Newton's Third Law Examples: 43 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Newton's Third Law.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

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

When you push something, it pushes back on you just as hard.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Newton's Third Law asks students to choose the object, list external interactions, and reason from the resulting force or torque pattern.

Common stuck point: Students often know a formula related to newton's third law but skip the recognition step: Have I isolated one system and listed the external forces or torques acting on it before applying a law? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Have I isolated one system and listed the external forces or torques acting on it before applying a law?

Worked Examples

Example 1

easy

A person pushes against a wall with a force of

50 \text{ N}

. What force does the wall exert on the person?

Answer

F_{wall on person} = 50 N (opposite direction)

First step

Identify the action force: the person pushes on the wall with

50 \text{ N}

Full solution

2
Apply Newton's third law: every action force has a reaction force equal in magnitude and opposite in direction.
3
The wall therefore exerts a reaction force of $50 \text{ N}$ back on the person, directed away from the wall.

Newton's third law states that forces always come in action-reaction pairs. The wall pushes back on the person with the same magnitude but opposite direction.

Example 2

medium

70 \text{ kg}

skater pushes a

50 \text{ kg}

skater with a force of

100 \text{ N}

. What is the acceleration of each skater?

The 50 kg skater receives 100 N rightward (reaction). a = 100/50 = 2 m/s²

Example 3

medium

A book of mass

1 \text{ kg}

sits on a table. Earth pulls it down with

9.8 \text{ N}

. What is the third-law partner of this gravitational force, and on what object does it act?

Example 4

medium

A truck collides head-on with a small car. Compare the magnitudes of (a) the force of the truck on the car, and (b) the force of the car on the truck.

Example 5

hard

2 \text{ kg}

block A pushes a

3 \text{ kg}

block B; they sit side-by-side on a frictionless surface. A horizontal force of

25 \text{ N}

is applied to A. Find the force A exerts on B, and the force B exerts on A.

System a = 25/5 = 5 m/s². Force A exerts on B = 3×5 = 15 N. By third law B exerts 15 N back on A.

Example 6

challenge

On a frictionless floor a

50 \text{ kg}

student stands on a

10 \text{ kg}

cart and walks at

1 \text{ m/s}

relative to the ground. Find the cart's velocity (assume system started at rest).

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

A hammer strikes a nail with

200 \text{ N}

of force. What force does the nail exert on the hammer?

Example 2

easy

A rocket pushes exhaust gases backward with a force of

4.0 \times 10^4 \text{ N}

. What force do the gases exert on the rocket?

Example 3

easy

State Newton's third law.

Example 4

easy

You push a wall with

30\text{ N}

. How hard does the wall push back?

Example 5

easy

Do action and reaction forces act on the same object?

Example 6

easy

A rocket pushes gas backward. What pushes the rocket forward?

Example 7

easy

When you jump, you push down on Earth. What pushes you up?

Example 8

easy

Are weight and the normal force on a book a Newton's third-law pair?

Example 9

easy

50\text{ N}

force from a bat hits a ball. What force does the ball exert on the bat?

Example 10

easy

Do action and reaction forces happen at the same time?

Example 11

medium

60\text{ kg}

skater pushes an

80\text{ kg}

skater with

120\text{ N}

. Find each skater's acceleration magnitude.

Equal 120 N acts on each skater; lighter 60 kg skater gets a

Example 12

medium

A horse pulls a cart. If forces are equal and opposite, why does the system accelerate?

Example 13

medium

2\text{ kg}

ball exerts

19.6\text{ N}

down on Earth (

g=9.8

). What force does Earth exert on the ball, and what is its acceleration?

Example 14

medium

Identify the reaction force to 'the floor pushes up on your feet with

700\text{ N}

Example 15

medium

Two carts,

1\text{ kg}

and

4\text{ kg}

, push apart via a spring. If the

1\text{ kg}

cart accelerates at

8\text{ m/s}^2

, find the

4\text{ kg}

cart's acceleration.

Spring exerts equal 8 N on both carts. 4 kg cart: a = 8/4 = 2 m/s²; 1 kg cart: a

Example 16

medium

Why can you not lift yourself by pulling up on your own belt?

Example 17

challenge

3\text{ kg}

astronaut throws a

1\text{ kg}

wrench at

6\text{ m/s}

in deep space. Find the astronaut's recoil speed.

