When the body is sliding, or on the point of moving (limiting equilibrium).

What direction does friction act?

Parallel to the surface, opposing motion or the tendency to move.

Condition for a block to stay at rest on a slope?

\tan\alpha\le\mu, i.e. mg\sin\alpha\le\mu mg\cos\alpha.

What does \mu=\tan\alpha mean for a block on a slope?

The block is in limiting equilibrium, on the point of sliding.

How do you decide whether a body at rest starts to move?

Compare the friction needed for equilibrium with \mu R; if it is greater, the body moves.

What does 'smooth' mean?

\mu=0: no friction, only a normal reaction.

FrictionAQA A-Level Maths: Flashcards

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State the friction model.

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State the friction model.: $F\le\mu R$ , where $R$ is the normal reaction and $\mu$ the coefficient of friction.
When is $F=\mu R$ ?: When the body is sliding, or on the point of moving (limiting equilibrium).
What direction does friction act?: Parallel to the surface, opposing motion or the tendency to move.
What is limiting friction?: The maximum friction, $\mu R$ .
Does the coefficient of friction have a unit?: No, it is a pure number.
Normal reaction for a mass $m$ on horizontal ground with no other vertical forces?: $R=mg$ .
Normal reaction on a slope of angle $\alpha$ (no other perpendicular forces)?: $R=mg\cos\alpha$ .
Deceleration of a body sliding to rest on horizontal ground?: $\mu g$ , independent of mass.
Condition for a block to stay at rest on a slope?: $\tan\alpha\le\mu$ , i.e. $mg\sin\alpha\le\mu mg\cos\alpha$ .
What does $\mu=\tan\alpha$ mean for a block on a slope?: The block is in limiting equilibrium, on the point of sliding.
A rope pulls at angle $\theta$ above horizontal. What is $R$ ?: $R=mg-T\sin\theta$ .
How do you decide whether a body at rest starts to move?: Compare the friction needed for equilibrium with $\mu R$ ; if it is greater, the body moves.
What does 'smooth' mean?: $\mu=0$ : no friction, only a normal reaction.

Exam questions on Friction

A box of mass $10$ kg rests on rough horizontal ground. The coefficient of friction between the box and the ground is $0.4$ . Take $g=9.8\ \text{m s}^{-2}$ .
A horizontal force of magnitude $30$ N is applied to the box. Find the magnitude of the friction force, justifying your answer.2 marks
A block of mass $5$ kg is placed at rest on a rough plane inclined at $20^\circ$ to the horizontal. The coefficient of friction between the block and the plane is $0.5$ . Take $g=9.8\ \text{m s}^{-2}$ .
Show that the block does remain at rest.2 marks
A crate of mass $20$ kg is pulled from rest along rough horizontal ground by a horizontal rope with tension $90$ N. The coefficient of friction between the crate and the ground is $0.3$ . Take $g=9.8\ \text{m s}^{-2}$ .
Find the acceleration of the crate.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).