A large refrigerator (mass 80kg) sits at rest inside a house. The homeowner wants to move the refrigerator across the room, so she begins to push it. The coefficient of static friction between the refrigerator and the floor is 0.65, and the coefficient of kinetic friction is 0.35.The homeowner applies a horizontal force of 400N on the refrigerator. What is the magnitude of the force of friction acting on the refrigerator as she applies that force?

400 N

Explanation:

By the law of friction,

is the maximum frictional force, is the coefficient of friction and is the reaction on the refrigerator. On a horizontal surface, the reaction is equal to the weight of the refrigerator.

While not moving, the fricition on the refrigerator is static friction. So,

This is the maximum frictional force and is more than the applied horizontal force of 400 N. Frictional force cannot be more than the applied force, else it would actually pull the refrigerator backwards (a strange thing, if it were to happen). It is equal to the extent of the applied force because the applied force is not enough to overcome the maximum.

Hence the frictional force is 400 N.

PS: Note that we do not use the coefficient of kinetic friction because applied force could not overcome the static friction.