Block on a Friction Ramp: Finding the Static-Friction Threshold

1 · Predict

A block sits on a fixed 30° ramp, currently held in place by static friction. If you lower the friction between the block and the ramp, will it start to slide — and at what point?

Two rules apply in order. The block holds for any μs ≥ tan(30°) ≈ 0.58, regardless of mass — and once it lets go, it is μk, not μs, that sets how fast it accelerates.
The block will slip a little more each time you lower μs, even while μs is still above tan(30°) — friction just gets weaker gradually.
A heavier block needs a lower μs to start sliding than a lighter one — mass affects the threshold too.

2 · Set Up

Open the Friction Ramp preset. Note the ramp's fixed tilt angle (30°) and the block sitting on it, currently held static by friction.
Use the Properties panel (or a shared link) to set the block's coefficients of static (μs) and kinetic (μk) friction for this trial. Keep μk ≤ μs — the app enforces it, since a surface cannot grip less when at rest than it does while sliding. Mass stays fixed.
Run the simulation for a few seconds and read the block's speed off the probe. Record whether it stayed at rest or began sliding.

3 · Collect Data

Block Mass (kg)	Static Friction (μs)	Kinetic Friction (μk)
1.00	0.90	0.40
2.00	0.70	0.40
3.00	0.50	0.40
2.00	0.50	0.30
2.00	0.50	0.20

Graph Gravity Force Along Ramp (y-axis) against Block Mass (x-axis) for all five trials. Is the relationship a straight line? What does the slope represent? Three rows use the same mass — do they also share the same driving force?

4 · Analyze

For each row, compute tan(30°) and compare it to your μs value. Does that comparison predict whether the block stays at rest?
Rows 1–2 stay put; rows 3–5 slide, at three different rates. Explain why mass drops out of BOTH the static-friction condition and the sliding acceleration, even though these rows use three different masses.

5 · Extend

There are two ways to make the block let go: lower its μs until it falls below tan(30°) ≈ 0.577, or steepen the ramp until the angle passes atan(μs) ≈ 35°. Try both. Are they really the same condition written two ways?
A hiking boot sole and a smooth dress shoe have very different μs values on the same wet trail. Explain, in terms of this experiment, why one is much safer on a steep slope than the other.

The Physics Behind This Experiment

Gravity Component Along the Incline

F = m·a applied with a = g sin θ gives the piece of the block's weight that pulls it down the slope. Static friction has to cancel it completely for the block to stay put; once the block slides, kinetic friction only cancels part of it.

Kinetic Friction Force

Once the block is actually sliding, friction stops being a threshold and becomes a definite force: f = μk·m·g·cos θ, where μk is the coefficient of KINETIC friction. It is subtracted from the gravity component along the slope, so the block accelerates at g(sin θ − μk·cos θ) rather than the frictionless g·sin θ. Mass cancels from that expression entirely, which is why the sliding rows below do not depend on it.

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Mechanics

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