Friction

The idea

Friction opposes motion or the tendency to move, and can grow up to a limit: $F \le \mu R$ . When sliding, or about to slide (limiting equilibrium), $F = \mu R$ .

Find the normal reaction $R$ first.
Maximum friction $= \mu R$ .
If the pulling force is bigger, the object moves: resultant $= ma$ . If not, friction just balances it.

Watch out Friction is only $\mu R$ when the object is moving or about to move.

See it worked

Worked example

A $10\text{ kg}$ box on a rough floor ( $\mu = 0.3$ ) is pulled horizontally with $50\text{ N}$ . Find its acceleration.

$R = 10g = 98\text{ N}$ ; maximum friction $= 0.3 \times 98 = 29.4\text{ N}$ .
$50 > 29.4$ , so it moves: $50 - 29.4 = 10a$ .
$a = 2.06\text{ m s}^{-2}$ .

Answer $2.06\text{ m s}^{-2}$

Your turn

Question 1Non-calculator3 marks

A $5\text{ kg}$ block rests on rough horizontal ground with $\mu = 0.4$ . Find the limiting friction.

Question 2Calculator allowed3 marks

A $3\text{ kg}$ box on rough horizontal ground ( $\mu = 0.5$ ) is pulled horizontally with $20\text{ N}$ . Find its acceleration to 3 significant figures.

Question 3Calculator allowed3 marks

A block is on the point of slipping down a rough plane inclined at $25^\circ$ . Find $\mu$ to 3 significant figures.

In past papers

43 official questions in 29 papers since 2018. The latest:

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