A $12$ wedge is used to split a log$.$ The coefficients of static and kinetic friction are $0\mathrm{.}4.$ A force P of

$3\mathrm{.}2$ kN was required to insert the wedge into the log$.$

$($a$)$ Determine the magnitude of the normal forces between the wedge and log with the $3\mathrm{.}2$ kN force still applied. $($Hint$,$ assume impending slippage inward.$)$

$($b$)$ Determine the ratio between the friction force and the normal between the wedge and log after the $3\mathrm{.}2$ kN force is removed. Note we cannot determine the magnitudes of the normal and the friction forces, but we can find their ratio. $($Hint$,$ assume wedge wants to pop out in FBD$.)$

$($c$)$ Does the wedge stay in place after the $3\mathrm{.}2$ kN is removed? $($Hint$,$ can the maximum ratio of friction to normal get as large as ratio calculated in b$?)$