$11.(10$ points$)$ A box of mass $\backslash (\backslash$mathbf$\{$m$\}=\backslash$mathbf$\{10\}\backslash$mathbf$\{$~ k g$\}\backslash )$ is placed at rest on a ramp which makes an angle of $\backslash (\backslash$mathbf$\{30\}\backslash )$ degrees with the horizontal. The coefficients of friction between the ramp and box are $\backslash (\backslash$boldsymbol$\{\backslash$mu$\}\_\{\backslash$mathrm$\{$k$\}\}=\backslash$mathbf$\{0.15\}\backslash )$ and $\backslash (\backslash$mu$\_\{\backslash$mathrm$\{$s$\}\}=\backslash$mathbf$\{0.35\}\backslash ).$ A force of $\backslash (\backslash$mathbf$\{70\}\backslash$mathrm$\{$N$\}\backslash )$ is then applied to the box, parallel to the ramp as shown.

$($a$)$ Does the box move? Show that the box does or does not move.

$($b$)$ What is the magnitude of frictional force acting on the box?