What you are looking at
A block on an adjustable ramp with its four forces drawn live: weight mg straight down, the normal force N
perpendicular to the surface, friction f along the surface, and (dashed) the down-slope component of
gravity, mg·sinθ, that friction has to fight. The meter at the top compares tan θ against μs — the whole
stick–slip story in one bar.
Static friction is lazy — and that's the point
Static friction is not a fixed force. It supplies
exactly as much as needed to prevent sliding —
no more — up to a ceiling set by the surfaces and the normal force:
f_static = mg·sinθ (whatever is needed) ≤ f_max = μs·N = μs·mg·cosθ
The block holds as long as the demand stays below the ceiling: mg·sinθ ≤ μs·mg·cosθ. Cancel mg and you get
the beautifully simple threshold:
tan θ ≤ μs ⇒ θc = atan(μs)
Mass cancels completely — a coin and a brick let go at the same angle. Measuring that angle is the classic
lab method for measuring μs.
Once it slips, it's a different law
Kinetic friction is genuinely weaker than static grip (μk < μs) and roughly constant while sliding:
a = g·(sinθ − μk·cosθ)
That gap between μs and μk is why the block
lurches instead of easing away, why ABS brakes
pump to stay in the static regime, and why chalk squeals on a blackboard — the stick–slip cycle repeating
hundreds of times a second.
Things to try
Tilt up one degree at a time and find the exact release angle; check it equals atan(μs). Change the mass and
confirm the release angle doesn't budge. Then push μk close to μs (slow, smooth start) versus far below it
(violent lurch), and watch the acceleration readout follow g(sinθ − μk cosθ).