$(12$ points$)$ A $65$ lb $.$ crate rests on a $20$ rough ramp. A force of $P=40lb.$ is applied at an angle of $30$

with respect to the ramp surface as shown

What minimum coefficient of friction $({}_s)$ between the crate and the ramp is required to keep the crate from moving up the ramp? $($Hint: Use the $x-$y coordinate system shown$).$