Problem $2(60$pts$)$:

A worker applies the force described below to push a box that weighs $40$ lb with center of gravity at point $G.$ The surface between the box and ramp has coefficient of friction ${}_s={}_k=0\mathrm{.}25.$ Determine the normal force and friction force between the box and ramp and determine if the box will slide up the ramp, down the ramp, or remain at rest.

$($a$)$ The worker applies a $30$ lb force parallel to the ramp.

$($b$)$ The worker applies a $35$ lb force that is horizontal.