While in the process of moving, you attempt to push a 15 kg box across your horizontal floor. The coefficient of static friction and kinetic friction between the box and the floor is μs = 0.8 and μk = 0.4 respectively.

a. If you apply a horizontal force of 50 N to the box while it is at rest, what is the magnitude of the friction force acting on the box?

b. What horizontal force must you apply to the box for it to slide across the floor at a constant speed (assume the box is already moving)?

c. If you slide the box 5 m to the right and then 5 m to the left back to its starting position, how much work did friction do on the box across the entire path?