Static and Kinetic Friction; Laws of Friction

Friction is the force that appears at the surface of contact between two bodies whenever one tends to slide, or actually slides, over the other, and it always acts along the contact surface, in the direction that opposes the relative sliding motion (or the tendency toward it).

Static friction acts between two surfaces that are not yet sliding relative to each other, but where an applied force is tending to make them slide. Static friction is a self-adjusting force: as an applied force is gradually increased from zero, static friction increases to match it exactly, keeping the body in equilibrium (at rest), right up to a certain maximum value it cannot exceed -- the limiting friction, $f_{s(\text{max})} = \mu_s N$, where $N$ is the normal reaction between the two surfaces and $\mu_s$ is the coefficient of static friction for that particular pair of surfaces. Once the applied force exceeds this limiting value, static friction can no longer hold the body in place, and it begins to slide.

Kinetic friction (also called sliding friction) acts once the two surfaces are actually sliding relative to each other, and it is given, to a good approximation, by $f_k = \mu_k N$, where $\mu_k$ is the coefficient of kinetic friction. For any given pair of surfaces, $\mu_k$ is always somewhat smaller than $\mu_s$, which is exactly why the graph of friction against applied force (the figure accompanying this section) shows a small drop, rather than a smooth continuation, at the moment sliding actually begins -- it is generally a little easier to keep a body sliding once it has started than it was to get it moving from rest in the first place.

The behaviour of both static and kinetic friction is summarised by a small set of (approximate, empirical) laws of friction, found by experiment rather than derived from any more fundamental principle:

1. The force of friction between two given surfaces is directly proportional to the normal reaction $N$ pressing the two surfaces together ($f \propto N$, giving $f = \mu N$).
2. Friction is (to a good approximation) independent of the apparent area of contact between the two surfaces -- a brick resting on its largest face and the same brick resting on its smallest face experience very nearly the same friction against the same floor, for the same weight, because the true (microscopic) area of contact, and not the visible, apparent area, is what actually governs friction.
3. Once sliding has begun, kinetic friction is (to a good approximation) independent of the relative speed of sliding, over ordinary ranges of speed. …