Kinetic Friction Force (f = μₖN)

Once a surface is already sliding, friction settles to a nearly constant value proportional to how hard the surfaces are pressed together: f = μₖN. Push a 200 N-loaded crate across a floor with μₖ = 0.3 and it resists with 60 N no matter how fast you shove it. The startling part — that friction depends on load but essentially not on contact area or speed — was established by Guillaume Amontons in 1699 and confirmed in Charles-Augustin de Coulomb's prize-winning 1785 study of rope, axles and rigging for the French navy, work so thorough that dry friction is still called Coulomb friction.

Typical coefficients: rubber on dry asphalt around 0.7, steel on steel about 0.6 lubricated down to 0.05, waxed ski on snow near 0.05, and PTFE on steel about 0.04. The trap is assuming N equals the weight — true only on level ground with no extra push or pull. On a slope N shrinks to mg cos θ, and a downward-angled push or a car's aerodynamic downforce raises it. Note also that kinetic friction always runs slightly below the static maximum, which is why a heavy box lurches forward the instant it breaks free.