A child pushes a box that has mass m up an incline plane at an angle `alpha` above the horizontal. The coefficients of friction between the incline and the box are `mu_(s)` and `mu_(k)`. The force applied by the child is horizontal, (a )If `mu_(s)` is greater than some critical value, the child cannot start the box moving up the incline, no matter how hard he pushes. Calculate this critical value of `mu_(s)`. (b) Assume that `mu_(s)` is less than this critical value. What magnitude of force must the child apply to keep the box moving up the plane at constant speed.
`[cot alpha,(mg(sinalpha+mu_(k)cosalpha))/(cosalpha-mu_(k)sinalpha)]`