A 46.2-kg crate rests on a level floor at a shipping dock. The coefficients of static and kinetic friction are 0.686 and 0.410, respectively. What horizontal pushing force is required to (a) just start the crate moving and (b) slide the crate across the dock at a constant speed?

To get the box moving you have to overcome its static friction force, which is equal to the box's normal forceagainst the floor (i.e its weight in this case) times the coefficient of static friction. Then to keep it moving you have to overcome kinetic friction, which is equal to the box's normal force against the floor times the coefficient of kinetic friction.