Homework H$\mathrm{.}5.$H

Given: A homogeneous disk of mass $m$ and outer radius $R$ is supported by the cable$-$pulley system shown. The pulley $($having a mass of $m$ and with an outer radius of $R)$ is supported by a smooth shaft at its center O$.$ Block A $($with a mass of $m)$ is supported at the center E of the disk. A constant force F is applied to the free end of the cable. The system is released from rest. Assume the pulley and disk do not slip on the cable.

Find:

$($a$)$ Determine the direction of motion of block A on release; and

$($b$)$ Determine the speed of block A after A has moved through a distance of $s_A.$

Use the following parameters in your analysis: $m=15kg,R=0\mathrm{.}25m,s_A=0\mathrm{.}5m$ and $F=300$ N$.$