Problem $4(25$ points$)$:

The device shown in Figure $4$ is used to hold an elevator door open. If the spring has a stiffness of $k=40\frac{N}{m}$ and it is compressed $0\mathrm{.}2$ m $.$

$($a$)$ Draw the free$-$body diagram of the system $(5\%)$

$($b$)$ Find the resultant force at the wheel bearing $B(10\%)$

$($c$)$ Find the reactions in both horizontal and vertical directions at the pin $A(10\%)$