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 $==0\mathrm{.}25.$ 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.