Chapter 6 of 8

All 8 chapters
  1. 1Scalars and vectors, readunderstood
  2. 2Velocity and acceleration, readunderstood
  3. 3Newton's first law, readunderstood
  4. 4Newton's second law, readunderstood
  5. 5Weight and falling, readunderstood
  6. 6Newton's third law, readunderstood
  7. 7Momentum, readunderstood
  8. 8Stopping distances, readunderstood

S4.8.6 Chapter 6

Newton's third law

If every push has an equal push back, how can anything ever start to move?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Identify force pairs in walking, swimming and rockets
  • Explain why the two forces in a pair act on different objects

When you push a wall, the wall seems to do nothing. In fact it pushes back on you. Forces always come in pairs.

Newton’s third law: if object A exerts a force on object B, then B exerts a force on A. The two forces are equal in size, opposite in direction, and of the same type. They act at the same time.

Take the four parts one at a time. Size: the two forces have the same number of newtons. Direction: they point opposite ways. Type: both are contact forces, or both are gravity, or both are electric, or both are magnetic. Place: each acts on a different object.

Name each force by what pushes and what is pushed. One is the "force of the hand on the wall". The other is the "force of the wall on the hand". The two names swap the objects. We call the two forces a force pair.

Two blocks, each with its own arrow. The first, titled on the wall, is a block labelled wall with an arrow to the right labelled hand, 30 N. The second, titled on the hand, is a block labelled hand with an arrow to the left of the same length labelled wall, 30 N.on the wallwallhand30 Non the handhandwall30 N
Each arrow is named for what pushes. The two arrows are the same length and point opposite ways. They are on different blocks.

The forces of a pair do not cancel. To cancel, two forces must act on the same object. The force of the hand acts on the wall. The force of the wall acts on the hand. One object has only one of the two.

See it three ways

As a picture

Two blocks, each with its own arrow. The first, titled on the ball, is a block labelled ball with an arrow to the right labelled bat, 200 N. The second, titled on the bat, is a block labelled bat with an arrow to the left of the same length labelled ball, 200 N.on the ballballbat200 Non the batbatball200 N

In words

When a bat hits a ball, each pushes the other. The two forces are equal in size and opposite in direction, and each acts on a different object.

In symbols

force of bat on ball = force of ball on bat = 200 N

Now walking. You walk by pushing the ground backward with your foot. The ground pushes your foot forward. That forward push is a friction force, and it is what moves you.

Two blocks, each with its own arrow. The first, titled on the foot, is a block labelled foot with an arrow to the right labelled ground, 120 N. The second, titled on the ground, is a block labelled ground with an arrow to the left of the same length labelled foot, 120 N.on the footfootground120 Non the groundgroundfoot120 N
The foot pushes the ground back. The ground pushes the foot forward with a force of the same size.

On smooth ice there is almost no friction. Your foot cannot push the ground back with much force, so the ground cannot push you forward. You slip.

A swimmer pushes the water backward with her hands and feet. The water pushes her forward. A boat does the same with its oars or propeller.

Two blocks, each with its own arrow. The first, titled on the hand, is a block labelled hand with an arrow to the right labelled water, 80 N. The second, titled on the water, is a block labelled water with an arrow to the left of the same length labelled hand, 80 N.on the handhandwater80 Non the waterwaterhand80 N
The hand pushes the water back. The water pushes the hand, and the swimmer, forward.

A rocket pushes hot gas down and out of its engine. The gas pushes the rocket up. The rocket does not push on the air or the ground. So it works in empty space, where there is nothing to push against.

Two blocks, each with its own arrow. The first, titled on the rocket, is a block labelled rocket with an arrow up labelled gas 300 N. The second, titled on the gas, is a block labelled gas with an arrow down of the same length labelled rocket 300 N.on the rocketrocketgas 300 Non the gasgasrocket 300 N
The rocket pushes the gas down. The gas pushes the rocket up with a force of the same size.

Worked example

A small rocket has a mass of 20 kg. Its engine pushes gas down with 300 N. Find the acceleration of the rocket at lift-off. Use g = 9.8 N/kg.

  1. By the third law, the gas pushes the rocket up with 300 N, the same as the rocket pushes the gas down.
  2. The weight is 20 kg × 9.8 N/kg = 196 N, down.
  3. The resultant is 300 N − 196 N = 104 N, up.
  4. a = 104 N ÷ 20 kg = 5.2 m/s², up.

