🚀 A rocket and its exhaust gases
The rocket pushes its hot exhaust gases backwards. The gases push the rocket forwards with an equal force. The rocket does not need air to push against, so this works in space.
Forces, Movement, Shape and Momentum » Newton's Third Law
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 1.29P
- What Newton's third law says about two bodies that interact
- How to spot a third law pair of forces in everyday examples
- Why a third law pair is not the same as balanced forces
- How the third law links to momentum in collisions
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Unlock This CourseForces come in pairs
This lesson is examined in Paper 2 only.
Push hard against a wall with your hand. You can feel the wall pushing back on your hand. You cannot push the wall without the wall pushing you. This is true for every force. A force is always part of an interaction between two bodies, so forces always come in pairs.
Newton's third law: when two bodies interact, the forces they exert on each other are equal in size and opposite in direction.
In physics, "body" just means an object. It could be a person, a ball, a rocket or the whole Earth.
A simple way to write any pair is to swap the two names over:
- Body A exerts a force on body B.
- Body B exerts an equal and opposite force on body A.
So "the hand pushes the wall" becomes "the wall pushes the hand". If the hand pushes the wall with 40 N to the right, the wall pushes the hand with 40 N to the left.
Key terms:
- Newton's third law: when two bodies interact, the forces they exert on each other are equal in size and opposite in direction.
- Interact: two bodies interact when each one exerts a force on the other.
- Third law pair: the two forces in one interaction. They act on different bodies and are the same type of force.
The rules for a third law pair
The two forces in a third law pair always follow these four rules:
- They are equal in size.
- They act in opposite directions.
- They act on two different bodies. One force acts on A and the other acts on B.
- They are the same type of force. If one is a gravitational force, so is the other. If one is friction, so is the other.
The two forces also exist for exactly the same time. Neither one comes first.
The sizes are equal even when the two bodies are very different. When a lorry hits a small car, the force of the lorry on the car is exactly the same size as the force of the car on the lorry. The car is affected more because it has a much smaller mass, not because it feels a bigger force.
Third law pairs in action
Many things move by pushing something else backwards. The third law pair is what moves them forwards.
🏊 A swimmer and the water
The swimmer's hands and feet push the water backwards. The water pushes the swimmer forwards with an equal force.
🚶 Walking
Your foot pushes backwards on the ground. The ground pushes forwards on your foot with an equal force. Both forces are friction. On ice there is very little friction, so it is hard to walk.
🎯 Recoil
When a rifle is fired, the rifle pushes the bullet forwards. The bullet pushes the rifle backwards with an equal force, so the rifle kicks back into the shooter's shoulder.
In every example the two forces act on different bodies: one on the rocket and one on the gases, one on the swimmer and one on the water.
A book on a table
A book rests on a table. This simple situation contains two separate third law pairs. Imagine drawing each pair as two arrows of equal length pointing in opposite directions, each on a different body.
🌍 Pair 1: the book and the Earth
The Earth pulls the book down. This is the book's weight. The book pulls the Earth up with an equal force. Both are gravitational forces.
📚 Pair 2: the book and the table
The book pushes down on the table. The table pushes up on the book with an equal force. Both are normal contact forces.
It may seem strange that a book pulls the Earth upwards, but it does. The force is the same size as the book's weight. The mass of the Earth is so huge that this force gives it an acceleration far too small to notice.
Not the same as balanced forces
Now look only at the book. Two forces act on it: its weight pulling down and the normal contact force from the table pushing up. They are equal in size and opposite in direction, and the book stays still.
These two forces are balanced forces. They are not a third law pair, for two reasons:
- They both act on the same body, the book.
- They are different types of force. One is gravitational and one is a normal contact force.
⚖️ Balanced forces
Act on one body. Can be different types of force. They cancel, so the resultant force on that body is zero. Two opposite forces on one body do not have to be equal. They are only balanced when the body is at rest or moving at a constant velocity.
🤝 Third law pair
Act on two different bodies. Always the same type of force. They never cancel, because they are not on the same body. They are always equal, whatever the bodies are doing.
This clears up a famous puzzle: "If every force has an equal and opposite force, how can anything ever speed up?" The answer is that the two forces act on different bodies. To decide how one body moves, you only look at the forces acting on that body.
Worked example
A dog of weight 150 N stands still on the floor. The floor pushes up on the dog with a normal contact force of 150 N. Describe the third law partner of each of these forces.
Step 1: write each force as "A acts on B". The weight is "the Earth pulls the dog down with a gravitational force of 150 N".
Step 2: swap the names. The partner is "the dog pulls the Earth up with a gravitational force of 150 N".
Step 3: do the same for the other force. "The floor pushes up on the dog with 150 N" becomes "the dog pushes down on the floor with a normal contact force of 150 N".
The dog's weight and the push from the floor are not partners. They both act on the dog.
The link to momentum
Newton's third law explains why momentum is conserved in a collision. Remember, force = change in momentum / time taken.
- When two bodies collide, the forces they exert on each other are equal in size and opposite in direction.
- The two forces act for the same time, because the bodies touch each other for the same time.
- So the changes in momentum of the two bodies are equal in size and opposite in direction.
- What one body loses, the other gains. The total momentum stays the same.
The same reasoning explains recoil. The bullet gains momentum forwards and the rifle gains an equal amount of momentum backwards.
Common mistakes
- Calling weight and the normal contact force a third law pair. They act on the same body and are different types of force. They are balanced forces.
- Saying the bigger body exerts the bigger force. The two forces are always equal in size, even for a lorry and a car.
- Saying the pair cancels out. Forces can only cancel if they act on the same body. A third law pair acts on two different bodies.
- Being vague about the bodies. Always say which body exerts the force and which body it acts on.
- Saying a rocket pushes against the air or the ground. It pushes against its own exhaust gases.
Exam-style question
A girl of mass 50 kg stands on roller skates next to a wall. She pushes on the wall with a force of 100 N to the left.
(a) State Newton's third law. [2 marks]
(b) State the size and direction of the force that the wall exerts on the girl. [2 marks]
(c) Calculate the acceleration of the girl while she is pushing. Ignore friction. [2 marks]
(d) Later, the girl stands still on the floor. Her weight is 500 N and the normal contact force from the floor on the girl is 500 N. A student says these two forces are a Newton's third law pair. Explain why the student is wrong. [3 marks]
Model answer
(a) When two bodies interact, the forces they exert on each other are equal in size (1) and opposite in direction (1).
(b) 100 N (1) to the right (1).
(c) a = F / m = 100 / 50 (1)
a = 2 m/s2 (1)
(d) Both forces act on the same body, the girl (1). A third law pair acts on two different bodies (1). The two forces are different types, one gravitational and one a normal contact force, but a third law pair is always the same type of force (1).
Exam tip
In part (d), do not just write "they are balanced forces". Compare the two forces with the rules for a third law pair: different bodies and the same type of force. In part (b), a force needs a size and a direction, so give both.