The force $P$ is applied to the $30-kg$ block when it is at rest. Determine the magnitude and direction of the friction force exerted by the surface on the block if $($a$)P=0,($b$)P=156N,$ and $(c)P=229N.($d$)$ What value of $P$ is required to initiate motion up the incline? The static and kinetic coefficients of friction between the block and the incline are ${}_s=0\mathrm{.}33$ and ${}_k=0\mathrm{.}27,$ respectively. The friction force is positive if up the incline, negative if down the incline.

Answers:

$($a$)F=$ N

$($b$)F=$ N

$($c$)F=$ N

$($d$)P=$ N