Energy and Work Calculations

Work Done and Energy Transfer

Every time you drag a heavy suitcase across an airport floor, you are transferring energy.
In physics, this specific mechanism is known as work done.
Edexcel classifies work done by a force as a mechanical pathway, which is the process that moves energy from one store to another when a system changes.
The amount of energy transferred is exactly equal to the work done, meaning Energy transferred (J) = Work done (J).
When work is done against frictional forces (like braking a bicycle), energy is transferred from the kinetic store to the thermal store of the brakes and surroundings.
When lifting an object, work is done against gravity, transferring energy into the object's gravitational potential energy (GPE) store.
Crucially, work is not done if the object does not move, even if a massive force is applied.
Furthermore, if the movement is exactly perpendicular to the direction of the force (such as carrying a heavy box horizontally at a constant height), zero work is done by that lifting force.

Calculating Work Done

Understanding exactly how much energy is transferred allows engineers to design safe braking distances for vehicles.
The work done is calculated using the following equation:

E = F \times d

Where:

$E$ = work done, or energy transferred, measured in Joules (J)
$F$ = force applied, measured in Newtons (N)
$d$ = distance moved in the direction of the force, measured in metres (m)
One Joule is defined as the work done when a force of $1$ N moves an object through a distance of $1$ m in the direction of the force (meaning $1$ J = $1$ Nm).
If multiple forces act on an object (like a ship's engine pushing forward against water resistance), you must calculate the resultant force to find the work done to accelerate the object.

Worked Examples

How do we apply this formula in an exam situation?

A cyclist applies a braking force of $450$ N to stop their bike. The bike travels $15$ m before coming to a complete stop. Calculate the work done by the brakes.

Step 1: Identify the known values.

$F = 450$ N, $d = 15$ m

Step 2: State the equation and substitute the values.

$E = F \times d$
$E = 450 \times 15$

Step 3: Calculate the final answer with units.

$E = 6750$ J

A crane transfers $120$ kJ of energy while lifting a steel beam. If the crane applies a steady upward force of $8000$ N, calculate the vertical distance the beam is lifted.

Step 1: Convert units to standard SI units.

$120$ kJ = $120{,}000$ J

Step 2: Rearrange the equation to make distance the subject.

$d = E \div F$

Step 3: Substitute the values and calculate.

$d = 120{,}000 \div 8000$
$d = 15$ m

Work and Power

You can slowly push a broken-down car up a hill over an hour, or a powerful tow truck can pull it up in seconds.
The work done in both scenarios is identical, but the power is vastly different.
Power is the rate at which work is done or energy is transferred.
It is calculated using the equation $P = E \div t$ and is measured in Watts (W), where $1$ W equals $1$ J of energy transferred per second.

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Exam Tips

Common Mistake
Students often think work is being done when carrying a heavy object horizontally, but because the movement is perpendicular to the upward lifting force, the work done by that lifting force is actually zero.
2
In Edexcel 'Show that' calculation questions, examiners award a specific mark for showing the substitution of values into the formula; a 'bald' answer with no working will score zero marks.
3
Always check your units before substituting into the equation — you must convert kilojoules (kJ) to Joules (J) and centimetres (cm) to metres (m) to access full marks.
4
If a question asks you to describe the energy transfer when a vehicle brakes, explicitly state that energy is transferred from the kinetic store to the thermal store of the brakes and surroundings.

Key Terms(7)

Work done: The amount of energy transferred when a force causes an object to move through a distance.
Mechanical pathway: The specific energy transfer process used when a force moves an object.
System: An object or a group of objects being studied in physics.
Joules (J): The SI unit of energy; 1 Joule is the work done when a force of 1 Newton moves an object 1 metre in the direction of the force.
Distance moved in the direction of the force: The specific displacement relevant to calculating work done; it excludes any movement at right angles to the applied force.
Resultant force: The single overall force acting on an object when all individual forces are combined.
Power: The rate at which work is done or energy is transferred, measured in Watts (W).

Previous Subtopic: Work Done EquationWork Done Equation Next Subtopic: GPE EquationGPE Equation

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Key Terms(7)

Work done: The amount of energy transferred when a force causes an object to move through a distance.
Mechanical pathway: The specific energy transfer process used when a force moves an object.
System: An object or a group of objects being studied in physics.
Joules (J): The SI unit of energy; 1 Joule is the work done when a force of 1 Newton moves an object 1 metre in the direction of the force.
Distance moved in the direction of the force: The specific displacement relevant to calculating work done; it excludes any movement at right angles to the applied force.
Resultant force: The single overall force acting on an object when all individual forces are combined.
Power: The rate at which work is done or energy is transferred, measured in Watts (W).

