C. Forces · Forces

Newton's Third Law: Action-Reaction Pairs

C3.3 C2.2 C2.1About 65 minutes

Learning goals

I can state Newton's third law.
I can identify action-reaction pairs and explain why they do not cancel.
I can tell the difference between a third-law pair and two balanced forces on one object.
I can explain walking, swimming, paddling and rockets using the third law, and calculate the accelerations of interacting objects.

Words to know

Newton's third law
For every action force there is a reaction force that is equal in magnitude and opposite in direction. If A pushes on B, B pushes on A just as hard, the other way.

action-reaction pair
The two forces in one interaction between two objects. They act on different objects, are the same kind of force, and occur at the same time.

interaction
Two objects pushing or pulling on each other. Every force is one half of an interaction.

propulsion
Moving an object forward by pushing something else backward (the ground, water, air or exhaust gas).

You can't touch without being touched

Push on a wall and the wall pushes back on your hand: you can feel it. Two skaters at a rink face each other and push; both glide backward, even the one who "didn't push". A canoeist pushes water backward with the paddle, and the canoe moves forward.

Newton realized that forces always come in pairs. A single, lonely force does not exist. This is his third law, and it explains how anything (you, a car, a rocket) gets moving at all.

Newton's third law

For every action force there is a simultaneous reaction force, equal in magnitude and opposite in direction.

If object A exerts a force on object B, then B exerts a force on A that is equal in size and opposite in direction: F(A on B) = −F(B on A).

How to spot a third-law pair

The two forces in a pair:

act on two different objects (A on B, B on A);
are equal in size and opposite in direction;
are the same kind of force (both gravitational, both normal, both friction...);
happen at the same time. Neither comes "first".

To find the partner of a force, swap the words: "Earth pulls the book down" becomes "the book pulls Earth up".

Why don't they cancel?

Forces cancel only when they act on the same object. The two forces in a pair act on different objects, so each one goes in a different free-body diagram. When two skaters push apart, skater A's FBD contains only the push on A, and skater B's FBD contains only the push on B. Each skater has a net force, so each accelerates.

Equal forces do not mean equal accelerations. By the second law, a = F/m, so the object with less mass accelerates more.

The two pushes form an action-reaction pair: equal in size, opposite in direction, acting on different skaters. The same 90 N gives the lighter skater the larger acceleration.

Worked example

Example 1: Skaters pushing apart

Skater A (60 kg) and skater B (45 kg) stand still on smooth ice and push on each other. A pushes B with 90 N to the right. Find the force on A and each skater's acceleration.

Third law: B pushes A with 90 N to the left.
Ignoring friction, each skater's net force is the push from the other.
A: a = F/m = 90 ÷ 60 = 1.5 m/s² left.
B: a = 90 ÷ 45 = 2.0 m/s² right.
Same force, different masses, different accelerations.

90 N on A, to the left. A: 1.5 m/s² left; B: 2.0 m/s² right.

Getting around with the third law

Walking and running: your shoe pushes backward on the ground (static friction); the ground pushes forward on your shoe. That forward push is what accelerates you. On ice, the ground can't push back much, so you can't push off well.
Cars: the tires push backward on the road; the road pushes forward on the tires.
Swimming and paddling: you push water backward; the water pushes you or the canoe forward.
Rockets: the rocket engine pushes exhaust gas out backward (downward at launch); the gas pushes the rocket forward. A rocket does not need air to push against, which is why it works in space.
Jumping: your legs push down on the floor; the floor pushes up on you with more than your weight, so you accelerate up.

Worked example

Example 2: Pair or balanced?

A 2.0 kg book rests on a table. (a) Name the two forces on the book. Are they a third-law pair? (b) Give the reaction partner of each.

(a) Forces on the book: Fg = 19.6 N down (Earth on book) and FN = 19.6 N up (table on book).
They are equal and opposite, but they act on the same object and are different kinds of force (gravity and normal). So they are not a third-law pair. They are equal because the book is in equilibrium (first law).
(b) Partner of "Earth pulls book down": the book pulls Earth up with 19.6 N (gravitational).
Partner of "table pushes book up": the book pushes the table down with 19.6 N (normal).

