball with mass m = 0.300 kg attached to the end of a thin rod with length L = 0.515 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 up position, with zero speed there.

How much work is done on the ball by the gravitational force from the initial point to the following points?

(a) the lowest point

(b) the highest point

(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 the following points?

(d) the lowest point

(e) the highest point

(f) the point on the right level with the initial point

(g) Suppose the rod were pushed harder so that the ball passed through the highest point with a nonzero speed. Would Ug from the lowest point to the highest point then be greater than, less than, or the same as it was when the ball stopped at the highest point?

The figure below shows a ball with mass m 0.300 kg attached to the end of a thin rod with length L 0.515 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 up position, with zero speed there. How much work is done on the ball by the gravitational force from the initial point to the following points? (a) the lowest point (b) the highest point (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 the following points? (d) the lowest point (e) the highest point (f) the point on the right level with the initial point (g) Suppose the rod were pushed harder so that the ball passed through the highest point with a nonzero speed. Would AUg from the lowest pointto the highest point then be greater than, less than, or the same as it was when the ball stopped at the highest point? greater than less than the same as

Explanation / Answer

here,
mass of ball, m = 0.3 kg
length of rod, l = 0.515 m

distance moved by ball vertically, d = 0.515/2
distance moved by ball vertically, d = 0.258 m

Part 1:

part a:
work done by gravity, w = f * d
work done by gravity, w = mg * d
work done by gravity, w = 0.3*9.81*0.25
work done by gravity, w = 0.736 J

part b:
When it is again horizontal this energy will be lost and to go up it must have and additional energy

work done by gravity, w = -f * d
work done by gravity, w = -mg * d
work done by gravity, w = -0.3*9.81*0.25
work done by gravity, w = -0.736 J

part c:
work done = 0

part 2:

part a:
work done by gravity, w = -f * d
work done by gravity, w = -mg * d
work done by gravity, w = -0.3*9.81*0.25
work done by gravity, w = -0.736 J

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