A ball of mass m is attached to a string of length L. It is swung in a vertical

Question

A ball of mass m is attached to a string of length L. It is swung in a vertical circle with enough speed to keep the string taut throughout the motion. Assume the ball travels freely in the circle with negligible loss of mechanical energy. Determine if the following six statements are true or false

The tension in the string is less at the top of the circle than at the bottom of the circle.

The tensions at the top and at the bottom of the circle depend on the average speed of the ball.

The magnitude of the difference between the kinetic energy of the ball at the top and the bottom of the circle is 2mgL.

mvb2/L = Tb+mg, where vb and Tb are the speed of the ball and the tension of the string at the bottom of the circle.

The tension in the string at the top of the circle is always greater than the weight of the ball.

The acceleration of the ball at the top of the circle is directed `down'.

Explanation / Answer

The tension in the string is less at the top of the circle than at the bottom of the circle. The magnitude of the difference between the kinetic energy of the ball at the top and the bottom of the circle is 2mgL. he acceleration of the ball at the top of the circle is directed `down'. mvb2/L = Tb+mg, where vb and Tb are the speed of the ball and the tension of the string at the bottom of the circle.

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