A massless rigid rod of length L has a ball of mass m attached to one end (figur

Question

A massless rigid rod of length L has a ball of mass m attached to one end (figure below). The other end is pivoted in such a way that the ball will move in a vertical circle. First, assume that there is no friction at the pivot. The system is launched downward from the horizontal position A with initial speed v0. The ball just barely reaches point D and then stops. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.)

(a) Derive an expression forv0in terms ofL,m, andg.

(b) What is the tension in the rod when the ball passes throughB?

(c) A little grit is placed on the pivot to increase the friction there. Then the ball just barely reachesCwhen launched fromAwith the same speed as before. What is the magnitude of decrease in the mechanical energy during this motion?

(d) What is the magnitude of decrease in the mechanical energy by the time the ball finally comes to rest atBafter several oscillations?

Explanation / Answer

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