Newton's Third Law: Action and Reaction – Newton's Laws of Motion (Senior 1 Physics) | Ganzaa

Newton's Laws of Motion

Lessons

Senior 1 · Physics

Newton's Laws of Motion

5 lessons

Lesson 4 of 5

Newton's Third Law: Action and Reaction

24 min

Who pushed whom?

A defender heads the ball away and feels the blow on his own forehead. A fisherman steps from his canoe onto the shore of Lake Kivu, and the canoe slides away from the shore. A rocket has nothing to push against in space, yet it speeds up. In each case a force on one body seems to come with a force on another. Newton noticed that forces always come in pairs.

Definition

Newton's third law of motion: if body A exerts a force on body B, then body B exerts a force on body A that is equal in size and opposite in direction.

The two forces are called an action–reaction pair. They act on different bodies, at the same moment, and are the same type of force (both contact forces, or both gravitational). Example: your foot pushes the ground backwards with 600 N; the ground pushes your foot forwards with 600 N.

Experiment 1: two newton meters

Hook two newton meters together. One pupil holds each end and pulls. Try pulling gently, then hard; let one pupil pull while the other only holds still.

Figure 4.1: The force of Keza's meter on Mugisha's, and of Mugisha's meter on Keza's, are an action–reaction pair, so the readings are always equal.

Experiment 2: push apart

Two pupils sit on skateboards (or wheeled chairs) facing each other on a smooth floor. One pushes the other with her hands. Both roll away, in opposite directions, even though only one pushed. The lighter pupil rolls away faster.

Important

Safety. Push gently, on a flat floor with space all round, and wear a helmet on a skateboard. Keep your feet off the wheels.

Explanation: pairs on different bodies

Figure 4.2: In each pair the two forces are equal and opposite, but one acts on each body. The wall pushes back on the person; the gases push back on the rocket.

The rocket works by pushing hot gases out of its nozzle downwards. By the third law the gases push the rocket upwards with an equal force, called the thrust. The rocket does not need air or ground to push against: it pushes against its own exhaust. That is why rockets work in space.

	Balanced forces (first law)	Action–reaction pair (third law)
Act on	the SAME body	two DIFFERENT bodies
Example	weight of a book and the table's push up on the book	the book pushes down on the table; the table pushes up on the book
Type of force	can be different types	always the same type
Always equal?	only when the body is not accelerating	always, in every situation

Warning

Action and reaction never cancel. They act on different bodies, so each one can change the motion of the body it acts on. A common mistake is to call a book's weight and the table's upward push an action–reaction pair. They are not: both act on the book. The reaction to the book's weight is the book's gravitational pull upwards on the Earth.

Worked example 1: pushing off on skateboards

Uwase (mass 40 kg) and Gatete (mass 60 kg) stand on skateboards. Uwase pushes Gatete with a force of 120 N. Find the force on each and each one's acceleration.

By the third law, Gatete pushes back on Uwase with 120 N in the opposite direction.

a_{\text{Gatete}} = \frac{120\,\mathrm{N}}{60\,\mathrm{kg}} = 2.0\,\mathrm{m\,s^{-2}}, \qquad a_{\text{Uwase}} = \frac{120\,\mathrm{N}}{40\,\mathrm{kg}} = 3.0\,\mathrm{m\,s^{-2}}

The forces are equal, but the lighter pupil has the larger acceleration.

Worked example 2: a water rocket

A school water rocket has a mass of 0.50 kg. At launch the water it pushes out pushes it upwards with a thrust of 20 N. Find its acceleration ( $g = 9.8\,\mathrm{N\,kg^{-1}}$ ).

W = mg = 0.50 \times 9.8 = 4.9\,\mathrm{N}

F_{\text{resultant}} = 20\,\mathrm{N} - 4.9\,\mathrm{N} = 15.1\,\mathrm{N} \text{ upwards}

a = \frac{F}{m} = \frac{15.1\,\mathrm{N}}{0.50\,\mathrm{kg}} = 30.2\,\mathrm{m\,s^{-2}} \approx 30\,\mathrm{m\,s^{-2}}

Worked example 3: the mango pulls the Earth

A mango of mass 0.30 kg falls from a tree. The Earth pulls it down with its weight; by the third law the mango pulls the Earth up with an equal force. The Earth's mass is $6.0 \times 10^{24}\,\mathrm{kg}$ . Find both accelerations.

