A $12$ lb block B slides inside a frictionless slot that is cut in bar OA$,$

which rotates in a horizontal plane, as shown in Figure $1.$ The distance from the pivot point O to

the end point A of the bar is $4$ ft$.$ At any time t$,$ the orientation of the bar and the radial position of

the block are given by angle $\backslash$theta $($t$)$ and position r$($t$),$ respectively, as shown.

Bar OA rotates with a constant angular acceleration $=10$ rad$/$sec$2$ for all times $>=0$ sec$.$ At

time t $=0$ sec$,$ bar OA starts at an initial angle $(=0)=0$ rad with an initial angular velocity

$(=0)=2$ rad$/$sec$.$ At time t $=0$ sec$,$ the radial position of the block is $(=0)=1\mathrm{.}5$ ft and

its initial radial speed is $(=0)=1$ ft$/$sec$.$ At time t $=2$ sec$,$ the block hits the end A of the slot.

a$)$ Draw a free body diagram of block B at any time t before it hits the end of the slot at A$.$

b$)$ Calculate the rate of change $(=0)$ of the block$$s radial speed and the component$($s$)$ of

the force exerted by the slot on the block at t $=0$ sec$.$

c$)$ Draw a free body diagram of block B at any time t $>2$ sec after it comes in contact with the

end A of the slot.

d$)$ Calculate the component$($s$)$ of the force exerted by the slot on the block at t $=2\mathrm{.}5$ sec