Kinetic Friction

Slide a phone across a table and it soon stops. Kinetic friction did that, and it follows two rules about direction and size that are easy to state and easy to misapply.

Direction#

When body A slides over body B, the friction on A acts so as to oppose the slipping. Precisely:

By the third law the friction on B (due to A) is opposite to that, which is the same as opposite to B’s velocity relative to A. The two rules agree.

Here is where intuition slips. A small block sits on a long wheeled trolley rolling to the right, and the block is sliding toward the back of the trolley. From the road, both move to the right (the block more slowly). But relative to the trolley the block moves left, so friction on the block points right, in the direction it is already moving over the road. Explore it:

Size#

The magnitude of kinetic friction is proportional to the normal force between the surfaces:

The constant $\mu_k$ is the coefficient of kinetic friction. It depends on the two materials and on how smooth or rough their surfaces are: small for polished surfaces, large for rough ones.

What it does not depend on

• Speed. Once sliding, the friction is $\mu_kN$ whatever the speed. This is a good approximation for modest relative speeds (up to roughly 10 m/s).
• Contact area. For a given normal force, a brick slid on its broad face and on its narrow end feels the same friction.