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 [tex]\mu_s[/tex] and [tex]\mu_k[/tex], respectively. A woman pushes downward on the crate at an angle θ below the horizontal with a force [tex]\vec F[/tex] on the crate at an angle θ below the horizontal.
(a) What magnitude of force [tex]\vec F[/tex] is required to keep the crate moving at constant velocity?
(b) If [tex]\mu_s[/tex] is greater than some critical value, the woman cannot start the crate moving no matter how hard she pushes. Calculate this critical value of [tex]\mu_s[/tex].