Unit 7 · Force and Motion

Newton's Third Law of Motion

ScienceSubject
8 minEstimated read

The push the ground gives back

Watch your own walking for a moment. At every step your sole presses the ground downward and backward. Can you move forward without pressing on the ground like that? Try it once. You cannot. The instant your foot pushes the ground backward, the ground pushes your foot forward with exactly the same force. That returned push is what carries you forward, not the force of your own leg acting on itself.

This also explains why walking on ice or a wet, slippery floor is so hard. On a slippery surface the foot cannot grip and press the ground properly, so the ground cannot return a proper push, and we slip instead of moving ahead. Hidden inside this small everyday experience is one of the great rules of nature: a force never acts alone. Forces always act in pairs.

Two spring balances in a tug

This pairing of forces can be seen with your own eyes. Take two identical spring balances. Fix one end of spring balance B against a wall and join the hook of spring balance A to the free hook of B. Now pull the free end of A slowly outward. Something remarkable shows up: both balances always display the same reading. When A reads 4 N, B reads exactly 4 N as well. Pull harder and both readings rise together, yet the directions of the two pulls are exactly opposite.

When spring balance A is pulled outward, balance B shows exactly the same reading, so the balance being pulled is itself pulling back with an equal force in the opposite direction.
When spring balance A is pulled outward, balance B shows exactly the same reading, so the balance being pulled is itself pulling back with an equal force in the opposite direction.

The meaning is clear. While balance A pulls balance B, balance B is pulling balance A just as hard in the opposite direction. Even though the pulling was started from one side only, an equal force appears on both sides at the same time.

Newton's third law of motion

Newton expressed this observation as a law. Whenever one body applies a force on a second body, the second body applies a force of the same magnitude on the first body, in exactly the opposite direction. Of this pair of forces acting on the two bodies, one is called the action and the other is called the reaction.

Definition

Newton's third law of motion: for every action there is an equal and opposite reaction.

Definition

Action: of the pair of forces between two bodies, the force that the first body applies on the second body is called the action.

Definition

Reaction: the equal force that the second body applies back on the first body, in the opposite direction, is called the reaction.

Key idea

Forces always act in pairs. A single, lonely force does not exist anywhere: the moment an action appears on one body, its reaction appears on the other body at that very instant.

A volleyball game shows these force pairs beautifully. When a player digs the ball with her wrists, the ball presses down on the wrists while the wrists push the ball upward with an equal force. When two players press the ball at the net at the same moment, each player's hands exert a force on the ball, and the ball returns an equal force onto both players' hands.

In a dig, the ball presses on the player's wrists and the wrists push back on the ball with an equal and opposite force.
In a dig, the ball presses on the player's wrists and the wrists push back on the ball with an equal and opposite force.
At the net, both players' hands push on the ball while the ball pushes back on both pairs of hands with equal force.
At the net, both players' hands push on the ball while the ball pushes back on both pairs of hands with equal force.

Action and reaction never cancel each other

A natural question comes up here. If action and reaction are equal and opposite, should they not cut each other out, so that nothing could ever start moving? No. The resultant force becomes zero only when two equal and opposite forces act on the same body. Action and reaction always act on two different bodies: the action on one body, the reaction on the other. Since they never sit on the same body, there is no question of adding them up to zero. That is why action and reaction never cancel each other.

Common mistake

It is wrong to think that action and reaction cancel each other just because they are equal and opposite. Forces can cancel only when both act on the same body, and action and reaction always act on two different bodies. An answer that leaves out this reason is not complete.

Action and reaction in daily life

In every activity around us that sets a body moving, we can pick out the action and the reaction. When a boatman rows, the oar pushes the water backward: that is the action. The water applies an equal force back on the oar, and the boat is pushed forward: that is the reaction. Swimming works exactly the same way: the swimmer's hands push the water backward, the water returns an equal force to the hands, and the body shoots forward.

The oar pushes the water backward, and the water pushes the boat forward with an equal force.
The oar pushes the water backward, and the water pushes the boat forward with an equal force.
The swimmer's hands push the water backward, and the water drives the body forward.
The swimmer's hands push the water backward, and the water drives the body forward.

Look also at what happens when a ball is bounced on the ground. The ball strikes the ground, pressing on it downward: that is the action. The ground returns an equal force on the ball, directed upward: that is the reaction. The ball rises again precisely because of that reaction force from the ground.

The force of the ball pressing on the ground is the action, and the upward force the ground returns on the ball is the reaction. It is the reaction that makes the ball bounce.
The force of the ball pressing on the ground is the action, and the upward force the ground returns on the ball is the reaction. It is the reaction that makes the ball bounce.

The same law is at work when a rocket is launched, when a bird flies and when a gun is fired. The table below separates the action and the reaction in each of these examples.

ExampleActionReaction
Rowing a boatThe oar pushes the water backward.The water pushes the boat forward with an equal force.
Swimming in waterThe hands push the water backward.The water drives the body forward with an equal force.
Bouncing a ball on the groundThe ball presses on the ground downward.The ground pushes the ball upward with an equal force, so the ball bounces.
Launching a rocketThe rocket throws the hot gases from its burnt fuel downward at great speed.The gases push the rocket upward with an equal force.
A bird flyingThe bird's wings push the air downward.The air pushes the bird upward with an equal force.
Firing a gunThe gun applies a large forward force on the bullet.The bullet pushes the gun backward with an equal force, which is why the gun recoils.

The balloon rocket

You can demonstrate Newton's third law for yourself. Thread a string through a drinking straw, tie both ends of the string to two supports, and tape an inflated balloon to the straw. The moment you release the balloon's mouth, the air inside rushes out backward through the mouth: that is the action. The escaping air applies an equal forward force on the balloon: that is the reaction. Because the balloon is taped to the straw, it has a straight track to follow, and it races along the string like a rocket.

The air rushing backward out of the mouth is the action, and the force pushing the balloon forward is the reaction. The balloon races along the string like a rocket.
The air rushing backward out of the mouth is the action, and the force pushing the balloon forward is the reaction. The balloon races along the string like a rocket.

A real rocket flies in exactly the same way. It throws the hot gases from its burning fuel downward at great speed, and those gases push the rocket upward with an equal force. A balloon's air and a rocket's exhaust are different things, but the rule behind them is one and the same: for every action there is an equal and opposite reaction.

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