Inclined Plane Calculator
Use the inclined plane calculator to solve exercises about objects sliding down an inclined plane with a friction coefficient.
The formula
F = µN, with N = mg cos θ on a slope
Area does not appear, and neither does mass
Friction is proportional to the force pressing the surfaces together, not to how much of them touch. A wide tyre and a narrow one of the same rubber, under the same load, generate the same friction in the simple model. Real tyres are more complicated, but the first-order result is genuinely area-independent.
The angle at which an object begins to slide is arctan µ, with no mass term at all — because increasing the mass raises the driving component and the friction in exactly the same proportion. A heavy crate and a light one of the same material slide at the same angle, which is a reliably surprising result.
Static friction is usually larger than kinetic, so more force is needed to start something moving than to keep it moving. That is the jerk you feel when a stuck drawer finally gives, and it is why this page takes a single coefficient: use the static value to ask whether it moves, and the kinetic value to ask how fast.