A-level · Work, energy & power

Work done by a forceExam-style questions

The work done by a constant force, W = Fd when the force is along the motion and W = Fd cosθ when it acts at an angle, together with work done against gravity and against resistance — and the sign convention that makes a force opposing the motion do negative work.

Start practising Read the lesson

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

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
Figure 1Diagram not accurately drawn.

A straight plank is fixed with its lower end on horizontal ground and its upper end on top of a vertical wall. The plank is inclined to the horizontal at an angle $\theta$ , where $\tan\theta = \frac{5}{12}$ , and the upper surface of the plank is rough.

A small block of mass $3$ kg is projected up the plank from the point $A$ with speed $U\ \text{m s}^{-1}$ . The block slides along a line of greatest slope of the plank and comes to instantaneous rest at the point $B$ , as shown in Figure 1. The point $B$ is $1.5$ m vertically above $A$ .

The coefficient of friction between the block and the plank is $\frac{1}{4}$

The block is modelled as a particle.
(a) Find the work done by the block against friction as it travels from $A$ to $B$ .

(3 marks)
(b) Use the work–energy principle to find the value of $U$ .

(4 marks)

The block then slides back down the plank.
(c) Use the work–energy principle to find the speed with which the block passes back through $A$ .

(3 marks)
Level 4 · 10 marksTry it
2
A small ring $P$ of mass $m$ is threaded on a fixed rough straight wire. The wire lies in a vertical plane and is inclined to the horizontal at an angle $\alpha$ , where $\tan\alpha = \frac{8}{15}$

The coefficient of friction between $P$ and the wire is $\frac{1}{3}$

The ring is modelled as a particle.
(a) Show that, while $P$ is moving along the wire, the magnitude of the frictional force acting on $P$ is $\frac{5}{17}mg$

(2 marks)

The points $A$ and $B$ lie on the wire, with $B$ higher than $A$ and $AB = 17a$ , where $a$ is a positive constant. The ring is projected up the wire from $A$ and first comes to instantaneous rest at $B$ .
(b) Use the work–energy principle to find, in terms of $a$ and $g$ , the speed with which $P$ is projected from $A$ .

(4 marks)

The ring then slides back down the wire towards $A$ .
(c) Use the work–energy principle to find, in terms of $a$ and $g$ , the speed with which $P$ passes back through $A$ .

(4 marks)
Level 4 · 10 marksTry it
3
A block of mass $2\text{ kg}$ is released from rest and slides $5\text{ m}$ down the line of greatest slope of a rough plane inclined at angle $\theta$ , where $\sin\theta = 0.6$ . It reaches the bottom moving at $5\text{ m s}^{-1}$ . Take $g = 10\text{ m s}^{-2}$ .
(a) Find the potential energy lost. (2 marks)
(b) Find the kinetic energy gained. (1 mark)
(c) Hence find the work done against friction. (2 marks)
Level 4 · 5 marksTry it
4
A force acts on a sledge along its direction of motion. Over a $12\text{ m}$ stretch the force decreases uniformly from $50\text{ N}$ to $20\text{ N}$ .

Find the work done by the force over this stretch. (3 marks)
Level 4 · 3 marksTry it