5.3MechanicsStretch

Friction and the Coefficient of Friction

Friction opposes motion (or attempted motion) between surfaces. It can take any value up to a maximum that depends on the normal reaction and the coefficient of friction μ.

26 min Video by Zeeshan Zamurred Forces and Friction

Edexcel A Level Maths: 5.3 Friction (Fmax and Coefficient of Friction)Watch the full walkthrough before the notes below.

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What you'll be able to do

Understand friction as a variable force
Use F ≤ μR, with F = μR at the point of slipping
Combine friction with resolving and slopes
Decide whether an object moves

Limiting friction

Friction adjusts to prevent motion up to a maximum $F_{m a x} = μ R$ , where $R$ is the normal reaction. At the point of slipping (limiting equilibrium), $F = μ R$ .

F \leq μ R, F_{m a x} = μ R

Friction and the coefficient μ.

F_{m a x} = μ R = 0.4 \times 20

= 8

Answer

8

Tip — Friction is only equal to μR when the object is moving or on the point of slipping; otherwise it is whatever is needed (≤ μR).

Deciding if it moves

Compare the applied (driving) force with $F_{m a x} = μ R$ . If the driving force exceeds $μ R$ , the object moves; otherwise friction holds it in equilibrium.

Formula recap

F \leq μ R

Friction is at most μR.

F_{m a x} = μ R

At the point of slipping.

Common mistakes to avoid

Always setting F = μR.

Only at the point of slipping; otherwise F ≤ μR.

Using the weight instead of the normal reaction in μR.

Use R, which on a slope is mg cos θ (not mg).

Key takeaways

Friction opposes motion, with F ≤ μR.
At the point of slipping, F = μR.
On a slope R = mg cos θ, not mg.

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