Coefficient of Friction
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flagWhat you'll discover
- arrow_forwardDefine static and kinetic coefficients of friction
- arrow_forwardMeasure the angle of repose and use μₛ = tan θᵣ
- arrow_forwardFind μ from a horizontal pull with a spring balance
- arrow_forwardShow that friction depends on the surfaces, not the contact area
Static vs kinetic friction
Friction is the contact force opposing relative sliding. While the block is still, static friction matches your push exactly, up to a maximum fₛ(max) = μₛN. Once sliding starts, kinetic friction takes over with the slightly smaller value f = μₖN — which is why a block "breaks free" and then accelerates.
Both coefficients depend only on the pair of surfaces (wood on wood ≈ 0.3-0.5, rubber on concrete ≈ 0.7, ice ≈ 0.05) and, surprisingly, not on the apparent contact area. Flip a brick onto its small face and it slides at the same angle.
Method 1: angle of repose
Tilt the plane slowly. Gravity’s component along the slope is mg sinθ while the maximum static friction is μₛ mg cosθ. The block slips at the instant mg sinθ exceeds μₛ mg cosθ, i.e. at tanθᵣ = μₛ. Measure the angle of repose θᵣ and the coefficient drops out with no force measurement at all — the mass even cancels.
Raise the angle in tiny steps near the slipping point, and repeat several times taking the mean. The "just slips" moment is genuinely fuzzy on real surfaces (dust, humidity), which is the main random error in this method.
Method 2: horizontal pull, and precautions
On a horizontal table, pull the block through a spring balance. The reading when the block JUST starts to move equals μₛN = μₛmg; while it slides steadily at constant speed the reading equals μₖmg. Keep the string horizontal — an angled pull lifts the block and reduces N, faking a smaller μ.
Precautions: clean and dust the surfaces, pull smoothly without jerks, read the balance at eye level, and add weights to repeat with different normal forces — the graph of limiting friction vs N is a straight line through the origin whose slope is μ. Report tanθᵣ and the pull method side by side and discuss why they differ slightly.