Definition

Work done

The energy transferred when a force moves an object through a distance in the direction of the force.

Definition

Line of action

The straight line along which a force acts.

Definition

Joule

The unit of energy, equal to the work done when a force of one newton moves an object one metre along the line of action of the force.

Work is done whenever a force makes an object move.
The work done depends on the size of the force and how far the object moves along the line of action of the force.
The work done is calculated with $done=force×distance\text{work done}=\text{force}\times\text{distance}$ , an equation you must recall.
In symbols the equation is $W = F s$ .
1. $W$ is the work done in joules, $J\text{J}$ .
2. $F$ is the force in newtons, $N\text{N}$ .
3. $s$ is the distance moved along the line of action of the force, in metres, $m\text{m}$ .
One joule of work is done when a force of $N1\ \text{N}$ moves an object through $m1\ \text{m}$ along the line of action of the force.
Rearranging the equation gives $F=WsF=\dfrac{W}{s}$ to find a force and $s=WFs=\dfrac{W}{F}$ to find a distance.

Distance along the line of action

Only movement in the direction of the force counts towards the work done by that force.
When you lift a bag of shopping onto a table, the lifting force acts upwards, so the distance to use is the vertical height the bag is raised.
When you push a wheelie bin along a path, the push acts horizontally, so the distance to use is the horizontal distance moved.
If an object does not move, no work is done on it, however large the force.
1. Pushing hard against a solid wall does no work on the wall, because the wall does not move.
A force at right angles to the motion does no work.
1. When you carry a box along a level corridor, your upward supporting force does no work on the box, because the box moves horizontally, not upwards.
When a force opposes the motion, such as friction or air resistance, work is still done, but it is work done against the motion.

Energy transferred by work

Definition

Energy store

A way in which energy is held by an object or system, such as a kinetic, gravitational, elastic, thermal or chemical store.

Doing work is a way of transferring energy, so the work done by a force equals the energy it transfers.
A transfer by a force is called a mechanical transfer, which is one of the main ways energy moves between stores.
Every time work is done, energy leaves one energy store and enters another.
1. Lifting a box transfers energy from the chemical store of your muscles to the gravitational store of the box.
2. A car engine accelerating a car transfers energy from the chemical store of the fuel to the kinetic store of the car.
3. Stretching a spring transfers energy to the elastic store of the spring.
Work done against friction transfers energy to the thermal stores of the surfaces, which is why your hands warm up when you rub them together.
When a car brakes, the brakes do work against the motion, so energy is transferred from the kinetic store of the car to the thermal store of the brake discs and pads.
To describe a transfer fully, name the force doing the work, the store that loses energy and the store that gains energy.

Example

Work done pushing a wheelie bin

A resident pushes a wheelie bin $m15\ \text{m}$ down a path with a steady horizontal force of $N40\ \text{N}$ .

W = F s

W=40\ \text{N}\times15\ \text{m}=600\ \text{J}

The push does $J600\ \text{J}$ of work, transferring $J600\ \text{J}$ of energy, which is dissipated to the thermal stores of the wheels, the path and the surroundings by friction.

Example

Work done lifting a suitcase

A suitcase with a weight of $N180\ \text{N}$ is lifted at a steady speed onto a luggage rack $m1.6\ \text{m}$ above the floor.
Lifting at a steady speed needs a force equal to the weight, so $NF=180\ \text{N}$ , and the distance along the line of action is the vertical height.

W=Fs=180\ \text{N}\times1.6\ \text{m}=288\ \text{J}

The work done is $J288\ \text{J}$ , so $J288\ \text{J}$ is transferred to the gravitational store of the suitcase.

Example

Distance from the work done

A tow truck does $J36\,000\ \text{J}$ of work pulling a car with a force of $N1800\ \text{N}$ .

s=\dfrac{W}{F}=\dfrac{36\,000\ \text{J}}{1800\ \text{N}}=20\ \text{m}

The car is pulled $m20\ \text{m}$ along the line of the tow rope.