Answer: 5.2 m/s²

The two forces of a pair are always equal. The accelerations they cause are not equal if the masses differ. Each acceleration is a = F ÷ m for its own object.

Worked example

Skater A has a mass of 40 kg. Skater B has a mass of 60 kg. They stand on smooth ice and push each other apart with a force of 120 N. Find each acceleration.

  1. The forces are a pair, so each skater feels 120 N, in opposite directions.
  2. Skater A: a = 120 N ÷ 40 kg = 3 m/s².
  3. Skater B: a = 120 N ÷ 60 kg = 2 m/s².
  4. The lighter skater accelerates more. Both forces are the same.

Answer: A 3 m/s², B 2 m/s²

Two blocks, each with its own arrow. The first, titled skater A, 40 kg, is a block labelled skater A with an arrow to the left labelled skater B, 120 N. The second, titled skater B, 60 kg, is a block labelled skater B with an arrow to the right of the same length labelled skater A, 120 N.skater A, 40 kgskater Askater B120 Nskater B, 60 kgskater Bskater A120 N
The arrows are the same. The skaters have different masses, so their accelerations differ.

The same idea explains why the Earth does not seem to move when you jump. The Earth pulls you down with your weight. You pull the Earth up with a force of the same size. The Earth has so much mass that its acceleration is far too small to notice.

Now a trap. A book lies on a table. The weight of the book pulls it down. The table pushes it up. These forces are equal and opposite. Are they a third law pair? They are not.

A block labelled book with an arrow up labelled table 4.9 N and an arrow down of the same length labelled Earth 4.9 N. A bar marked bar = 2 N shows the scale.booktable 4.9 NEarth 4.9 Nbar = 2 N
Both forces act on the book. They are balanced forces, so they are not a pair.

They act on the same object, the book. They are different types, because weight is gravity and the push of the table is a contact force. A pair has the forces on two objects, of one type.

The real pairs are these. The push of the table on the book pairs with the push of the book on the table, both contact forces. The pull of the Earth on the book pairs with the pull of the book on the Earth, both gravity.

Two blocks, each with its own arrow. The first, titled on the book, is a block labelled book with an arrow up labelled table 4.9 N. The second, titled on the table, is a block labelled table with an arrow down of the same length labelled book 4.9 N.on the bookbooktable 4.9 Non the tabletablebook 4.9 N
The push of the table on the book, and the push of the book on the table, are a real pair. They act on two objects.

There is a simple test. Take the table away. The weight stays, but the push of the table is gone. The two forces of a real pair appear and vanish together.

Try it

Two rubber bands pulling

You need: two rubber bands of the same kind, a friend, a ruler.

Be safe: Stretch the bands gently, with both hands, and never let go of a stretched band. A band can snap back and sting. Keep it away from your face and from other people’s faces.

  1. Join the two bands in a chain by looping one through the other.
  2. You hold the free end of one band. A friend holds the free end of the other.
  3. Pull gently apart until the bands are stretched. Measure the length of each band.
  4. Now swap sides, and let the stronger of you pull harder. Measure again.

What you will see: The two bands stretch to the same length, however hard each of you tries. Each of you feels the band pull back on your hand. That pull equals the pull of your hand on the band. A band can pull on you only as hard as you pull on it.

If you cannot try it, this is what happens.
A table of one set of results, with the columns Band and Length. Yours: 18 cm. Friend: 18 cm.BandLengthyours18 cmfriend18 cm

A wrong idea many people have

Equal and opposite forces always cancel, so nothing can ever start to move.

Why it feels right: Balanced forces do cancel, and the words "equal and opposite" sound the same.

The test that breaks it: Two skaters push each other apart. The force on skater A is 120 N one way. The force on skater B is 120 N the other way. Neither skater feels both forces, and both skaters move.

What is true: Two forces cancel only if they act on the same object. The two forces of a pair act on different objects, so each object has an unbalanced force on it and accelerates.

A wrong idea many people have

In a collision, the bigger object pushes harder on the smaller one.

Why it feels right: A truck does far more damage to a fly than the fly does to the truck.

The test that breaks it: Look at the pair of forces in a crash between a truck and a fly. The force of the truck on the fly and the force of the fly on the truck are equal. Their size is the same, and the directions are opposite.

What is true: A pair of forces is always equal. The fly is thrown aside because its mass is tiny, so a = F ÷ m is huge. The truck has a huge mass, so its acceleration is tiny.

