Kinetic and Static Friction

Friction comes in two kinds. When two surfaces slide, kinetic friction acts: a steady μ_k·N against the slide, the same whether the block creeps or races. When they are not sliding, static friction acts, and this is the one that costs points. It has no fixed value. It pushes back with exactly as much force as it takes to stop slipping, growing as you push harder, up to a ceiling of μ_s·N. Push past that ceiling and the block lets go, and kinetic friction takes over.

Friction costs points in three familiar spots. Calling static friction μ_s·N while the block still sits under a gentle push, instead of the smaller value that just balances it. Assuming friction always points backward, when under a walking foot, a car's drive wheels, or a box in an accelerating truck it points forward. And setting the normal force equal to the weight on an incline, where it is really N = m·g·cosθ, so the friction is μ·m·g·cosθ, not μ·m·g.