Problem #$1$: $(40$ points$)$ 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 $4ft.$ At any time $t,$ the orientation of the bar and the radial position of

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

Bar $OA$ rotates with a constant angular acceleration ${}^{}=10ra\frac{d}{sec}$ for all times $t0sec.$ At

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

${}^{}(t=0)=2ra\frac{d}{sec}.$ At time $t=0sec,$ the radial position of the block is $r(t=0)=1\mathrm{.}5ft$ and

its initial radial speed is $r^{}(t=0)=1f\frac{t}{sec}.$ At time $t=2sec,$ 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 $r^{}(t=0)$ of the block's radial speed and the component$($s$)$ of

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

c$)$ Draw a free body diagram of block $B$ at any time $t>2sec$ 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 $t=2\mathrm{.}5sec.$

Please show all work in detials!!