Newton's Third Law

What you'll learn

How to state Newton’s Third Law clearly.
How to identify the two forces in a third-law pair.
How third-law pairs are different from balanced forces.
How to apply the law to equilibrium situations.

The ideas you need first

A force is a push or pull on an object. Forces can be caused by contact interactions, like a hand pushing a wall, or non-contact interactions, like the Earth pulling a book down by gravity.

A force is a vector, which means it has both a size and a direction. The size of a force is called its magnitude, measured in newtons (N).

When several forces act on one object, we often care about their overall effect.

Definition

Resultant force

The resultant force is the single overall force on an object after all the forces acting on that object have been combined. If the resultant force is not zero, the object accelerates.

Definition

Equilibrium

An object is in equilibrium when its resultant force is zero, so it has no acceleration. It may be stationary, or it may be moving at a constant velocity.

Example

Checking equilibrium

A box has a force of $N8\ \text{N}$ pulling it to the right and a force of $N5\ \text{N}$ pulling it to the left. Is it in equilibrium horizontally?

Consider only the forces acting on the box in the horizontal direction: $N8\ \text{N}$ right and $N5\ \text{N}$ left.
Subtract the smaller opposing force from the larger one: $NF_\text{resultant} = 8\ \text{N} - 5\ \text{N} = 3\ \text{N}$ to the right.
Since the resultant force is not zero, the box is not in equilibrium horizontally. If it is free to move, it will accelerate to the right.

Newton’s Third Law

Newton’s Third Law is about what happens when two objects interact.

Definition

Newton's Third Law

Whenever two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction.

This means forces come in pairs:

object A exerts a force on object B
object B exerts a force on object A
the two forces are the same size
the two forces act in opposite directions
the two forces act on different objects

A useful way to write a force pair is:

“force of A on B”
“force of B on A”

That wording helps you keep track of which object each force acts on.

Key Idea

The key phrase

A Newton’s Third Law pair is equal and opposite, but the two forces act on different objects.

Example

Identifying a force pair in a push

A student pushes a wall with a force of $N40\ \text{N}$ forwards. What force does the wall exert on the student?

Identify the two interacting objects: the student and the wall.
The student exerts a force of $N40\ \text{N}$ on the wall, so Newton’s Third Law says the wall exerts an equal-sized force on the student.
The wall’s force is in the opposite direction, so the wall exerts a force of $N40\ \text{N}$ backwards on the student.

Third-law pairs are not the same as balanced forces

This is the most important exam distinction in this topic.

Balanced forces act on the same object and can make the resultant force zero.

A Newton’s Third Law pair acts on two different objects, so the two forces do not cancel each other out for one object.

The diagram below shows the difference for a book resting on a table.

Diagram comparing balanced forces on a book with the Newton's third law pair between the book and table

Common Mistake

Cancelling a third-law pair

Do not add “table on book” and “book on table” together to find the resultant force on the book. One of those forces acts on the table, not on the book.

Book on a table

For a book resting on a table, there are two different ideas happening at once.

For the book’s equilibrium, look only at forces acting on the book:

the Earth pulls the book down with its weight
the table pushes the book up with a contact force

If the book is stationary, these two forces are balanced.

For Newton’s Third Law, look at force pairs between two objects:

the table pushes up on the book
the book pushes down on the table

Those two forces form a third-law pair because they are the same interaction between the book and the table.

Example

Sorting balanced forces from third-law pairs

A book rests on a table. The table pushes up on the book with $N12\ \text{N}$ . The book’s weight is also $N12\ \text{N}$ downwards.

To check equilibrium of the book, include only forces acting on the book: $N12\ \text{N}$ up from the table and $N12\ \text{N}$ down from the Earth.
These two forces are equal and opposite on the same object, so the resultant force on the book is zero.
The third-law pair for “table on book” is not the book’s weight. It is “book on table”, a $N12\ \text{N}$ downward force acting on the table.
The third-law pair for the book’s weight is the gravitational force of the book pulling on the Earth.