Fg and FN on the book balance but are not a pair. Their partners: book pulls Earth up; book pushes table down.

Left: the two forces on the book balance, but they are not a third-law pair (they act on the same object and are different kinds of force). Right: each one's real partner acts on a different object.

Just for fun

When you jump, you push Earth away from you, and by the third law Earth gets the same size push. Earth really does accelerate, but its mass is about 6 × 10²⁴ kg, so a 600 N push gives it about 10⁻²² m/s². Don't worry: the planet will survive your next basketball game.

Hands-on activity

Balloon rocket

You need: a long piece of string (3 to 5 m), a drinking straw, a balloon, tape, and two chairs. A grown-up should help with the balloon; keep balloons and broken balloon pieces away from young children (choking hazard).

Thread the string through the straw and tie it tight between two chairs.
Blow up the balloon, pinch the neck closed (don't tie it), and tape it under the straw.
Let go. Measure how far the balloon travels.
Explain using the third law: the balloon squeezes air backward out of the neck; the air pushes the balloon forward.
Try a bigger and a smaller balloon fill. Predict and test which goes farther.
Bonus: sit on a wheeled office chair on a hard floor, holding a heavy ball, and push the ball away from your chest (toss it gently to a helper). Which way do you roll? Do this only on a hard, clear floor.

Your turn

State Newton's third law.

A hammer hits a nail with 400 N. How hard does the nail push on the hammer?

Give the reaction force: "A swimmer's hands push water backward."

Why do action-reaction forces not cancel each other?

A 75 kg adult and a 25 kg child on skates push apart with a force of 150 N. Find each acceleration.

How does a rocket accelerate in space, where there is no air to push against?

More practice: warm-up

Do the forces in an action-reaction pair act on the same object or on different objects?

Are the two forces in a pair equal in size?

Earth pulls an apple down with 1 N. What does the apple do to Earth?

When you walk, which way do your feet push on the ground?

Is it the action or the reaction that happens first?

More practice: on your own

A bug hits a car's windshield. Compare the force on the bug with the force on the car. Why is the outcome so different?

A horse pulls a sleigh. A student says, "The sleigh pulls back on the horse just as hard, so they can never move." Explain the mistake.

A book sits on a table. Is the normal force on the book the reaction to its weight? Explain.

Why is it hard to walk on smooth ice?

A 50 kg student on a skateboard (total 52 kg) throws a 4.0 kg medicine ball forward with an average force of 26 N. Find the acceleration of the ball and of the student (ignore friction).

Challenge

A truck and a small car collide head-on. Which experiences the greater force? Which experiences the greater acceleration? Which occupants are at greater risk, and why?

A 60 kg student stands on a bathroom scale. Identify every force acting on the student and on the scale, and all the third-law pairs. (Ignore the scale's own weight.)

A 40 kg child pushes off a wall on skates with a 120 N push lasting 0.50 s. Find the child's speed afterward. Which force actually accelerated the child?

Check your understanding

Quiz

A hockey stick hits a puck with 300 N. The puck hits the stick with:

Action-reaction forces do not cancel because they:

The reaction to "Earth pulls a falling apple down" is:

What pushes a runner forward?

Two skaters push apart with equal forces. The lighter skater:

For a book at rest on a table, the weight and the normal force are:

For parents and teachers

Big idea: Newton's third law (C3.3): forces come in equal and opposite pairs acting on different objects. Students use it with free-body diagrams (C2.2).

How to help: Practise "swap the words": for any force your teen names ("the bat hits the ball"), ask for its partner ("the ball hits the bat"). Then ask which force goes in which object's free-body diagram.

Common difficulties:

Pairing weight and normal force. They often balance, but they are not a third-law pair.
Thinking the pair cancels, so nothing can move.
Thinking the bigger or faster object exerts the bigger force. The forces are always equal; the effects (accelerations) differ.