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.) Derive an expression for vQ in terms of L, m, and g. v0 = What is the tension in the rod when the ball passes through B? T = A little grit is placed on the pivot to increase the friction there. Then the ball just barely reaches C when launched from A with the same speed as before. What is the magnitude of decrease in the mechanical energy during this motion? E = What is the magnitude of decrease in the mechanical energy by the time the ball finally comes to rest at B after several oscillations? E =

Explanation / Answer

(a)(2gl)
(b)mg
(c)0 j
(d)1/2mv0^2+mgl

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