# Pendulum Conservation of Momentum Problem

#### bluemouse

I know the attached image has something to do with conservation of momentum, but I am not sure how to proceed....

#### Cervesa

Conservation of momentum: $mv_0 = (m+M)v_f$

In order to make it around the top of the circle, the speed of the combined masses at the uppermost position needs to satisfy the equation $F_c = (m+M)g = \dfrac{(m+M) \cdot v^2}{R}$, where $F_c$ is the minimum centripetal force necessary to complete the desired circular motion. At the uppermost position, the total mechanical energy of the combined masses (kinetic + gravitational potential) has to $\ge$ the kinetic energy of the combined masses immediately after the collision at the bottom.

See what you can do from here.

topsquark

#### bluemouse

Is 29.4 m/s right?

Why not?

#### topsquark

Forum Staff
Please post what you did and we can point out the mistake.

-Dan