What is the smallest value of v sufficient to cause the pendulum to swing clear over the top of its arc?

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.





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?|||This is a two part problem. First you should use the conservation of energy to determine how much kinetic energy the combination of the two masses will need to supply the potential energy it will have at the top of the circle... this gives a value of v(after collision) = sqrt(2g*2l).





Then you need to do a perfectly inelastic collision problem (momentum conservation) to get the v(befor the collision of v(before collision) = (M+m)*v(after collision)/m





or substituting all the stuff...





v = 2*(M+m)*((lg)^(0.5))/m