A large crate with mass m rests on a horizontal floor. The static and kinetic coefficients of friction between the crate and the floor are and , respectively. A woman pushes downward on the crate at an angle θ below the horizontal with a force on the crate at an angle θ below the horizontal.
(a) What magnitude of force is required to keep the crate moving at constant velocity?
(b) If is greater than some critical value, the woman cannot start the crate moving no matter how hard she pushes. Calculate this critical value of .