Work done and energy transfer

What you'll learn

What physicists mean by work done.
How to use and rearrange $W = F s$ .
Why work done is an energy transfer.
How friction can make objects warmer.

The starting point: forces and movement

A force is a push or pull on an object. Forces can change an object’s speed, shape, or direction.

For this topic, the key idea is: a force only does work if it causes movement in the direction of that force.

Definition

Displacement

Displacement means a change in position in a particular direction. In this topic, the specification often describes it as the distance moved along the line of action of the force.

Definition

Line of action

The line of action of a force is the straight line in the direction the force acts. For example, if you pull a box horizontally to the right, the force’s line of action is horizontal to the right.

If you push a wall and it does not move, you may feel tired, but in GCSE physics no work is done on the wall because there is no displacement of the wall.

Key Idea

Work needs force and movement

A force does work on an object when the force causes the object to move through a distance in the direction of the force.

Example

Deciding whether work is done

A student considers three situations:

pushing a stuck door that does not move
lifting a box upwards
carrying a bag horizontally at constant height

Which situations involve work done by the named force?

For the stuck door, there is a force but no displacement of the door. So the pushing force does no work on the door.
For the lifted box, the upward force causes an upward displacement. The force and movement are in the same direction, so work is done on the box.
For the carried bag, the student’s upward support force is vertical, but the bag’s displacement is horizontal. The displacement is not along the line of action of the upward force, so that upward force does no work on the bag in this GCSE model.

Here is the main picture to keep in your head: a force pulls an object through a distance, while friction acts against the motion and transfers energy to thermal stores.

A box pulled horizontally across a rough surface, showing force, displacement, friction, energy transfer, and the equation W equals F s

Work done is an energy transfer

Definition

Work done

Work done is the energy transferred when a force moves an object through a distance along the line of action of the force.

This is why work done is measured in joules, J — the same unit used for energy.

For example, when you lift a bag, energy is transferred from the chemical store in your muscles to the gravitational potential energy store of the bag. You have done work on the bag.

Key Idea

Work done and energy

Whenever work is done, energy is transferred from one store to another.

Example

Describing energy transfer when lifting a book

A student lifts a book from the floor onto a desk. Describe the energy transfer.

The student applies an upward force to the book and the book moves upwards, so the student does work on the book.
Energy is transferred from the chemical energy store of the student’s muscles.
The book gains energy in its gravitational potential energy store because it is now higher above the floor.

The work done equation

The GCSE equation for work done is:

W = F s

where:

$W$ is work done, measured in joules, J
$F$ is force, measured in newtons, N
$s$ is distance moved along the line of action of the force, measured in metres, m

In words:

done=force×distance\text{work done} = \text{force} \times \text{distance}

Tip

Unit check

If force is in newtons and distance is in metres, your answer will be in joules.

Example

Calculating work done

A student pulls a suitcase with a horizontal force of 45 N. The suitcase moves 12 m in the direction of the force. Calculate the work done by the pulling force.

Choose the work done equation because you know force and distance: $W = F s$ .
Substitute the values, keeping the units: $45\ \text{N} \times 12\ \text{m}$ .
Calculate the answer: $540\ \text{J}$ .

Common Mistake

Using the wrong distance

In $W = F s$ , the distance $s$ must be the distance moved along the line of action of the force, not necessarily any random distance mentioned in the question.

Rearranging the equation

You may need to find force or distance instead of work done.

Starting from:

W = F s

To find force:

\frac{W}{s}

To find distance:

\frac{W}{F}

Example

Finding the force needed

A force does 800 J of work on a crate as it moves 5.0 m. Calculate the force.

Choose the rearranged equation because work done and distance are given: $\frac{W}{s}$ .
Substitute the values: $\frac{800\ \text{J}}{5.0\ \text{m}}$ .
Calculate the force: $160\ \text{N}$ .

Tip

A quick rearranging check

If you divide joules by metres, you get newtons. So $\frac{W}{s}$ gives a force, which makes sense.

What exactly is one joule?

One joule of work is done when a force of one newton causes a displacement of one metre in the direction of the force.

So:

m1\ \text{J} = 1\ \text{N m}

A newton-metre and a joule are equivalent units for work done and energy transferred.

Definition

Joule

One joule, J, is the work done when a force of 1 N moves an object 1 m in the direction of the force.

Example

Converting newton-metres and joules

A force calculation gives a result of 72 N m. Write this as work done in joules.

Use the relationship $m1\ \text{J} = 1\ \text{N m}$ .
Match the numerical value: 72 N m is the same amount of work as 72 J.
State the answer using the energy unit: $72\ \text{J}$ .

Common Mistake

Treating N m and J as different sizes

Do not multiply or divide by 1000 when converting between newton-metres and joules. They are equal: 1 N m = 1 J.

