Just figured it out on my own. But to answer your question it ends up being
μs = (w sin ∅) + (583 cos ∅) / (w cos ∅) - (583 sin ∅)
Thanks for the help!
Homework Statement
A crate, mass = 275 kg, sits at rest on a surface that is inclined at 20.0° above the horizontal. A horizontal force (parallel to the ground), F = 583 N is required to just start the crate moving down the incline.
2. The attempt at a solution
U = (((mg sin (∅)) +...