A large 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 with a force on the crate at an angle ? below the horizontal. (a) What magnitude of force is required to keep the crate moving at constant velocity? (b) If µs is greater than some critical value, the woman cannot start the crate moving no matter how hard she pushes. Calculate this critical value of µs.

Solution 39E Step 1 of 4: The free body diagram for the given problem is given below, Step 2 of 4: (a) What magnitude of force is required to keep the crate moving at constant velocity The horizontal force, that is pushing the carte horizontally = F cos Similarly the vertical force pushing the carte into the floor= F sin As in the FBD, the weight of the carte also pushes the carte into the floor, preventing the carte motion. Hence there is no vertical motion of the carte. Somehow if we set the carte into motion with constant speed, then the frictional force acts horizontally, That is, f = k(mg + F sin)