Energy and Work Calculations

Work Done and Energy Transfer

Every time you drag a heavy suitcase across an airport floor, you are transferring energy.
In physics, this specific mechanism is known as work done.
Edexcel classifies work done by a force as a mechanical pathway, which is the process that moves energy from one store to another when a system changes.
The amount of energy transferred is exactly equal to the work done, meaning Energy transferred (J) = Work done (J).
When work is done against frictional forces (like braking a bicycle), energy is transferred from the kinetic store to the thermal store of the brakes and surroundings.
When lifting an object, work is done against gravity, transferring energy into the object's gravitational potential energy (GPE) store.
Crucially, work is not done if the object does not move, even if a massive force is applied.
Furthermore, if the movement is exactly perpendicular to the direction of the force (such as carrying a heavy box horizontally at a constant height), zero work is done by that lifting force.

Calculating Work Done

Understanding exactly how much energy is transferred allows engineers to design safe braking distances for vehicles.
The work done is calculated using the following equation:

E = F \times d

Where:

$E$ = work done, or energy transferred, measured in Joules (J)
$F$ = force applied, measured in Newtons (N)
$d$ = distance moved in the direction of the force, measured in metres (m)
One Joule is defined as the work done when a force of $1$ N moves an object through a distance of $1$ m in the direction of the force (meaning $1$ J = $1$ Nm).
If multiple forces act on an object (like a ship's engine pushing forward against water resistance), you must calculate the resultant force to find the work done to accelerate the object.

Worked Examples

How do we apply this formula in an exam situation?

A cyclist applies a braking force of $450$ N to stop their bike. The bike travels $15$ m before coming to a complete stop. Calculate the work done by the brakes.

Step 1: Identify the known values.

$F = 450$ N, $d = 15$ m

Step 2: State the equation and substitute the values.

$E = F \times d$
$E = 450 \times 15$

Step 3: Calculate the final answer with units.

$E = 6750$ J

A crane transfers $120$ kJ of energy while lifting a steel beam. If the crane applies a steady upward force of $8000$ N, calculate the vertical distance the beam is lifted.

Step 1: Convert units to standard SI units.

$120$ kJ = $120{,}000$ J

Step 2: Rearrange the equation to make distance the subject.

$d = E \div F$

Step 3: Substitute the values and calculate.

$d = 120{,}000 \div 8000$
$d = 15$ m

Work and Power

You can slowly push a broken-down car up a hill over an hour, or a powerful tow truck can pull it up in seconds.
The work done in both scenarios is identical, but the power is vastly different.
Power is the rate at which work is done or energy is transferred.
It is calculated using the equation $P = E \div t$ and is measured in Watts (W), where $1$ W equals $1$ J of energy transferred per second.

Sign up to continue reading

Get full access to revision notes, key terms, and exam tips for every subtopic.

Exam Tips

Common Mistake
Students often think work is being done when carrying a heavy object horizontally, but because the movement is perpendicular to the upward lifting force, the work done by that lifting force is actually zero.
2
In Edexcel 'Show that' calculation questions, examiners award a specific mark for showing the substitution of values into the formula; a 'bald' answer with no working will score zero marks.
3
Always check your units before substituting into the equation — you must convert kilojoules (kJ) to Joules (J) and centimetres (cm) to metres (m) to access full marks.
4
If a question asks you to describe the energy transfer when a vehicle brakes, explicitly state that energy is transferred from the kinetic store to the thermal store of the brakes and surroundings.

Key Terms(7)

Work done: The amount of energy transferred when a force causes an object to move through a distance.
Mechanical pathway: The specific energy transfer process used when a force moves an object.
System: An object or a group of objects being studied in physics.
Joules (J): The SI unit of energy; 1 Joule is the work done when a force of 1 Newton moves an object 1 metre in the direction of the force.
Distance moved in the direction of the force: The specific displacement relevant to calculating work done; it excludes any movement at right angles to the applied force.
Resultant force: The single overall force acting on an object when all individual forces are combined.
Power: The rate at which work is done or energy is transferred, measured in Watts (W).

Previous Subtopic: Work Done EquationWork Done Equation Next Subtopic: GPE EquationGPE Equation

Back to Energy and Work Calculations

Put your knowledge into practice — try past paper questions for Physics

Key Terms(7)

Work done: The amount of energy transferred when a force causes an object to move through a distance.
Mechanical pathway: The specific energy transfer process used when a force moves an object.
System: An object or a group of objects being studied in physics.
Joules (J): The SI unit of energy; 1 Joule is the work done when a force of 1 Newton moves an object 1 metre in the direction of the force.
Distance moved in the direction of the force: The specific displacement relevant to calculating work done; it excludes any movement at right angles to the applied force.
Resultant force: The single overall force acting on an object when all individual forces are combined.
Power: The rate at which work is done or energy is transferred, measured in Watts (W).