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 sledge $P$ of mass $m$ is pulled up a rough slope by a rope. The slope is modelled as a rough plane inclined to the horizontal at an angle $\alpha$ , where $\tan\alpha = \frac{7}{24}$

The sledge is modelled as a particle and the rope is modelled as a light inextensible string.

The rope is inclined to the slope at an angle $\beta$ , where $\tan\beta = \frac{3}{4}$ , and the tension in the rope is $\frac{4}{5}mg$ , as shown in Figure 1. The rope lies in the vertical plane containing a line of greatest slope of the plane.

The coefficient of friction between the sledge and the slope is $\frac{1}{4}$

The sledge starts from rest at the point $A$ on the slope and moves up the line of greatest slope through $A$ .
(a) Show that the acceleration of the sledge is $\frac{6}{25}g$

(8 marks)

The sledge passes through the point $B$ , where $AB = 3$ m.
(b) Find the speed of the sledge at $B$ .

(2 marks)

When the sledge reaches $B$ , the rope is released. The sledge continues to move up the slope and comes to instantaneous rest at the point $C$ .
(c) Find the distance $BC$ .

(3 marks)
(d) Determine whether the sledge remains at rest at $C$ . You must justify your reasoning.

(2 marks)
Level 5 · 15 marksTry it
2
A box of mass $8$ kg rests on a rough horizontal floor. The coefficient of friction between the box and the floor is $0.25$ . A rope pulls the box with a force of $40$ N at an angle of $30^\circ$ above the horizontal. Take $g = 9.8$ m s⁻².(a) Show that the normal reaction of the floor on the box is $58.4$ N. (3 marks)
(b) Explain why the normal reaction is less than the weight of the box, and find the acceleration of the box. (6 marks)
(c) When the box is moving at $6$ m s⁻¹, the rope is released. Find the distance the box travels before coming to rest. (4 marks)
Level 5 · 13 marksTry it
3
A parcel of mass $11$ kg is at rest on a rough plane inclined at an angle $\alpha$ to the horizontal, where $\tan\alpha = \dfrac{3}{4}$ . The coefficient of friction between the parcel and the plane is $\dfrac{1}{2}$ .

A horizontal force of magnitude $P$ newtons acts on the parcel, in the vertical plane containing a line of greatest slope of the inclined plane, in the direction that tends to push the parcel up the slope. Take $g = 9.8$ m s⁻².
(a) Given that the parcel is on the point of sliding up the plane, show that $P = 215.6$ . (5 marks)
(b) Find the range of values of $P$ for which the parcel remains at rest. (4 marks)
(c) The force is removed. Show that the parcel begins to slide down the plane, and find its speed after it has travelled $2$ m. (4 marks)
Level 5 · 13 marksTry it
4
Figure 3 shows a block of mass $15$ kg resting on a rough horizontal floor. A force of magnitude $P$ N is applied to the block at an angle of $20^\circ$ above the horizontal.Figure 3 (not accurately drawn)

The coefficient of friction between the block and the floor is $0.35$ . Take $g = 9.8$ m s⁻².
(a) Find the value of $P$ for which the block is on the point of moving, giving your answer to $3$ significant figures. (6 marks)
(b) Find the acceleration of the block when $P = 70$ , giving your answer to $3$ significant figures. (4 marks)
Level 5 · 10 marksTry it
5
In this question use $g = 9.8\ \text{m s}^{-2}$

A roofer is working on a rough roof that slopes at $30^\circ$ to the horizontal. Along a line of greatest slope, the roof measures $6$ metres from its lower edge to its top edge.

A bag of tools, of mass $15$ kg, rests on the roof at the point $A$ . The point $O$ is on the lower edge of the roof, directly down the slope from $A$ .

The roofer, standing at the top edge, hauls the bag up the roof with a rope. The rope runs straight up the roof from the bag, along a line of greatest slope, and is kept taut throughout.
(a) The roofer pulls on the rope with a constant force of $170$ N. The bag moves from rest with an acceleration of $0.5\ \text{m s}^{-2}$ up the roof.

Find the coefficient of friction between the bag and the roof.

(7 marks)
(b) (i) The bag reaches the top edge of the roof $4$ seconds after it starts to move.

Find the distance of $A$ from $O$ .

(ii) Apart from ignoring air resistance, state one modelling assumption about the bag on which your answer to part (b)(i) depends.

(4 marks)
Level 5 · 11 marksTry it

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