Newton's third law of motion

You push, and you are pushed

Push a wall and you feel it push back on your hands. Step off a boat onto the jetty and the boat slides back. Forces always come in pairs.

Newton's third law

When one object pushes on a second, the second pushes back on the first with a force of the same size in the opposite direction.

The two forces of a pair:

• are equal in size and opposite in direction;
• act on different objects;
• are of the same kind (both contact, or both gravity);
• start and stop together.

Why do they not cancel?

They act on different objects, so they never add up on one object. Each object moves according to the force on it.

Equal forces, different results

Two skaters push apart with the same force, but the lighter one gets the larger acceleration: $a = \dfrac{F}{m}$.

You should find that the lighter skater always moves off faster, but the momentum of each, $F \times t$, is the same: equal and opposite.

Watch out. The weight of a book and the push of the table on it are equal and opposite, but they are not a third-law pair: both act on the book. The pair of the book's weight is the book's pull on the Earth.

A worked example

Riya ($40\ \text{kg}$) and Dev ($60\ \text{kg}$) push apart on skates with $120\ \text{N}$ for $0.5\ \text{s}$. Find each one's acceleration and speed.

1. Riya. $a = \dfrac{120\ \text{N}}{40\ \text{kg}} = 3\ \text{m/s}^2$, so $v = 3\ \text{m/s}^2 \times 0.5\ \text{s} = 1.5\ \text{m/s}$.
2. Dev. $a = \dfrac{120\ \text{N}}{60\ \text{kg}} = 2\ \text{m/s}^2$, so $v = 1\ \text{m/s}$.
3. Momentum. $40\ \text{kg} \times 1.5\ \text{m/s} = 60\ \text{kg} \times 1\ \text{m/s} = 60\ \text{kg m/s}$ each, in opposite directions.

Practise with new numbers

Try it in Python

The program works out the two skaters.

Remember these

• Forces come in pairs: equal in size, opposite in direction, on different objects.
• Pair forces never cancel, because they act on different objects.
• Equal forces give the lighter object the larger acceleration.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. A swimmer pushes the water backward. What pushes the swimmer forward?

2. A horse pulls a cart. Does the cart pull back on the horse?

3. A gun fires a bullet. Why does the gun move back much more slowly than the bullet moves forward?

4. The Earth pulls an apple down with $1\ \text{N}$. How hard does the apple pull the Earth?