Applying Newton’s Third Law to equilibrium situations

The spec expects you to apply Newton’s Third Law to examples where objects are in equilibrium.

The method is:

Choose the object you are analysing.
Identify the forces acting on that object.
Use equilibrium to say the resultant force is zero.
If asked for a third-law pair, name the force on the other object.

Key Idea

Equilibrium is a one-object question

To decide whether an object is in equilibrium, only combine forces acting on that one object.

Example

A hanging mass in equilibrium

A mass of $kg2.0\ \text{kg}$ hangs still from a string. Take gravitational field strength as $9.8\ \text{N/kg}$ . Find the tension in the string, then identify the third-law pair for the tension force.

Calculate the weight of the mass using $W = m g$ :
$2.0\ \text{kg} \times 9.8\ \text{N/kg} = 19.6\ \text{N}$ downwards.
The mass is hanging still, so it is in equilibrium. The upward tension on the mass must therefore be $N19.6\ \text{N}$ .
The third-law pair for “string pulls up on mass” is “mass pulls down on string”. This force is also $N19.6\ \text{N}$ , but it acts on the string.

Equal forces can have different effects

A common question is: if forces are equal and opposite, why does one object sometimes move more than the other?

The answer is that the forces are equal, but the objects may have different masses. Acceleration depends on both force and mass:

F = ma

So for the same force, a smaller mass has a larger acceleration.

For example, when a car and a lorry collide, the car pushes on the lorry and the lorry pushes on the car with equal-sized forces. But the car usually has a much smaller mass, so its acceleration is larger.

Example

Comparing accelerations in a collision

A car of mass $kg1000\ \text{kg}$ and a lorry of mass $kg6000\ \text{kg}$ exert forces of $N3000\ \text{N}$ on each other during a collision. Compare their accelerations.

Use Newton’s Third Law first: the force on the car and the force on the lorry are equal in size, $N3000\ \text{N}$ , but opposite in direction.
Use $\frac{F}{m}$ for the car:
$\frac{3000\ \text{N}}{1000\ \text{kg}} = 3.0\ \text{m/s}^2$ .
Use $\frac{F}{m}$ for the lorry:
$\frac{3000\ \text{N}}{6000\ \text{kg}} = 0.50\ \text{m/s}^2$ .
The car has the larger acceleration because it has the smaller mass, even though the forces are equal in size.

Tip

A high-value sentence

When explaining Newton’s Third Law, write: “The forces are equal and opposite, but they act on different objects.”

Everyday examples

Walking

When you walk, your foot pushes backwards on the ground. The ground pushes forwards on your foot. That forward force helps accelerate you forwards.

Swimming

A swimmer pushes water backwards. The water pushes the swimmer forwards with an equal and opposite force.

Rocket launch

A rocket pushes hot gases downwards. The gases push the rocket upwards with an equal and opposite force.

In each case, do not just say “action and reaction”. Say clearly which object acts on which other object.

Exam technique

In the exam

Use “force of A on B” and “force of B on A” wording to identify a third-law pair clearly.
For equilibrium questions, choose one object and only combine forces acting on that object.
If two objects have different accelerations, explain that the forces are equal but the masses may be different.

Self review

Check yourself

A swimmer pushes water backwards. What is the Newton’s Third Law force pair?
Why are the upward contact force on a book and the book’s weight not a third-law pair?
A mass hangs still from a string. Which forces are balanced, and what is the third-law pair for the tension?

Newton's Third Law

What you'll learn

How to state Newton’s Third Law clearly.
How to identify the two forces in a third-law pair.
How third-law pairs are different from balanced forces.
How to apply the law to equilibrium situations.

The ideas you need first

A force is a vector, which means it has both a size and a direction. The size of a force is called its magnitude, measured in newtons (N).

When several forces act on one object, we often care about their overall effect.

