Problem $3(25$ points$)$:

The beam $AB$ has a negligible mass and thickness and is subjected to a triangular distributed loading, as shown in Figure $3.$ It is supported at one end by a pin and at the other end by a post having a mass of $50$ kg and negligible thickness. The coefficients of static friction at $B$ and $C$ are ${}_B=0\mathrm{.}2$ and ${}_C=0\mathrm{.}4,$ respectively.

$($a$)$ Draw the free body diagram of $AB$ and $BC,$ respectively. $(5\%)$

$($b$)$ Start by assuming the post slips at $C,$ determine the minimum force $P$ needed to move the post. $(20\%)$