A wrong idea many people have

The weight of a book and the push of the table on it are a third law pair.

Why it feels right: They are equal and opposite, which is what the third law says.

The test that breaks it: Both forces act on the book. One is gravity, and the other is a contact force. The weight stays if the table is taken away, and the push does not.

What is true: A pair is two forces of the same type, on two different objects. The push of the table on the book pairs with the push of the book on the table.

Key words

third law
if A exerts a force on B, then B exerts a force of equal size and opposite direction on A.
force pair
the two forces of the third law. They have the same size and type, opposite directions, and act on different objects.
contact force
a force between two things that touch, such as a push, friction or the push of a table.

Back to your guess

The answer is C: The two forces act on different objects, so they do not cancel.

The two forces of a pair act on different objects. Forces cancel only when they act on the same object, so a pair never cancels itself.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. A book rests on a table. Which two forces are a third law pair?

    Tap your answer.

    1. Not this one. Both forces act on the book. A pair acts on two objects. These two are balanced forces on one object. Try another.

    2. Not this one. The weight of the table is gravity on the table. It is not the partner of a contact force on the book. Try another.

    3. Not this one. These forces are on different objects, but they are of different types and are not partners. Try another.

    4. Yes, that is right. The pair has two forces of the same type, on two objects. The table pushes the book and the book pushes the table.

    See the answer

    The push of the table on the book, and the push of the book on the table.

    The pair has two forces of the same type, on two objects. The table pushes the book and the book pushes the table.

    • If you chose A: Both forces act on the book. A pair acts on two objects. These two are balanced forces on one object.
    • If you chose B: The weight of the table is gravity on the table. It is not the partner of a contact force on the book.
    • If you chose C: These forces are on different objects, but they are of different types and are not partners.

  2. Which statement about the two forces of a third law pair is true?

    Tap your answer.

    1. Yes, that is right. The force of A on B acts on B. The force of B on A acts on A. This is why a pair does not cancel.

    2. Not this one. Forces that cancel act on one object. A pair always acts on two objects, so it never cancels. Try another.

    3. Not this one. The two forces of a pair are always equal, whatever the sizes of the objects. Try another.

    See the answer

    They act on different objects.

    The force of A on B acts on B. The force of B on A acts on A. This is why a pair does not cancel.

    • If you chose B: Forces that cancel act on one object. A pair always acts on two objects, so it never cancels.
    • If you chose C: The two forces of a pair are always equal, whatever the sizes of the objects.

  3. How does a person start to walk forward?

    Tap your answer.

    1. Not this one. That would move the ground forward and push her back. Her foot pushes the ground backward. Try another.

    2. Not this one. The air is not the cause. Walking works the same way in a room with no wind. Try another.

    3. Yes, that is right. The forces are a pair. The forward friction force of the ground on her foot is the one that accelerates her.

    See the answer

    Her foot pushes the ground backward, and the ground pushes her foot forward.

    The forces are a pair. The forward friction force of the ground on her foot is the one that accelerates her.

    • If you chose A: That would move the ground forward and push her back. Her foot pushes the ground backward.
    • If you chose B: The air is not the cause. Walking works the same way in a room with no wind.

  4. Why can a rocket speed up in empty space, where there is no air?

    Tap your answer.

    1. Not this one. There is no air in space. A rocket works there, so it does not need air to push on. Try another.

    2. Not this one. The pad is left behind at lift-off. The rocket works long after it has gone. Try another.

    3. Not this one. With no force, the velocity stays the same. Speeding up needs a resultant force, and the gas gives it. Go to S4.8.3. Try another.

    4. Yes, that is right. The rocket pushes the gas and the gas pushes the rocket. These are a pair, and the gas is carried with the rocket, so no air is needed.

    See the answer

    It pushes gas out backward, and the gas pushes the rocket forward.

    The rocket pushes the gas and the gas pushes the rocket. These are a pair, and the gas is carried with the rocket, so no air is needed.

    • If you chose A: There is no air in space. A rocket works there, so it does not need air to push on.
    • If you chose B: The pad is left behind at lift-off. The rocket works long after it has gone.
    • If you chose C: With no force, the velocity stays the same. Speeding up needs a resultant force, and the gas gives it. Go to S4.8.3.

  5. Two skaters on smooth ice push each other apart. Skater A has a mass of 40 kg. Skater B has a mass of 60 kg. Which statement is true?

