A ball of mass $M$ is attached to a string of length $L$. It is driven around a vertical circle at constant speed, and at the bottom the ball just clears the ground. The tension at the bottom of the path is $3$ times the weight of the ball. Give all answers in terms of $M$, $L$, and $g$.

Question

A ball of mass $M$ is attached to a string of length $L$. It is driven around a vertical circle at constant speed, and at the bottom the ball just clears the ground. The tension at the bottom of the path is $3$ times the weight of the ball. Give all answers in terms of $M$, $L$, and $g$.(a) What is the magnitude and direction of the net force on the ball when it is at the top?
, (b) What is the velocity of the ball at the top?
, (c) The string is cut exactly when the ball is at the top. How long does it take to reach the ground?
, (d) How far does the ball travel horizontally before hitting the ground?
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Jason · Accepted Answer

(a) $ 2Mg $, downward.
(b) $ v = \sqrt{2gL} $.
(c) $ \sqrt{\frac{4L}{g}} $.
(d) $ \sqrt{8}L $

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