Figure 8-31 shows a ball with mass m ? 0.341 kg attached to the end of...

Figure 8-31 shows a ball with mass m ? 0.341 kg attached to the end of a thin rod with length L ? 0.452 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 (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? (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?

Solutions

Expert Solution

The main point to be kept in mind while solving this problem is that gravity is a conservative force and only depends on the initial and final position of the object.

a) the lowest point

The work done by the gravity will be

b) the highest point

Since the motion is in the opposite direction, the work done will be negative

c) the point on the right level with the initial point

Since the vertical displacement is zero, the work done by gravity is zero.

The gravity potential energy at

d) the lowest point

The gravitational potential energy will be the negative of the work done by gravity.

Therefore, here it will be

e) the highest point

Here, it will be

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

Here, it will be zero

Suppose the rod were pushed harder so that the ball passed through the highest point with a nonzero speed. Would 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 depends on the height( or vertical displacement) only. Therefore, at a given height, it will be the same regardless of the speed.

genius_generous answered 1 year ago

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