How Static and Kinetic Friction Differ

Static and kinetic friction both oppose relative motion between contacting surfaces, but they apply to different contact conditions and use different mathematical rules.

Static friction adjusts before sliding

When the surfaces are not sliding relative to one another, static friction can match the tangential force trying to start sliding, up to a maximum:

$$0\le f_s\le\mu_sN.$$

The equality $f_s=\mu_sN$ applies only at the threshold of slipping. If a horizontal push is small, static friction normally matches that push rather than immediately taking its maximum value.

Kinetic friction applies during sliding

Once the surfaces slide relative to one another, the simple dry-friction model uses

$$f_k=\mu_kN.$$

The force points opposite the relative sliding direction. For many material pairs, $\mu_k<\mu_s$, so maintaining sliding requires less force than initiating it. These equations are empirical approximations, not universal laws for every surface or speed.

A new example

A $12\,\text{kg}$ crate rests on a level floor with $\mu_s=0.40$ and $\mu_k=0.25$. With no other vertical forces,

$$N=mg=(12)(9.8)=117.6\,\text{N}.$$

The maximum static friction is

$$f_{s,\max}=(0.40)(117.6)=47.0\,\text{N}.$$

A $30\,\text{N}$ horizontal push does not make the crate slide; static friction is $30\,\text{N}$ in the opposite direction. A $55\,\text{N}$ push exceeds the static limit, so sliding begins. During sliding,

$$f_k=(0.25)(117.6)=29.4\,\text{N}.$$

If the push remains $55\,\text{N}$, the horizontal net force is $25.6\,\text{N}$ and the acceleration is about $2.13\,\text{m/s}^2$.

Motion of the object is not enough information

Choose the friction type from the relative motion at the contact. A wheel can move across the ground without slipping; its instantaneous contact point may be at rest relative to the ground, so any friction there is static rather than kinetic. Fluid resistance and rolling resistance require different models.