Once the box starts to slide, as in FIGURE 6.13, the static friction force is replaced by a kinetic friction force $\vec{f}{}_{\text{k}}$. Experiments show that kinetic friction, unlike static friction, has a nearly constant magnitude. Furthermore, the size of the kinetic friction force is less than the maximum static friction, $f_{\text{k}}{<}_{}{f}_{\text{s max}}$, which explains why it is easier to keep the box moving than it was to start it moving. The direction of $\vec{f}{}_{\text{k}}$ is always opposite to the direction in which an object slides across the surface.

FIGURE 6.13 The kinetic friction force is opposite the direction of motion.

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

where ${\mu }_{\text{k}}$ is called the coefficient of kinetic friction. Table 6.1 includes typical values of ${\mu }_{\text{k}}$. You can see that ${\mu }_{\text{k}}<{\mu }_{\text{s}}$, causing the kinetic friction to be less than the maximum static friction.