Example 18

challenge

A book (

W=20\text{ N}

) rests on a table. List the third-law partner of its weight and of the normal force.

Example 19

challenge

1500\text{ kg}

car pushes against the ground; the ground's reaction accelerates it at

3\text{ m/s}^2

. What force does the car exert on the ground, ignoring drag?

Car exerts 4500 N backward on the ground; ground's reaction is 4500 N forward (= ma

Example 20

medium

A swimmer pushes water backward with

80\text{ N}

. State the reaction and its effect.

Example 21

medium

2\text{ kg}

cart pushes a

6\text{ kg}

cart with

24\text{ N}

. By the third law, what force does the

6\text{ kg}

cart push back, and find its acceleration.

2 kg cart pushes 6 kg cart with 24 N; reaction: 6 kg cart pushes 2 kg cart with 24 N. a₆

Example 22

medium

A gun of mass

4\text{ kg}

fires a

0.02\text{ kg}

bullet at

400\text{ m/s}

. Find the gun's recoil speed.

Example 23

easy

A swimmer pushes water backward with a force of

80 \text{ N}

. What force pushes the swimmer forward?

Example 24

easy

Earth pulls a

2 \text{ kg}

apple downward with a force of

19.6 \text{ N}

. With what force does the apple pull on the Earth?

Example 25

easy

A horse pulls a cart with

400 \text{ N}

. What is the force of the cart on the horse?

Example 26

medium

A bullet of mass

0.020 \text{ kg}

leaves a

3 \text{ kg}

rifle at

400 \text{ m/s}

. Assuming the rifle was at rest, find the rifle's recoil speed.

Example 27

medium

Two ice skaters (

80 \text{ kg}

and

60 \text{ kg}

) push off each other. If the

80 \text{ kg}

skater moves at

1.5 \text{ m/s}

, how fast does the other move?

80 kg skater moves at 1.5 m/s; by momentum conservation 60 kg skater moves at 80×1.5/60

Example 28

medium

0.5 \text{ kg}

ball hits a wall and bounces off. The wall exerts

200 \text{ N}

on the ball during contact. What force does the ball exert on the wall?

Example 29

medium

60 \text{ kg}

person on roller skates pushes a

30 \text{ kg}

wagon with a force of

90 \text{ N}

. Find the magnitude of the person's acceleration. (Friction is negligible.)

Person pushes 30 kg wagon right with 90 N; by third law wagon pushes person left 90 N → a

Example 30

medium

A jet engine exerts a thrust of

1.5 \times 10^5 \text{ N}

by expelling gas backward. With what force does the gas push the jet forward?

Example 31

medium

5 \text{ kg}

box rests on the floor. Earth pulls it down with

49 \text{ N}

. Name the reaction partner and the object on which it acts.

Example 32

hard

40 \text{ kg}

child stands on a

5 \text{ kg}

skateboard on frictionless ice. The child jumps forward off the board at

3 \text{ m/s}

relative to the ground. Find the board's speed afterward.

Example 33

hard

0.5 \text{ kg}

bird sits on a

4 \text{ kg}

branch. Earth pulls the bird with

4.9 \text{ N}

. What is the force the branch exerts on the bird, and what is the third-law partner of THAT force?

Example 34

hard

50 \text{ kg}

swimmer pushes off a pool wall with a force of

250 \text{ N}

for

0.4 \text{ s}

. Find the swimmer's speed after pushing off (start from rest, ignore drag).

Example 35

hard

Two carts, masses

m

and

3m

, are connected by a compressed spring and released on a frictionless track. The light cart moves off at

6 \text{ m/s}

. Find the heavy cart's speed.

Example 36

challenge

A toy rocket of total mass

0.50 \text{ kg}

expels gas at

20 \text{ g/s}

with exhaust speed

200 \text{ m/s}

relative to the rocket. Find the initial upward thrust on the rocket.

Example 37

challenge

Explain in one sentence why a horse can accelerate a cart despite Newton's third law saying the cart pulls the horse equally hard.

← Back to Newton's Third Law Practice Mode

Related Concepts

Force Newton's First Law Momentum Impulse

Background Knowledge

These ideas may be useful before you work through the harder examples.

forcenewtons first law