A pendulum consists of a mass M hanging at the bottom end of a massless rod of l

Question

A pendulum consists of a mass M hanging at the bottom end of a massless rod of length l, which has a frictionless pivot at its top end. A mass m, moving as shown in the figure with velocity v impacts M and becomes embedded. (Figure 1)

What is the smallest value of v sufficient to cause the pendulum (with embedded mass m) to swing clear over the top of its arc?

Express your answer in terms of the variables m, M, l, and g.

A pendulum consists of a mass M hanging at the bottom end of a massless rod of length I, which has a frictionless pivot at its top end. A mass m, moving as shown in the figure with velocity v impacts M and becomes embedded. (Figure 1) What is the smallest value of v sufficient to cause the pendulum (with embedded mass m) to swing clear over the top of its arc? Express your answer in terms of the variables m, M,1, and g Submit My Answers Give Ug Figure 1 of 1 iIn

Explanation / Answer

BY the law of conservation of angular momentum

initial angular momentum = final angular momentum

m v L = (m + M)*L * V1

so Speed V1 = mv /(m + M)-----------------------1

by conservation of energy , initial KE = final KE

0.5 * (m + M) * v1^2 = (m + M) * g * h

here h = 2L

so V1 = sqrt(4gL)-------------------------2

so by subtituing 2 in 1

v = (m + M)/m * V1

V smallest possible = sqrt(4 g L) * (m+M)/m

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