Problem $4$:

This is a difficult problem. The easiest way to solve it is to compute the force P to cause impending motion of block B to the left and block A upwards. Next do the opposite; compute the force P to cause impending motion of block B to the right and block A down. Then you can judge what will happen when the $50$ lb is actually applied. $($Hint: Remember Newton's $3^{rd}$ law.$)$

The coefficient of static friction for all contact surfaces in Fig. $7\mathrm{.}8$ is $\mathrm{.}2.$ Does the $50-lb$ force move the block $A$ up$,$ hold it in equilibrium, or is it too small to prevent A from coming down and $B$ from moving out? The $50-lb$ force is exerted at the midplane of the blocks so that we can consider this a coplanar problem.