Homework H$\mathrm{.}4.$M

Given: Particle B $($having a mass of $m)$ is constrained to move within a circular slot $($of radius $R)$ that is cut into block A $($having a mass of $M).$ The system is released from rest with particle B on a horizontal line passing through the circle's center O$.$ Consider all surfaces to be smooth.

Find: For this problem:

$($a$)$ Determine the velocities of A and B when B has moved position $2$ where B is directly below O $($write your answers as vectors$)$;

$($b$)$ Determine the work done on block A in moving from position $1$ to position $2.$

sIIs

Use the following parameters in your analysis: $m=20kg,M=40kg$ and $R=0\mathrm{.}5m.$