Law

Friction

f_{s} \leq μ_{s} N, f_{k} = μ_{k} N

Statement

Static friction takes whatever value up to a maximum is needed to prevent sliding; kinetic friction, once sliding starts, has a fixed magnitude proportional to the normal force.

Symbols and units

$f_{s}, f_{k}$	static and kinetic friction force	N
$μ_{s}, μ_{k}$	coefficients of friction	—
$N$	normal force	N

When it applies

Dry, sliding contact between two solid surfaces; μ depends on the pair of materials.

Don't use when

Not applicable to fluid drag or rolling resistance, which follow different force laws.

Derivation

Empirical: friction force is proportional to the normal force pressing the surfaces together, with a coefficient μ set by the pair of materials.

f_{s} \leq μ_{s} N, f_{k} = μ_{k} N

Worked examples

Does the box slide?

A 10 kg box on a surface with μ_s = 0.4 is pushed with 35 N horizontally:

f_{s, m a x} = μ_{s} N = (0.4) (10) (9.8) = 39.2 N

35 N < 39.2 N, so static friction matches the push exactly and the box does not move.

Watch out for

Static friction is not automatically equal to μ_sN — that is only its maximum possible value. Below the sliding threshold, it equals whatever is needed to keep the object at rest.