A-level · Forces & Newton's laws

Statics — equilibrium under several forcesExam-style questions

A particle in equilibrium has zero resultant, so resolving in two perpendicular directions gives two equations — used to find unknown forces or angles, including on rough slopes where friction is at its limit (F = μR) on the point of moving.

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17 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
A crate of mass $8$ kg is placed on a rough plane inclined at $25^{\circ}$ to the horizontal. The coefficient of friction is $0.6$ .

Show that the crate remains at rest, and find the magnitude of the frictional force acting on it. (5 marks)
Level 4 · 5 marksTry it
2
A uniform rod $AB$ , of length $2a$ and mass $M$ , rests with $A$ on rough horizontal ground and with the point $C$ of the rod in contact with a small smooth fixed horizontal peg, where $AC = 1.6a$

The rod makes an angle $\theta$ with the ground and is in a vertical plane at right angles to the peg, as shown in Figure 1.Diagram not accurately drawn.

The force exerted on the rod by the peg has magnitude $S$ .
(a) By taking moments about $A$ , show that

$S = \frac{5}{8}Mg\cos\theta$

(3 marks)

Given that $\tan\theta = \dfrac{5}{12}$ and that the rod is about to slip,
(b) find the coefficient of friction between the rod and the ground, giving your answer to 2 significant figures.

(6 marks)
Level 4 · 9 marksTry it