Definition

Resultant force

The resultant force is the single overall force on an object after all the forces acting on that object have been combined. If the resultant force is not zero, the object accelerates.

Definition

Equilibrium

An object is in equilibrium when its resultant force is zero, so it has no acceleration. It may be stationary, or it may be moving at a constant velocity.

Example

Checking equilibrium

A box has a force of $N8\ \text{N}$ pulling it to the right and a force of $N5\ \text{N}$ pulling it to the left. Is it in equilibrium horizontally?

Consider only the forces acting on the box in the horizontal direction: $N8\ \text{N}$ right and $N5\ \text{N}$ left.
Subtract the smaller opposing force from the larger one: $NF_\text{resultant} = 8\ \text{N} - 5\ \text{N} = 3\ \text{N}$ to the right.
Since the resultant force is not zero, the box is not in equilibrium horizontally. If it is free to move, it will accelerate to the right.

Newton’s Third Law

Newton’s Third Law is about what happens when two objects interact.

Definition

Newton's Third Law

Whenever two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction.

This means forces come in pairs:

object A exerts a force on object B
object B exerts a force on object A
the two forces are the same size
the two forces act in opposite directions
the two forces act on different objects

A useful way to write a force pair is:

“force of A on B”
“force of B on A”

That wording helps you keep track of which object each force acts on.

Key Idea

The key phrase

A Newton’s Third Law pair is equal and opposite, but the two forces act on different objects.

Example

Identifying a force pair in a push

A student pushes a wall with a force of $N40\ \text{N}$ forwards. What force does the wall exert on the student?

Identify the two interacting objects: the student and the wall.
The student exerts a force of $N40\ \text{N}$ on the wall, so Newton’s Third Law says the wall exerts an equal-sized force on the student.
The wall’s force is in the opposite direction, so the wall exerts a force of $N40\ \text{N}$ backwards on the student.

Third-law pairs are not the same as balanced forces

This is the most important exam distinction in this topic.

Balanced forces act on the same object and can make the resultant force zero.

A Newton’s Third Law pair acts on two different objects, so the two forces do not cancel each other out for one object.

The diagram below shows the difference for a book resting on a table.

Diagram comparing balanced forces on a book with the Newton's third law pair between the book and table

Common Mistake

Cancelling a third-law pair

Do not add “table on book” and “book on table” together to find the resultant force on the book. One of those forces acts on the table, not on the book.

Book on a table

For a book resting on a table, there are two different ideas happening at once.

For the book’s equilibrium, look only at forces acting on the book:

the Earth pulls the book down with its weight
the table pushes the book up with a contact force

If the book is stationary, these two forces are balanced.

For Newton’s Third Law, look at force pairs between two objects:

the table pushes up on the book
the book pushes down on the table

Those two forces form a third-law pair because they are the same interaction between the book and the table.

Example

Sorting balanced forces from third-law pairs

A book rests on a table. The table pushes up on the book with $N12\ \text{N}$ . The book’s weight is also $N12\ \text{N}$ downwards.

To check equilibrium of the book, include only forces acting on the book: $N12\ \text{N}$ up from the table and $N12\ \text{N}$ down from the Earth.
These two forces are equal and opposite on the same object, so the resultant force on the book is zero.
The third-law pair for “table on book” is not the book’s weight. It is “book on table”, a $N12\ \text{N}$ downward force acting on the table.
The third-law pair for the book’s weight is the gravitational force of the book pulling on the Earth.

Applying Newton’s Third Law to equilibrium situations

The spec expects you to apply Newton’s Third Law to examples where objects are in equilibrium.

The method is:

Choose the object you are analysing.
Identify the forces acting on that object.
Use equilibrium to say the resultant force is zero.
If asked for a third-law pair, name the force on the other object.

Key Idea

Equilibrium is a one-object question

To decide whether an object is in equilibrium, only combine forces acting on that one object.