Practical

Work done lifting weights and climbing stairs

Aim: to measure the work done in lifting weights and in walking up a flight of stairs.
Apparatus: a set of $kg1\ \text{kg}$ masses, a top-pan balance, bathroom scales, a metre rule, a tape measure and a flight of stairs.
Method, lifting weights:
- Measure the mass of the load on the top-pan balance and convert it to kilograms.
- Find the weight of the load in newtons by multiplying its mass in kilograms by the gravitational field strength, $N/kg10\ \text{N/kg}$ .
- Stand a metre rule upright on the bench and lift the load steadily from the bench top to a marked height, such as $m0.80\ \text{m}$ .
- Calculate the work done by multiplying the weight by the vertical height.
- Repeat with different loads and heights.
Method, climbing stairs:
- Measure your mass on the bathroom scales and convert it into a weight in newtons.
- Measure the height of one step with the metre rule, holding it vertically against the riser.
- Count the number of steps in the flight and multiply by the height of one step to find the total vertical height.
- Walk up the stairs at a steady pace.
- Calculate the work done against your weight by multiplying your weight by the total vertical height.
Results: a pupil with a weight of $N550\ \text{N}$ who climbs $15$ steps, each $m0.18\ \text{m}$ high, rises $m2.7\ \text{m}$ and does about $J1500\ \text{J}$ of work against their weight.
Conclusion: the work done depends only on the weight lifted and the vertical height gained, not on the length of the staircase or the path taken.
Watch out: the distance along the slope of the stairs is longer than the vertical height, so using it overestimates the work done against weight.
Safety: walk rather than run on the stairs, keep one hand on the rail, and lift loads with a straight back.

Common Mistake

Do not use the distance travelled along a slope or a staircase when the force is the weight, because the distance must be along the line of action of the force.
Do not give work done in newtons, because work done is an energy and is measured in joules.
Do not say that holding a heavy object still does work on it, because the object does not move.

Exam technique

Work done answers

Write $W = F s$ from memory, substitute the values and give the answer in joules.
Say explicitly which distance you used, such as "vertical height", when the question involves lifting.
When asked to describe the energy transfer, name the store that loses energy and the store that gains energy, not only "energy is transferred".
Use "thermal store" rather than "heat energy" when describing work done against friction.

Self review

Write the equation that links work done, force and distance.
What is meant by the line of action of a force?
Why is no work done when you push against a wall that does not move?
Calculate the work done when a $N250\ \text{N}$ force pushes a crate $m3.0\ \text{m}$ along the floor.
Describe the energy transfer when a person lifts a box onto a shelf.

Definition

Work done

The energy transferred when a force moves an object through a distance in the direction of the force.

Definition

Line of action

The straight line along which a force acts.

Definition

Joule

The unit of energy, equal to the work done when a force of one newton moves an object one metre along the line of action of the force.

Work is done whenever a force makes an object move.
The work done depends on the size of the force and how far the object moves along the line of action of the force.
The work done is calculated with $done=force×distance\text{work done}=\text{force}\times\text{distance}$ , an equation you must recall.
In symbols the equation is $W = F s$ .
1. $W$ is the work done in joules, $J\text{J}$ .
2. $F$ is the force in newtons, $N\text{N}$ .
3. $s$ is the distance moved along the line of action of the force, in metres, $m\text{m}$ .
One joule of work is done when a force of $N1\ \text{N}$ moves an object through $m1\ \text{m}$ along the line of action of the force.
Rearranging the equation gives $F=WsF=\dfrac{W}{s}$ to find a force and $s=WFs=\dfrac{W}{F}$ to find a distance.

Distance along the line of action

Only movement in the direction of the force counts towards the work done by that force.
When you lift a bag of shopping onto a table, the lifting force acts upwards, so the distance to use is the vertical height the bag is raised.
When you push a wheelie bin along a path, the push acts horizontally, so the distance to use is the horizontal distance moved.
If an object does not move, no work is done on it, however large the force.
1. Pushing hard against a solid wall does no work on the wall, because the wall does not move.
A force at right angles to the motion does no work.
1. When you carry a box along a level corridor, your upward supporting force does no work on the box, because the box moves horizontally, not upwards.
When a force opposes the motion, such as friction or air resistance, work is still done, but it is work done against the motion.

Energy transferred by work

Definition

Energy store

A way in which energy is held by an object or system, such as a kinetic, gravitational, elastic, thermal or chemical store.

Doing work is a way of transferring energy, so the work done by a force equals the energy it transfers.
A transfer by a force is called a mechanical transfer, which is one of the main ways energy moves between stores.
Every time work is done, energy leaves one energy store and enters another.
1. Lifting a box transfers energy from the chemical store of your muscles to the gravitational store of the box.
2. A car engine accelerating a car transfers energy from the chemical store of the fuel to the kinetic store of the car.
3. Stretching a spring transfers energy to the elastic store of the spring.
Work done against friction transfers energy to the thermal stores of the surfaces, which is why your hands warm up when you rub them together.
When a car brakes, the brakes do work against the motion, so energy is transferred from the kinetic store of the car to the thermal store of the brake discs and pads.
To describe a transfer fully, name the force doing the work, the store that loses energy and the store that gains energy.

Example

Work done pushing a wheelie bin

A resident pushes a wheelie bin $m15\ \text{m}$ down a path with a steady horizontal force of $N40\ \text{N}$ .

W = F s

W=40\ \text{N}\times15\ \text{m}=600\ \text{J}

The push does $J600\ \text{J}$ of work, transferring $J600\ \text{J}$ of energy, which is dissipated to the thermal stores of the wheels, the path and the surroundings by friction.

