Friction
Overview
Static friction: acts when surfaces are stationary relative to each other. Maximum static friction = μ_s · N. Kinetic (sliding) friction: acts when surfaces slide. f_k = μ_k · N. Always μ_k < μ_s — it is harder to start an object moving than to keep it moving. Friction always opposes the relative motion (or tendency of motion).
Static and kinetic friction
Static friction (f_s) acts when there is no relative motion between surfaces; it can take any value from 0 up to a maximum f_s,max = μ_s N. It exactly opposes the applied force until the object is about to move. Kinetic friction (f_k) acts when surfaces slide: f_k = μ_k N (constant magnitude). Always: μ_k < μ_s, so kinetic friction is less than maximum static friction — that's why it's easier to keep something sliding than to start sliding it.
The friction formula and normal force
f_k = μ_k × N. The friction force depends on: the coefficient of friction μ (dimensionless, depends on the materials) and the normal force N (how hard the surfaces press together). Crucially, friction does NOT depend on the contact area or the speed of sliding. On a flat surface, N = mg. On an incline, N = mg cos θ. If you push down on an object, N increases, and so does friction.
- ⚠Using weight (mg) instead of normal force N in f = μN — on inclines N ≠ mg
- ⚠Thinking friction depends on contact area — it doesn't
- ⚠Using μ_s instead of μ_k when the object is already sliding