Friction

Friction opposes the relative sliding of two surfaces in contact, and to first approximation it depends on only two things: the normal force pressing the surfaces together, and a coefficient that captures how rough or smooth that particular pair of surfaces is. f = μN. Neither the size of the contact patch nor how fast anything is moving appears in this simple model — a brick lying flat and the same brick standing on its narrow edge experience approximately the same friction, because although the standing brick has less contact area, the pressure per unit area is correspondingly higher, and the two effects cancel in this approximation.

Static friction is what must be overcome before motion starts at all, and it adjusts itself: pushing gently on a stationary box, static friction matches your push and the box stays put, right up until your push exceeds its maximum available value, μₛN. That maximum is a ceiling, not a fixed force — static friction is whatever is needed to prevent sliding, up to that limit.

Once sliding begins, kinetic friction takes over, and it is described by its own coefficient, μₖ, which is typically slightly smaller than μₛ. This is why a heavy object often "breaks free" with a jerk — the force needed to start it sliding briefly exceeds the (smaller) force needed to keep it sliding, so the object accelerates suddenly the instant it starts moving. Pressing down harder increases N and so increases both static and kinetic friction proportionally, which is why a fully loaded crate is harder to start sliding, and once sliding, harder to keep sliding, than an empty one.