Work done against friction

Friction is a contact force that acts to oppose motion between surfaces. If an object slides across a rough surface, friction acts in the opposite direction to the movement.

When work is done against frictional forces, energy is transferred to the thermal energy stores of the object and the surroundings. This causes a rise in temperature.

That is why rubbing your hands together makes them warmer: your muscles do work to move your hands, and friction transfers energy to their thermal stores.

Key Idea

Friction and heating

Work done against friction causes energy to be transferred to thermal stores, so the object and surroundings become warmer.

Example

Calculating energy transferred by friction

A wooden block slides 4.0 m across a rough surface. The frictional force is 15 N. Calculate the energy transferred to thermal stores by friction.

Use the work done equation because friction is a force acting over a distance: $W = F s$ .
Substitute the frictional force and distance: $15\ \text{N} \times 4.0\ \text{m}$ .
Calculate the work done against friction: $60\ \text{J}$ . So 60 J is transferred to thermal stores.

Common Mistake

Friction does not make energy disappear

Friction does not destroy energy. It transfers energy, usually to thermal stores, making the energy less useful for doing mechanical work.

Putting it together

When a force moves an object, work is done. The amount of work depends on:

the size of the force
the distance moved in the direction of that force

A bigger force, or a bigger distance, means more work is done and more energy is transferred.

For GCSE calculations, remember:

W = F s

and:

m1\ \text{J} = 1\ \text{N m}

Exam technique

In the exam

Check that the force actually causes movement along its line of action before saying work is done.
Use $W = F s$ , with force in N and distance in m, then give the answer in J.
For friction questions, explain the energy transfer: work done against friction transfers energy to thermal stores, causing a temperature rise.

Self review

Check yourself

Why is no work done on a wall if you push it but it does not move?
A 25 N force moves an object 3.0 m in the direction of the force. What equation would you use?
What energy store increases when work is done against friction?

Work done and energy transfer

What you'll learn

What physicists mean by work done.
How to use and rearrange $W = F s$ .
Why work done is an energy transfer.
How friction can make objects warmer.

The starting point: forces and movement

A force is a push or pull on an object. Forces can change an object’s speed, shape, or direction.

For this topic, the key idea is: a force only does work if it causes movement in the direction of that force.

Definition

Displacement

Displacement means a change in position in a particular direction. In this topic, the specification often describes it as the distance moved along the line of action of the force.

Definition

Line of action

If you push a wall and it does not move, you may feel tired, but in GCSE physics no work is done on the wall because there is no displacement of the wall.

Key Idea

Work needs force and movement

A force does work on an object when the force causes the object to move through a distance in the direction of the force.

Example

Deciding whether work is done

A student considers three situations:

pushing a stuck door that does not move
lifting a box upwards
carrying a bag horizontally at constant height

Which situations involve work done by the named force?

For the stuck door, there is a force but no displacement of the door. So the pushing force does no work on the door.
For the lifted box, the upward force causes an upward displacement. The force and movement are in the same direction, so work is done on the box.
For the carried bag, the student’s upward support force is vertical, but the bag’s displacement is horizontal. The displacement is not along the line of action of the upward force, so that upward force does no work on the bag in this GCSE model.

Here is the main picture to keep in your head: a force pulls an object through a distance, while friction acts against the motion and transfers energy to thermal stores.

A box pulled horizontally across a rough surface, showing force, displacement, friction, energy transfer, and the equation W equals F s

Work done is an energy transfer

Definition

Work done

Work done is the energy transferred when a force moves an object through a distance along the line of action of the force.

This is why work done is measured in joules, J — the same unit used for energy.

For example, when you lift a bag, energy is transferred from the chemical store in your muscles to the gravitational potential energy store of the bag. You have done work on the bag.

Key Idea

Work done and energy

Whenever work is done, energy is transferred from one store to another.

Example

Describing energy transfer when lifting a book

A student lifts a book from the floor onto a desk. Describe the energy transfer.

The student applies an upward force to the book and the book moves upwards, so the student does work on the book.
Energy is transferred from the chemical energy store of the student’s muscles.
The book gains energy in its gravitational potential energy store because it is now higher above the floor.

The work done equation

The GCSE equation for work done is:

W = F s

where:

$W$ is work done, measured in joules, J
$F$ is force, measured in newtons, N
$s$ is distance moved along the line of action of the force, measured in metres, m

In words:

done=force×distance\text{work done} = \text{force} \times \text{distance}

Tip

Unit check

If force is in newtons and distance is in metres, your answer will be in joules.

Example

Calculating work done

A student pulls a suitcase with a horizontal force of 45 N. The suitcase moves 12 m in the direction of the force. Calculate the work done by the pulling force.

