Alarge crate with mass m rests on a horizontal floor. the coefficients of friction between the crate and the floor are μs and μk. a woman pushes downward at an angle θ below the horizontal on the crate with a force
f.

Since the box will move only in the horizontal direction and no net vertical motion then the force for the horizontal motion is equal to fcos θ. then this force is equal to the normal force and friction force exerted by the floor.fcos θ = us (Mg + fsin θ)fcos θ = us Mg + us fsin θfcos θ - us fsin θ = us Mgf(cos θ - us sin θ) = us mgf = us Mg/ (cos θ - us sin θ)