Example

A hanging mass in equilibrium

Calculate the weight of the mass using $W = m g$ :
$2.0\ \text{kg} \times 9.8\ \text{N/kg} = 19.6\ \text{N}$ downwards.
The mass is hanging still, so it is in equilibrium. The upward tension on the mass must therefore be $N19.6\ \text{N}$ .
The third-law pair for “string pulls up on mass” is “mass pulls down on string”. This force is also $N19.6\ \text{N}$ , but it acts on the string.

Equal forces can have different effects

A common question is: if forces are equal and opposite, why does one object sometimes move more than the other?

The answer is that the forces are equal, but the objects may have different masses. Acceleration depends on both force and mass:

F = ma

So for the same force, a smaller mass has a larger acceleration.

Example

Comparing accelerations in a collision

A car of mass $kg1000\ \text{kg}$ and a lorry of mass $kg6000\ \text{kg}$ exert forces of $N3000\ \text{N}$ on each other during a collision. Compare their accelerations.

Use Newton’s Third Law first: the force on the car and the force on the lorry are equal in size, $N3000\ \text{N}$ , but opposite in direction.
Use $\frac{F}{m}$ for the car:
$\frac{3000\ \text{N}}{1000\ \text{kg}} = 3.0\ \text{m/s}^2$ .
Use $\frac{F}{m}$ for the lorry:
$\frac{3000\ \text{N}}{6000\ \text{kg}} = 0.50\ \text{m/s}^2$ .
The car has the larger acceleration because it has the smaller mass, even though the forces are equal in size.

Tip

A high-value sentence

When explaining Newton’s Third Law, write: “The forces are equal and opposite, but they act on different objects.”

Everyday examples

Walking

When you walk, your foot pushes backwards on the ground. The ground pushes forwards on your foot. That forward force helps accelerate you forwards.

Swimming

A swimmer pushes water backwards. The water pushes the swimmer forwards with an equal and opposite force.

Rocket launch

A rocket pushes hot gases downwards. The gases push the rocket upwards with an equal and opposite force.

In each case, do not just say “action and reaction”. Say clearly which object acts on which other object.

Exam technique

In the exam

Use “force of A on B” and “force of B on A” wording to identify a third-law pair clearly.
For equilibrium questions, choose one object and only combine forces acting on that object.
If two objects have different accelerations, explain that the forces are equal but the masses may be different.

Self review

Check yourself

A swimmer pushes water backwards. What is the Newton’s Third Law force pair?
Why are the upward contact force on a book and the book’s weight not a third-law pair?
A mass hangs still from a string. Which forces are balanced, and what is the third-law pair for the tension?

Newton's Third Law

What you'll learn

The ideas you need first

Newton’s Third Law

Third-law pairs are not the same as balanced forces

Book on a table

Applying Newton’s Third Law to equilibrium situations

Equal forces can have different effects

Everyday examples

Walking

Swimming

Rocket launch

You've reached the end

Newton's Third Law

What you'll learn

The ideas you need first

Newton’s Third Law

Third-law pairs are not the same as balanced forces

Book on a table

Applying Newton’s Third Law to equilibrium situations

Equal forces can have different effects

Everyday examples

Walking

Swimming

Rocket launch

You've reached the end

Newton's Third Law

What you'll learn

The ideas you need first

Newton’s Third Law

Third-law pairs are not the same as balanced forces

Book on a table

Applying Newton’s Third Law to equilibrium situations

Equal forces can have different effects

Everyday examples

Walking

Swimming

Rocket launch

You've reached the end

Newton's Third Law Revision Guide

Newton's Third Law

What you'll learn

The ideas you need first

Newton’s Third Law

Third-law pairs are not the same as balanced forces

Book on a table

Applying Newton’s Third Law to equilibrium situations

Equal forces can have different effects

Everyday examples

Walking

Swimming

Rocket launch

You've reached the end

Newton's Third Law Revision Guide