A block $($mass $=2\mathrm{.}0kg)$ is hanging from a massless cord that is wrapped around a pulley $($moment of inertia $=1\mathrm{.}1{10}^{-3}kg*m^2),$ as the drawing shows. Initially the pulley is prevented from rotating and the block is stationary. Then, the pulley is allowed to rotate as the block falls. The cord does not slip relative to the pulley as the block falls. Assume that the radius of the cord around the pulley remains constant at a value of $0\mathrm{.}040$ m during the block's descent. $($a$)$ Draw the free$-$body diagram showing the forces that act on the pulley. $($b$)$ Draw the free$-$body diagram showing the forces that act on the block. Find $($c$)$ the angular acceleration of the pulley and $($d$)$ the tension in the cord.

$($a$)$ Draw the free$-$body diagram showing the forces that act on the pulley.

Use the checkboxes to select the correct vectors as instructed above. Move the vectors to the correct starting points and orient them in the correct direction as instructed.

$m_{b}g$

f

T

$m_{p}g$

S

$F_x$

Key to Force Labels

$m_{b}g=$ Gravitational force on block

$f=$ Frictional force

$T=$ Tension in the cord

$m_{p}g=$ Gravitational force on pulley

$S=$ Force supporting pulley

$F_x=$ Spring force