Problem $5$: $(20$ points$)$

The uniform bar $BC$ with mass of $4\mathrm{.}5$ kg hangs vertically at pin $C$ from a moving conveyor belt, held by the wire $AB.$ The acceleration of the conveyor belt is $6\frac{m}{s^2}.$ Assume gravity $g=9\mathrm{.}81\frac{m}{s^2}.$ Show all work.

a$)$ Draw the appropriate free body and kinetic diagram$($s$).(2$ points$)$ Show this in a picture$/$visually in chegg answer please.

b$)$ Write the equations of motion for a rigid body based on the free body and kinetic diagram$($s$)$ written above. $(2$ points$)$

c$)$ Compute the expression of Newton's equation in $x$ direction. $(4$ points$)$

d$)$ Compute the expression of Newton's equation in $y$ direction. $(4$ points$)$

e$)$ Compute the expression of moment about center of gravity, G$.(4$ points$)$

f$)$ Determine the magnitude of the tension in the wire, $T.(2$ points$)$

g$)$ Determine the magnitude of the total force supported by the pin $C,F_C.(2$ points$)$