Question $3$:

$(30$ Points$)$

Determine the minimum horizontal force P required to hold the crate shown in Figure $\backslash (\backslash$mathbf$\{3\}\backslash )$ from sliding down the plane. The crate has a mass of $50$ kg and the coefficient of static friction between the crate and the plane is $\backslash (\backslash$mu$\_\{$s$\}=0\mathrm{.}25\backslash )$

Figure $3$: Illustration of the information provided in Question $3$