Example

Work done lifting a suitcase

A suitcase with a weight of $N180\ \text{N}$ is lifted at a steady speed onto a luggage rack $m1.6\ \text{m}$ above the floor.
Lifting at a steady speed needs a force equal to the weight, so $NF=180\ \text{N}$ , and the distance along the line of action is the vertical height.

W=Fs=180\ \text{N}\times1.6\ \text{m}=288\ \text{J}

The work done is $J288\ \text{J}$ , so $J288\ \text{J}$ is transferred to the gravitational store of the suitcase.

Example

Distance from the work done

A tow truck does $J36\,000\ \text{J}$ of work pulling a car with a force of $N1800\ \text{N}$ .

s=\dfrac{W}{F}=\dfrac{36\,000\ \text{J}}{1800\ \text{N}}=20\ \text{m}

The car is pulled $m20\ \text{m}$ along the line of the tow rope.

Practical

Work done lifting weights and climbing stairs

Aim: to measure the work done in lifting weights and in walking up a flight of stairs.
Apparatus: a set of $kg1\ \text{kg}$ masses, a top-pan balance, bathroom scales, a metre rule, a tape measure and a flight of stairs.
Method, lifting weights:
- Measure the mass of the load on the top-pan balance and convert it to kilograms.
- Find the weight of the load in newtons by multiplying its mass in kilograms by the gravitational field strength, $N/kg10\ \text{N/kg}$ .
- Stand a metre rule upright on the bench and lift the load steadily from the bench top to a marked height, such as $m0.80\ \text{m}$ .
- Calculate the work done by multiplying the weight by the vertical height.
- Repeat with different loads and heights.
Method, climbing stairs:
- Measure your mass on the bathroom scales and convert it into a weight in newtons.
- Measure the height of one step with the metre rule, holding it vertically against the riser.
- Count the number of steps in the flight and multiply by the height of one step to find the total vertical height.
- Walk up the stairs at a steady pace.
- Calculate the work done against your weight by multiplying your weight by the total vertical height.
Results: a pupil with a weight of $N550\ \text{N}$ who climbs $15$ steps, each $m0.18\ \text{m}$ high, rises $m2.7\ \text{m}$ and does about $J1500\ \text{J}$ of work against their weight.
Conclusion: the work done depends only on the weight lifted and the vertical height gained, not on the length of the staircase or the path taken.
Watch out: the distance along the slope of the stairs is longer than the vertical height, so using it overestimates the work done against weight.
Safety: walk rather than run on the stairs, keep one hand on the rail, and lift loads with a straight back.

Common Mistake

Do not use the distance travelled along a slope or a staircase when the force is the weight, because the distance must be along the line of action of the force.
Do not give work done in newtons, because work done is an energy and is measured in joules.
Do not say that holding a heavy object still does work on it, because the object does not move.

Exam technique

Work done answers

Write $W = F s$ from memory, substitute the values and give the answer in joules.
Say explicitly which distance you used, such as "vertical height", when the question involves lifting.
When asked to describe the energy transfer, name the store that loses energy and the store that gains energy, not only "energy is transferred".
Use "thermal store" rather than "heat energy" when describing work done against friction.

Self review

Write the equation that links work done, force and distance.
What is meant by the line of action of a force?
Why is no work done when you push against a wall that does not move?
Calculate the work done when a $N250\ \text{N}$ force pushes a crate $m3.0\ \text{m}$ along the floor.
Describe the energy transfer when a person lifts a box onto a shelf.

2.2.13 Work done by a force

Distance along the line of action

Energy transferred by work

Work done pushing a wheelie bin

Work done lifting a suitcase

Distance from the work done

Work done lifting weights and climbing stairs

Work done answers

Review 2.2.13 Work done by a force by teaching Genie

2.2.13 Work done by a force

Distance along the line of action

Energy transferred by work

Work done pushing a wheelie bin

Work done lifting a suitcase

Distance from the work done

Work done lifting weights and climbing stairs

Work done answers

Review 2.2.13 Work done by a force by teaching Genie

2.2.13 Work done by a force

Distance along the line of action

Energy transferred by work

Work done pushing a wheelie bin

Work done lifting a suitcase

Distance from the work done

Work done lifting weights and climbing stairs

Work done answers

Review 2.2.13 Work done by a force by teaching Genie

2.2.13 Work done by a force Revision Guide

2.2.13 Work done by a force

Distance along the line of action

Energy transferred by work

Work done pushing a wheelie bin

Work done lifting a suitcase

Distance from the work done

Work done lifting weights and climbing stairs

Work done answers

Review 2.2.13 Work done by a force by teaching Genie

2.2.13 Work done by a force Revision Guide