Choose the work done equation because you know force and distance: $W = F s$ .
Substitute the values, keeping the units: $45\ \text{N} \times 12\ \text{m}$ .
Calculate the answer: $540\ \text{J}$ .

Common Mistake

Using the wrong distance

In $W = F s$ , the distance $s$ must be the distance moved along the line of action of the force, not necessarily any random distance mentioned in the question.

Rearranging the equation

You may need to find force or distance instead of work done.

Starting from:

W = F s

To find force:

\frac{W}{s}

To find distance:

\frac{W}{F}

Example

Finding the force needed

A force does 800 J of work on a crate as it moves 5.0 m. Calculate the force.

Choose the rearranged equation because work done and distance are given: $\frac{W}{s}$ .
Substitute the values: $\frac{800\ \text{J}}{5.0\ \text{m}}$ .
Calculate the force: $160\ \text{N}$ .

Tip

A quick rearranging check

If you divide joules by metres, you get newtons. So $\frac{W}{s}$ gives a force, which makes sense.

What exactly is one joule?

One joule of work is done when a force of one newton causes a displacement of one metre in the direction of the force.

So:

m1\ \text{J} = 1\ \text{N m}

A newton-metre and a joule are equivalent units for work done and energy transferred.

Definition

Joule

One joule, J, is the work done when a force of 1 N moves an object 1 m in the direction of the force.

Example

Converting newton-metres and joules

A force calculation gives a result of 72 N m. Write this as work done in joules.

Use the relationship $m1\ \text{J} = 1\ \text{N m}$ .
Match the numerical value: 72 N m is the same amount of work as 72 J.
State the answer using the energy unit: $72\ \text{J}$ .

Common Mistake

Treating N m and J as different sizes

Do not multiply or divide by 1000 when converting between newton-metres and joules. They are equal: 1 N m = 1 J.

Work done against friction

Friction is a contact force that acts to oppose motion between surfaces. If an object slides across a rough surface, friction acts in the opposite direction to the movement.

When work is done against frictional forces, energy is transferred to the thermal energy stores of the object and the surroundings. This causes a rise in temperature.

That is why rubbing your hands together makes them warmer: your muscles do work to move your hands, and friction transfers energy to their thermal stores.

Key Idea

Friction and heating

Work done against friction causes energy to be transferred to thermal stores, so the object and surroundings become warmer.

Example

Calculating energy transferred by friction

A wooden block slides 4.0 m across a rough surface. The frictional force is 15 N. Calculate the energy transferred to thermal stores by friction.

Use the work done equation because friction is a force acting over a distance: $W = F s$ .
Substitute the frictional force and distance: $15\ \text{N} \times 4.0\ \text{m}$ .
Calculate the work done against friction: $60\ \text{J}$ . So 60 J is transferred to thermal stores.

Common Mistake

Friction does not make energy disappear

Friction does not destroy energy. It transfers energy, usually to thermal stores, making the energy less useful for doing mechanical work.

Putting it together

When a force moves an object, work is done. The amount of work depends on:

the size of the force
the distance moved in the direction of that force

A bigger force, or a bigger distance, means more work is done and more energy is transferred.

For GCSE calculations, remember:

W = F s

and:

m1\ \text{J} = 1\ \text{N m}

Exam technique

In the exam

Check that the force actually causes movement along its line of action before saying work is done.
Use $W = F s$ , with force in N and distance in m, then give the answer in J.
For friction questions, explain the energy transfer: work done against friction transfers energy to thermal stores, causing a temperature rise.

Self review

Check yourself

Why is no work done on a wall if you push it but it does not move?
A 25 N force moves an object 3.0 m in the direction of the force. What equation would you use?
What energy store increases when work is done against friction?

Work done and energy transfer

What you'll learn

The starting point: forces and movement

Work done is an energy transfer

The work done equation

Rearranging the equation

What exactly is one joule?

Work done against friction

Putting it together

Recap questions

You've reached the end

Work done and energy transfer

What you'll learn

The starting point: forces and movement

Work done is an energy transfer

The work done equation

Rearranging the equation

What exactly is one joule?

Work done against friction

Putting it together

Recap questions

You've reached the end

Work done and energy transfer

What you'll learn

The starting point: forces and movement

Work done is an energy transfer

The work done equation

Rearranging the equation

What exactly is one joule?

Work done against friction

Putting it together

Recap questions

You've reached the end

Work done and energy transfer Revision Guide

Work done and energy transfer

What you'll learn

The starting point: forces and movement

Work done is an energy transfer

The work done equation

Rearranging the equation

What exactly is one joule?

Work done against friction

Putting it together

Recap questions

You've reached the end

Work done and energy transfer Revision Guide