    Tap your answer.

    1. Not this one. The two forces of a pair are always equal, whatever the masses. Try another.

    2. Yes, that is right. The pair is equal in size. By the second law, a = F ÷ m, so the skater with less mass has the larger acceleration.

    3. Not this one. The forces are equal, but a = F ÷ m. The skaters have different masses, so different accelerations. Try another.

    See the answer

    The two forces are equal, and A accelerates more because A has less mass.

    The pair is equal in size. By the second law, a = F ÷ m, so the skater with less mass has the larger acceleration.

    • If you chose A: The two forces of a pair are always equal, whatever the masses.
    • If you chose C: The forces are equal, but a = F ÷ m. The skaters have different masses, so different accelerations.

  6. A swimmer pushes the water backward with her hands. What is the other force of this pair?

    Tap your answer.

    1. Not this one. Her weight is gravity, a different type of force, and it acts on the swimmer. The partner of a push on the water is a push by the water. Try another.

    2. Not this one. Backward is the way her hands push the water. The partner force points the opposite way, forward. Try another.

    3. Not this one. That is not a partner. Her hands already push the water backward. The partner acts on her hands, not on the water. Try another.

    4. Yes, that is right. Her hands push the water backward. By the third law the water pushes her hands forward with a force of the same size and type. This forward push moves her along.

    See the answer

    The water pushing her hands forward.

    Her hands push the water backward. By the third law the water pushes her hands forward with a force of the same size and type. This forward push moves her along.

    • If you chose A: Her weight is gravity, a different type of force, and it acts on the swimmer. The partner of a push on the water is a push by the water.
    • If you chose B: Backward is the way her hands push the water. The partner force points the opposite way, forward.
    • If you chose C: That is not a partner. Her hands already push the water backward. The partner acts on her hands, not on the water.

  7. A truck hits a fly. Which statement is true during the impact?

    Tap your answer.

    1. Yes, that is right. They are a third law pair, so they are equal in size and opposite in direction. They act on different objects.

    2. Not this one. The truck does more damage, but the two forces are equal. The fly has little mass, so it suffers a huge acceleration. Try another.

    3. Not this one. The fly exerts a force too. Forces come in pairs, so there are always two. Try another.

    See the answer

    The force of the truck on the fly equals the force of the fly on the truck.

    They are a third law pair, so they are equal in size and opposite in direction. They act on different objects.

    • If you chose B: The truck does more damage, but the two forces are equal. The fly has little mass, so it suffers a huge acceleration.
    • If you chose C: The fly exerts a force too. Forces come in pairs, so there are always two.

  8. From an earlier chapter

    What is the weight of a 4 kg bag on Earth, with g = 9.8 N/kg?

    Tap your answer.

    1. Not this one. You divided the mass by g. The weight is the mass times g. Go to S4.8.5. Try another.

    2. Yes, that is right. W = m × g = 4 kg × 9.8 N/kg = 39.2 N.

    3. Not this one. You added the mass and g. The weight is a product, W = m × g. Go to S4.8.5. Try another.

    See the answer

    39.2 N

    W = m × g = 4 kg × 9.8 N/kg = 39.2 N.

    • If you chose A: You divided the mass by g. The weight is the mass times g. Go to S4.8.5.
    • If you chose C: You added the mass and g. The weight is a product, W = m × g. Go to S4.8.5.

  9. Two skaters push each other apart with a force of 120 N. Skater A has a mass of 50 kg. What is the acceleration of skater A?

    See the answer

    2.4 m/s²

    The force on A is 120 N. a = F ÷ m = 120 N ÷ 50 kg = 2.4 m/s².

  10. A rocket has a mass of 500 kg. Its engine pushes gas down with 6 900 N. Use g = 9.8 N/kg. What is the acceleration of the rocket at lift-off?

    See the answer

    4 m/s²

    The gas pushes the rocket up with 6 900 N. The weight is 500 × 9.8 = 4 900 N. The resultant is 6 900 − 4 900 = 2 000 N. a = 2 000 N ÷ 500 kg = 4 m/s².

Keep it

Copy this into your exercise book.

Third law: the two forces of a pair are equal, opposite, of the same type, and on different objects. They never cancel. A weight and the push of a table on a book are not a pair.

Draw: Two blocks, each with one arrow of the same length, pointing opposite ways, labelled "A on B" and "B on A".

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (825 KB). It opens on any phone.