# The instability of dry friction

Based on Newton Dynamics, the kinetic force of friction of any moving object can be found by using formula,

$$F_f = \mu_k F_N$$

This means that if $\mu_k$ and $\ F_N$ remains constant, the force of friction would always be constant.

However, I just read an article and it says that "dry friction can induce several types of instabilities in mechanical systems which display a stable behaviour in the absence of friction.These instabilities may be caused by the decrease of the friction force with an increasing velocity of sliding..." Can we still apply the formula $\ F_f = \mu_k F_N$ when taking this instability into consideration? If so, what changes result in the change of friction- $\mu_k$ or $\ F_N$ ?

## 1 Answer

The formula you gave for kinetic friction, $$F_f=\mu_kF_N,$$ is a first-order, simplistic, phenomenological model. It describes systems for which the contact surfaces are uniform in space and time.

In the real world, if you want to refer to this model, one should expect the coefficient of friction to be a function of temperature, normal force, velocity, and other variables I can't think of right now. Imagine automotive tires on a race car: as the temperature changes, the friction will change even though the tire material and the road material and the normal force aren't changing. A closer examination will show that the coefficient of friction is also dependent on the normal force due the the compressibility of the rubber.