What is the work done by a constant force acting at 180° to the direction of motion?

The work done is −Fs, a negative quantity, because cos 180° = −1, so the force removes energy from the moving object.

A sledge is pulled 20 m along level ground by a rope with a tension of 150 N at 35° to the horizontal. Calculate the work done by the tension.

The work done is W = Fs cos θ = 150 × 20 × cos 35° = 2.46 × 10³ J, and 2457 J ÷ (150 × 20) = 0.819, which is cos 35°, confirming the result.

Apart from resolving the force, what other way of thinking about W = Fs cos θ gives the same answer?

You can instead resolve the displacement, taking the component s cos θ that lies along the line of the force, since F × (s cos θ) is the same product.

CCEA A-Level Physics 1210

Physical Quantities, Scalars and Vectors

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Work, Energy and Power

Calculating work done, including forces at an angle

3 things to know
Unit AS 1

Overview

Recall questions on W = Fs cos θ and why the cosine appears, the work done by a force at 90° and at 180° to the motion, the two ways of reading the equation, worked problems on a sledge, a lawnmower and a dragged crate, and why the force must be constant.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

State the equation for the work done by a constant force that is not along the line of motion, and define every symbol.

Key term

Why does the factor cos θ appear in the equation for work done by a force acting at an angle to the motion?

Key term

What is the work done by a force that acts at 90° to the direction of motion?

Questions from this subtopic

Each one with the model answer underneath.

1
State the equation for the work done by a constant force that is not along the line of motion, and define every symbol.
Model answer
The work done is W = Fs cos θ, where W is the work done in joules, F the magnitude of the force in newtons, s the distance moved in metres and θ the angle between the direction of the force and the direction of motion.
2
Why does the factor cos θ appear in the equation for work done by a force acting at an angle to the motion?
Model answer
Only the component of the force along the direction of motion does work, and that component has magnitude F cos θ.
3
What is the work done by a force that acts at 90° to the direction of motion?
Model answer
The work done is zero, because cos 90° = 0 and the force has no component along the direction of motion.
4
What is the work done by a constant force acting at 180° to the direction of motion?
Model answer
The work done is −Fs, a negative quantity, because cos 180° = −1, so the force removes energy from the moving object.
5
A sledge is pulled 20 m along level ground by a rope with a tension of 150 N at 35° to the horizontal. Calculate the work done by the tension.
Model answer
The work done is W = Fs cos θ = 150 × 20 × cos 35° = 2.46 × 10³ J, and 2457 J ÷ (150 × 20) = 0.819, which is cos 35°, confirming the result.
6
Apart from resolving the force, what other way of thinking about W = Fs cos θ gives the same answer?
Model answer
You can instead resolve the displacement, taking the component s cos θ that lies along the line of the force, since F × (s cos θ) is the same product.

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