Question

A ball is tied to the end of a length of string. A student holds one end of the string and whirls it so the ball travels in a vertical circle. First she whirls the ball at a very fast speed, and then she very gradually lowers the speed. Where is the ball most likely to be when the string begins to sag?

Answer 1

The top of the circle

Step-by-step explanation:

At the top of the circle, there are two forces pulling the ball towards the center of the circle: weight and tension.

∑F = ma

mg + T = mv²/r

As v goes down, T also goes down, until it eventually reaches 0.

At the bottom of the circle, weight is pulling down, or away from the center of the circle. Sum of the forces:

∑F = ma

T − mg = mv²/r

As v goes down, T also goes down. However, even at v=0, T cannot be less than mg.