Question

A ball of mass m on a string of length L is attached to a pivot. The ball is released from rest while the string is parallel to the floor. A bar is placed a distance d vertically below the pivot, such that when the string runs into the bar, it will wrap around the bar. Determine the minimum distance d the bar can be placed such that the ball successfully takes a circular path around the bar. Express your answer in terms of m, L, and physical constants.

Answer 1

L/2

Step-by-step explanation:

Neglect any air or other resistant, for the ball can wrap its string around the bar, it must rotate a full circle around the bar. This means the ball should be able to swing to the top position where it's directly above the bar. By the law of energy conservation, this happens when the ball is at the same level as where it's previously released vertically. It means the swinging radius around the bar must be at least half of the string length.

So the distance d between the bar and the pivot should be at least L/2