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
Figure 1 (not accurately drawn)

The ends of a light inextensible string are fixed to the points $A$ and $B$ on a horizontal beam, where $AB = 0.7$ m. A small smooth ring of mass $M$ kg is threaded on the string.

A horizontal force of magnitude $7$ N is applied to the ring. The ring hangs in equilibrium at the point $C$ , $2.4$ m vertically below $B$ , with the string taut, as shown in Figure 1. The horizontal force acts in the vertical plane containing the string.

The tension in the string is $T$ newtons.
(a) Find the value of $T$

(3 marks)
(b) Find the value of $M$

(3 marks)
Level 3 · 6 marksTry it
2
A particle of weight $50$ N rests on a rough horizontal plane. A force of $20$ N is applied at $30^\circ$ above the horizontal and the particle stays at rest. Find
(a) the normal reaction and (b) the friction force, to 3 s.f. ( $g = 9.8$ .)
Level 3 · 4 marksTry it
3
A particle of mass $4$ kg rests on a rough slope inclined at $25^\circ$ and is on the point of sliding down. Find the coefficient of friction, to 3 s.f.
Level 3 · 2 marksTry it
4
A particle of weight $40$ N hangs in equilibrium from two light strings making $30^\circ$ and $60^\circ$ with the horizontal, on opposite sides. Find the tensions $T_1$ (in the $30^\circ$ string) and $T_2$ (in the $60^\circ$ string), to 3 s.f.
Level 3 · 3 marksTry it
5
A particle of mass $2$ kg rests on a rough slope of $20^\circ$ with coefficient of friction $0.3$ . Find the least force, applied up the slope, needed to stop it sliding down, to 3 s.f. ( $g = 9.8$ .)
Level 3 · 2 marksTry it

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