Physics Question

Question

A ball of mass m swings in a horizontal circle at the end of a string of radius r at a constant tangential speed V₀ . A student gradually pulls the string inward such that the radius of the circle decreases while keeping the tangential speed of the ball constant, as shown below. Which of the following statements best expresses what happens to the net force on the ball as the radius decreases.

1) The radius has no effect on the net force because F =ma

2) As the radius decreases, the net force also decreases because moving in a smaller circle requires less force

3) As the radius decreases, the net force increases because the ball has to speed up to stay in the circle.

4) As the radius decreases the net for increases because force is inversely proportional to radius.

Answer 1

You are looking at centripetal force, which is F_{c =} (mv²)/r.....It told you the speed remain constant so the only thing changing here is the radius. The centripetal force is indirectly proportional to the radius. So if you decrease your radius (r), then Fc increases. So the answer is 4