What are friction's dependencies

Static Friction

• The actual magnitude of static friction ranges between 0 and a max value.
• From intuition we know that the harder we press our object against a surface, the greater friction we feel when trying to push it.
  • I.e. static friction (max value) depends on the force attaching it to the surface.
  • Since this would be weird to calculate, we can use the normal force.
  • Normal force = force holding object to surface; cuz they have to be the same unless the table is collapsing.

$$\begin{array}{r}{f}_{s,max}\propto F_N\\ f_{s,max}={\mu }_s{F}_N\end{array}$$

Where ${\mu }_s$ is the coefficient of static friction (just a proportionality constant).

Kinetic Friction

Similarly:

$$f_k={\mu }_k{F}_N$$

Where ${\mu }_k$ is the coefficient of kinetic friction.

• But static friction does not have a range, $f_k$ is the magnitude whenever the object is moving.