Real motion, not just a formula. Position and velocity are integrated over time — the block's speed at any instant is genuinely computed from its motion so far, not read off a shortcut equation.
Physics · motion & friction

Inclined Plane

A block on a slope — real friction, real motion, watched live.
a = g(sinθ − μcosθ)
30° · μ 0.30

Ramp & block

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Field notes

Why static and kinetic friction differ

How it works

Three forces, resolved along the slope

Three forces act on the block: gravity (straight down), the normal force (perpendicular to the ramp surface), and friction (along the surface, opposing motion or opposing the tendency to move). Resolve gravity into components parallel and perpendicular to the slope, and Newton's second law along the slope gives a = g(sinθ − μ cosθ) once the block is actually sliding. This tool doesn't stop at the formula — it integrates that acceleration forward through time to get real velocity and real position, frame by frame.

Worked example

At 30° with kinetic friction μₖ = 0.2, the acceleration once sliding is a = 9.81 × (sin30° − 0.2 cos30°) = 9.81 × (0.5 − 0.173) ≈ 3.2 m/s². But whether it starts sliding at all depends on static friction: if tanθ (≈ 0.577 at 30°) exceeds μₛ, gravity wins and it slides; if μₛ is higher than that, the block simply sits there no matter how long you wait.

Why are there two friction coefficients?

Static friction (μₛ) resists the start of motion — it's what holds a stationary block in place. Kinetic friction (μₖ) acts once something is already sliding, and is almost always slightly lower. That's why a stuck object needs a firm push to get going, but slides more easily once moving.

What does "tanθ vs. μₛ" actually mean physically?

tanθ is the ratio of the gravity component pulling the block down the slope to the component pressing it into the slope. μₛ is the maximum friction force available, as a fraction of that same pressing force. If gravity's pull exceeds friction's maximum grip, the block moves — otherwise it doesn't.

Why is mass missing from the acceleration formula?

Both the gravity component along the slope and the normal force scale with mass in exactly the same way, so mass cancels out of the acceleration entirely — a heavier block doesn't slide down faster or slower than a lighter one with the same friction coefficients. (Mass still matters for the actual forces involved, just not for the resulting acceleration.)

What happens right at the boundary, tanθ ≈ μₛ?

In theory it's perfectly balanced and stays put; in practice this is an unstable equilibrium — the smallest disturbance (a vibration, a slightly uneven surface) tips it into sliding. Real designs build in a margin rather than running right at the limit.