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The third law

Forces and motion · level 5, lesson 5 of 6

A question to start

You walk forward. What pushes you? Your legs push your body, but your body is part of you, and nothing can push itself along. So what force actually moves you forward?

The idea

Newton's third law: when object A pushes or pulls object B, B pushes or pulls A with a force equal in size and opposite in direction.

Forces always come in pairs, and the two forces in a pair:

  • are the same size,
  • point in opposite directions,
  • act on different objects,
  • are the same kind of force (both contact, both gravity, both magnetic).

When you walk, your foot pushes back on the ground. The ground pushes forward on your foot, just as hard. That forward push from the ground is what moves you.

wheel pushes ground background pushes wheel on

The two forces never cancel each other out, because they act on different things. The ground's push acts on you; your push acts on the ground. The Earth (or Mars) does move back a little, but its mass is so huge that the change is far too small to notice.

Worked examples

1. A rover. Each wheel pushes back on the ground; the ground pushes the wheel forward. On loose sand, the sand gives way and cannot push back hard: the rover slips.

2. A rocket. The rocket pushes hot gas out backwards; the gas pushes the rocket forwards. It needs no air or ground to push on, so it works in space.

3. Gravity pairs. Mars pulls a dropped rock down with 3.7 N for each kilogram. The rock pulls Mars up with exactly the same force. Mars hardly moves; the rock falls.

Try it

  1. A swimmer pushes water backwards. What is the paired force?
  2. A book rests on a table. Its weight is 10 N, down. What is the pair of that weight?
  3. Why don't the two forces in a third-law pair cancel each other?
  4. A lander's engines push gas down with 5,000 N. What force do they get, and on what?
Answers
  1. The water pushes the swimmer forwards.
  2. The book pulls the Earth up with 10 N (gravity). The table's push on the book is a different force.
  3. They act on different objects.
  4. 5,000 N upwards, on the lander, from the gas.

Common mistake

"The table pushing up on the book is the third-law pair of its weight." Both act on the book, so they cannot be a pair. They balance because of the first law. The pair of the weight is the book pulling the Earth.

Where it leads