Static Friction

Static friction ($f_s$) is the force that opposes the initiation of sliding motion of an object resting on a surface. For an object at rest with no horizontal force applied, static friction is exactly zero.

When an external force $F_{ext}$ (parallel to the surface) is applied, the surface's static friction exactly matches it in magnitude (opposite in direction), keeping the object at rest — up to a certain maximum. Experimentally, this maximum obeys:

Here $\mu_s$ is the (dimensionless) coefficient of static friction, depending only on the nature of the two surfaces in contact (not on the contact area), and $N$ is the normal force the surface exerts (equal to $mg$ only for a horizontal surface with no other vertical force).

If the applied force exceeds this maximum, $f_{s,max}=\mu_sN$, the surface can no longer supply enough opposing friction, and the object begins to slide. …