Chapter 6, Problem 13TE

Consider the identical balls released from rest on tracks A and B as shown. When they reach at the right ends of the tracks, which will have the greater speed? ( Hint: Will their KEs be the same at the end?) Which will get to the end in the shortest time? (Considering the extra speed in the lower part of the track B, which ball has the greatest average speed on the ramps?)

To determine

The ball that has greater speed and takes a shorter time to reach at the end of the tracks.

Answer to Problem 13TE

The speed of the ball at the end of the track is greater than the speed of the ball on track B and ball on the track A reaches at the right end in a shorter time than on the track B.

Explanation of Solution

According to energy conservation, the total mechanical energy of an object remains constant at any point. The potential energy of the object converts into kinetic energy of the object at various positions due to the motion of the object.

The total energy of both identical balls is the same at the left end of the tracks. As both balls start moving towards the right end of both tracks, then the potential energy of the ball converts into kinetic energy of the balls.

The track A is flat up to the right end of the track, and there is no variation in the height of the track. The track B has more ups and downs in the track, so the potential energy of the ball converts into kinetic energy at various points. The loss of energy occurs on track B due to variation in the height of the track. The energy lost on the track A is very less compared to energy loss on the track B. The speed of the ball at the track A is more than the speed of the ball at the right end of the track B, due to more kinetic energy of the ball at the right end of track A. The ball at the track A takes less time to reach at the end of the track because of the high speed of the ball than on the track B.

Conclusion:

Therefore, the speed of the ball at the end of the track is greater than the speed of the ball on track B and ball on the track A reaches at the right end in a shorter time than on the track B.