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 Forces and Friction

Edexcel A Level Maths: 5.3 Friction (Fmax and Coefficient of Friction)Curated by Kepler, not produced by us. Watch it 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 $F_{\max} = \mu R$ , where $R$ is the normal reaction. At the point of slipping (limiting equilibrium), $F = \mu R$ .

F \le \mu R, \quad F_{\max} = \mu R

Friction and the coefficient μ.

Example 1A block with R = 20 N and μ = 0.4. Find the maximum friction.

F_{\max} = \mu 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 $F_{\max} = \mu R$ . If the driving force exceeds $\mu R$ , the object moves; otherwise friction holds it in equilibrium.

Formula recap

F \le \mu R

Friction is at most μR.

F_{\max} = \mu 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.

Test yourself

Answer a few questions, then review anything you missed.

Prefer paper? Open the written self-check

Answer each question before opening its answer. This self-check does not record a quiz score.

The maximum friction force is:
- $\mu R$
- $\mu mg$ always
- $R$
- $\mu$
Show answer and explanation
Answer: $\mu R$
Coefficient × normal reaction.
Before slipping, friction satisfies:
- $F \le \mu R$
- $F = \mu R$
- $F > \mu R$
- $F = 0$
Show answer and explanation
Answer: $F \le \mu R$
It adjusts up to the max.
With R = 20 N and μ = 0.4, F_max is:
- $8$ N
- $20.4$ N
- $50$ N
- $0.4$ N
Show answer and explanation
Answer: $8$ N
0.4 × 20.
On a slope, the normal reaction is usually:
- $mg\cos\theta$
- $mg$
- $mg\sin\theta$
- $0$
Show answer and explanation
Answer: $mg\cos\theta$
Perpendicular to slope.
The object moves when the driving force:
- exceeds μR
- equals R
- is less than μR
- is zero
Show answer and explanation
Answer: exceeds μR
Friction is overcome.

Next step

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