Problem $4.(1$ point$)$

A horizontal force P is applied to a $3\mathrm{.}1$ kg block on a slope inclined at $\backslash (\backslash$theta$=50^\{\backslash$circ$\}\backslash )$ to the horizontal. The kinetic coefficient of friction between the block and the surface is $\backslash (\backslash$mu$\_\{$k$\}=0\mathrm{.}18\backslash ).$ The static coefficient of friction between the block and the surface is $\backslash (\backslash$mu$\_\{$s$\}=0\mathrm{.}36\backslash ).$ The force P is gradually increased until the block just starts to slide and then, exactly at that point in time, it $($ P $)$ is maintained constantly in both magnitude and direction.

$($a$)$ Draw a complete free body diagram and submit it to the teacher.

$($b$)$ Find the magnitude of the force $\backslash ($ P $\backslash ).$

$($c$)$ Calculate the magnitude of the acceleration of the block.

$\backslash ($ P $\backslash )$

Note: You can earn partial credit on this problem.