2.3 Work done and energy transfer — Learn

Prerequisites: Section 2.1, especially weight and resultant forces; Chapter 1, especially energy stores and transfers.

By the end of this section you can: explain what work done means; calculate the work done when a force moves an object; describe the energy transfer that happens; and change between newton-metres and joules.

1. Work done by a force

When a force causes an object to move, work is done on the object. The force must act along the line in which the object moves.

where $W$ is the work done in joules, $F$ is the force in newtons, and $s$ is the distance moved along the line of the force in metres.

One joule of work is done when a force of one newton moves an object one metre. Because a joule can be written as a newton metre, the two units are the same size.

Worked example 1. A force of 75 N pushes a box 6.0 m along the line of the force. Calculate the work done.

Worked example 2. A machine does 600 J of work over a distance of 8.0 m. Calculate the force.

Worked example 3. A force of 120 N does 480 J of work. Calculate the distance moved.

Try it: force, distance and work done

The figure shows the work done as the area of a rectangle on a force-distance graph.

Predict first. Do not move the sliders yet. Write down your answers.

1. A force of 60 N pushes a box 4.0 m. What is the work done?
2. If the force doubles and the distance stays the same, what happens to the work done?
3. If the distance doubles instead, what happens to the work done?

Test. Move the force slider and the distance slider. Watch the area of the rectangle and the value of the work done. Check your three predictions.

Explain. The work done is the product of the force and the distance. Why does doubling either one double the work done? Write your answer in two or three sentences.

2. Work done and energy transfer

Doing work transfers energy from one store to another. The work done is the amount of energy transferred.

• Lifting a box transfers energy from the chemical store of your muscles to the gravitational potential store of the box. The work done is $W = mgh$.
• Pushing a box against friction transfers energy from the kinetic store of the box to the thermal store of the box and the floor. The temperature of the surfaces rises.

Worked example 4. A box of mass 12 kg is lifted 2.5 m onto a shelf. Take $g = 9.8\,\text{N/kg}$. Calculate the work done against gravity.

The force needed is the weight of the box.

The same energy is gained by the gravitational potential store of the box, so $W = mgh$ gives the same answer.

Worked example 5. A friction force of 45 N acts on a crate that slides 12 m. Calculate the work done against friction.

This 540 J is transferred to the thermal store of the crate and the floor.

Watch out. Work is done only by the part of a force that acts along the line of motion. If you carry a heavy bag along a level corridor, your upward force keeps the bag at the same height, so it does no work on the bag. The distance moved is at right angles to the force. Re-check the direction of the force before you use $W = Fs$.

3. Power and work

Power is the rate at which energy is transferred, so it also tells you the rate at which work is done.

Worked example 6. A motor does 1800 J of work in 6.0 s. Calculate the power of the motor.

4. Progress check

Return to the chapter problem. A force of 150 N pushes the bike 8.0 m up the workshop ramp. Work out the work done. Then say which store receives the energy.

You should now be able to

• explain what is meant by work done by a force;
• calculate work done, force or distance, using $W = Fs$;
• describe the energy transfer when work is done, including work done against friction;
• change between newton-metres and joules;
• calculate the power of a transfer from the work done and the time taken.