F = mg = 0.30 \times 9.8 = 2.94\,\mathrm{N}

a_{\text{mango}} = \frac{2.94}{0.30} = 9.8\,\mathrm{m\,s^{-2}}, \qquad a_{\text{Earth}} = \frac{2.94}{6.0 \times 10^{24}} = 4.9 \times 10^{-25}\,\mathrm{m\,s^{-2}}

The forces are equal, but the Earth's acceleration is far too small ever to notice.

Action and reaction around you

Walking: your foot pushes the ground backwards; the ground pushes you forwards. On wet, muddy paths in the rainy season the ground cannot grip your foot, so it cannot push you forward and you slip.
Paddling a canoe: the paddle pushes water backwards; the water pushes the paddle, and so the canoe, forwards.
Swimming: hands and feet push water backwards; the water pushes the swimmer forwards.
Rockets and satellites: Rwanda's first Earth-observation satellite, RwaSat-1, rode into space in 2019 on a Japanese H-IIB rocket and was released into orbit from the International Space Station. Every one of those launches is the third law at work.

Tip

Name the pair in one sentence: “A pushes B, so B pushes A.” If you cannot swap the two bodies in your sentence, you have not found a third-law pair.

Newton's third law (FuseSchool). Watch for the everyday pairs of forces, and notice that each force in a pair acts on a different object.

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Practice

State Newton's third law of motion.
A boy pushes a wall with a force of 80 N. What force does the wall exert on the boy, and in which direction?
Explain how a canoe paddle makes the canoe move forwards.
A book rests on a table. Name the reaction to (a) the book's weight, (b) the table's upward push on the book.
Two pupils of masses 50 kg and 25 kg on skates push each other apart with a force of 100 N. Find each acceleration.
A rocket of mass 2000 kg has an engine thrust of 30 000 N. Find the resultant force on it at lift-off and its acceleration ( $g = 9.8\,\mathrm{N\,kg^{-1}}$ ).
A pupil says: “The horse pulls the cart and the cart pulls the horse back equally, so they cancel and the cart can never move.” What is wrong with this argument?

Show answersHide answers

If body A exerts a force on body B, then B exerts an equal and opposite force on A.
80 N, directed back towards the boy (opposite to his push).
The paddle pushes the water backwards; by the third law the water pushes the paddle (and the canoe) forwards with an equal force.
(a) the book's gravitational pull upwards on the Earth; (b) the book's downward push on the table.
$\frac{100}{50} = 2.0\,\mathrm{m\,s^{-2}}$ and $\frac{100}{25} = 4.0\,\mathrm{m\,s^{-2}}$ , in opposite directions.
$W = 2000 \times 9.8 = 19\,600\,\mathrm{N}$ ; resultant $= 30\,000 - 19\,600 = 10\,400\,\mathrm{N}$ upwards; $a = \frac{10\,400}{2000} = 5.2\,\mathrm{m\,s^{-2}}$
The two forces act on different bodies, so they do not cancel. The cart moves because the horse's pull on it is bigger than the friction on the cart; the horse moves because the ground pushes its hooves forward more than the cart pulls it back.

Key points

Third law: if A pushes or pulls B, then B pushes or pulls A with an equal and opposite force.
The two forces of a pair act on DIFFERENT bodies, at the same time, and are the same type of force.
Action–reaction pairs never cancel; balanced forces act on the same body.
Walking, swimming, paddling and rocket flight all work by pushing something backwards or downwards.

Sources and credits

4.4: Newton's Third Law of Motion: Symmetry in Forces, from College Physics (1st edition) by Paul Peter Urone and Roger Hinrichs, OpenStax, hosted by LibreTexts, licensed under CC BY 4.0. Consulted for the physics; no text was copied.
Photo: GRACE-FO Launch (NHQ201805220019).jpg by NASA / Bill Ingalls, Wikimedia Commons, in the public domain.
Video: Newton's Third Law | Forces & Motion | Physics | FuseSchool, FuseSchool - Global Education, embedded from YouTube.

Written by Ganzaa: the lesson text, the experiments, diagrams, comparison table, worked examples and practice exercises.

1Who pushed whom?

2Experiment 1: two newton meters

3Experiment 2: push apart

4Explanation: pairs on different bodies

5Action and reaction around you

Who pushed whom?

Experiment 1: two newton meters

Experiment 2: push apart

Explanation: pairs on different bodies

Action and reaction around you