A-level · Forces & Newton's laws

FrictionExam-style questions

Friction as a force opposing motion, with magnitude up to a maximum F ≤ μR (and F = μR at the point of slipping) — on rough horizontal surfaces and slopes, the angle of friction tanα = μ, and F = ma with friction included.

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

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
Figure 1 (not accurately drawn)

A box of mass $5$ kg is placed on a rough plane which is inclined at an angle $\alpha$ to the horizontal, where $\tan\alpha = \frac{8}{15}$

A horizontal force of magnitude $H$ newtons keeps the box at rest, as shown in Figure 1. The line of action of the force lies in a vertical plane which contains a line of greatest slope of the plane.

The box is modelled as a particle, and the coefficient of friction between the box and the plane is $\frac{1}{3}$
(a) Find the least value of $H$ for which the box remains at rest.

(6 marks)

The horizontal force is removed. Starting from rest, the box slides down a line of greatest slope of the plane.
(b) Find the time taken for the box to slide $2.5$ m down the plane.

(6 marks)
Level 4 · 12 marksTry it
2
Figure 1 (not accurately drawn)

A small block $P$ of mass $m$ lies on a fixed rough plane. The angle between the plane and the horizontal is $\alpha$ , where $\alpha < 45^\circ$

A light inextensible string is attached to $P$ . The string is pulled so that it makes an angle $\alpha$ with the plane, as shown in Figure 1, and the string lies in the vertical plane which contains the line of greatest slope of the inclined plane through $P$ .

The block is modelled as a particle.

The tension in the string is gradually increased. When the tension reaches $0.7mg$ , $P$ is about to slide up the plane.
(a) Find an expression, in terms of $m$ , $g$ and $\alpha$ , for the magnitude of the frictional force acting on $P$ at this instant.

(3 marks)

Given that the coefficient of friction between $P$ and the plane is $\frac{2}{5}$ ,
(b) show that $\tan\alpha = \frac{5}{12}$

(6 marks)

With $P$ still at rest, the string is cut.
(c) Determine, giving a reason, whether $P$ remains in equilibrium.

(3 marks)
Level 4 · 12 marksTry it
3
Figure 1 (not accurately drawn)

A bead of mass $0.6$ kg is threaded on a rough straight wire which is fixed in a vertical position. A light inextensible string is tied to the bead.

The string is pulled upwards at an angle $\theta$ to the wire, where $\tan\theta = \frac{3}{4}$ , as shown in Figure 1. The string and the wire lie in the same vertical plane.

When the tension in the string is $6$ N, the bead is at rest.
(a) Find the magnitude of the frictional force exerted on the bead by the wire.

(3 marks)
(b) State the direction of this frictional force.

(1 mark)

The coefficient of friction between the bead and the wire is $\frac{1}{2}$

The tension in the string is changed to $T$ newtons, with the string still at the angle $\theta$ to the wire. Given that the bead stays at rest,
(c) (i) find the least possible value of $T$

(ii) find the greatest possible value of $T$

(8 marks)
Level 4 · 12 marksTry it
4
A package of mass $5$ kg rests on a rough plane inclined at angle $\theta$ to the horizontal, where $\tan\theta = \dfrac{3}{4}$ . The coefficient of friction between the package and the plane is $0.5$ . Take $g = 9.8$ m s⁻².(a) Find the magnitude of the normal reaction of the plane on the package. (2 marks)
(b) A force of magnitude $P$ newtons, acting up the plane along the line of greatest slope, holds the package on the point of sliding up the plane. Find $P$ . (4 marks)
(c) The force is removed. Determine whether the package slides down the plane, and if it does, find its acceleration. (4 marks)
(d) Find the time the package takes to slide $4$ m from rest. (3 marks)
Level 4 · 13 marksTry it
5
A box of mass $20$ kg rests on a rough horizontal floor. A rope is attached to the box and makes an angle of $30^\circ$ with the horizontal. When the tension in the rope is $98$ N, the box is on the point of sliding. Take $g = 9.8$ m s⁻².
(a) Determine the coefficient of friction between the box and the floor, giving your answer in exact form. (5 marks)
(b) The tension in the rope is now increased to $120$ N, with the rope still at $30^\circ$ to the horizontal. Find the acceleration of the box, giving your answer to 3 significant figures. (5 marks)
Level 4 · 10 marksTry it

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