Newton’s Third Law of Motion

Newton’s Third Law of Motion - Definition, Formula, Examples and Numerical Problems

Newton’s Third Law of Motion is one of the important principles in physics. It explains how forces act between two interacting objects and why every force has an opposite partner. We can observe this law in everyday activities, such as walking, swimming, jumping rowing a boat and launching a rocket.

For example when you walk on the ground your foot pushes the ground backward. The ground pushes your foot forward. This forward force helps you move. Similarly when a rocket expels gases backward the gases exert a force that pushes the rocket forward.

In this article you will learn the definition of Newton’s Third Law of Motion its formula, mathematical explanation, solved problems, practical examples, applications and frequently asked questions.

What Is Newton’s Third Law of Motion?

Newton’s Third Law of Motion states:

“For every action there is an opposite reaction."

According to this law whenever one object exerts a force on another object the second object simultaneously exerts a force of magnitude in the opposite direction on the first object.

These forces are called the action force and reaction force.

For example when you push a wall with your hand your hand applies a force to the wall. At the time the wall applies an equal force in the opposite direction to your hand.

The wall may not move because other forces and the wall’s support keep it in place. However the interaction forces between your hand and the wall still exist.

One important point to remember is that action and reaction forces act on objects. Therefore they do not cancel each other when analysing the motion of either object

Newton’s Third Law of Motion Formula

Newton’s Third Law can be represented mathematically as:

Fₐᵦ = −Fᵦₐ

Where:

• Fₐᵦ = Force exerted by object A on object B.

• Fᵦₐ = Force exerted by object B on object A.

• The sign indicates that the forces act in opposite directions.

The magnitudes of the two forces are equal:

|Fₐᵦ| = |Fᵦₐ|

For example if object A pushes object B with a force of 20 N towards the right object B simultaneously pushes object A with a force of 20 N towards the left.

Therefore:

Force exerted by A on B = 20 N to the right.

Force exerted by B on A = 20 N to the left.

Remember: Action and reaction forces have magnitudes and opposite directions but they act on two different objects.

Explanation of Newton’s Third Law of Motion

Newton’s Third Law explains how forces occur in pairs during an interaction.

Consider two people standing on skateboards. If one person pushes the person the first person exerts a force on the second person. At the time the second person exerts an equal and opposite force on the first person.

Both people may move in directions. Their accelerations can be different because their masses and other forces may be different.

The law applies to contact forces, such as pushing and pulling, well as forces that act without direct contact, such as gravitational and electromagnetic interactions.

Important Characteristics of Newton’s Third Law

1. Equal magnitude: The two forces have magnitudes.

2. Direction: The forces act in opposite directions.

3. Interaction: Both forces occur together as part of the same interaction.

4. Different objects: Each force acts on an object.

5. Interaction: The forces belong to the same interaction between two objects.

6. Independent of motion: The objects can be stationary, moving or accelerating.

Real-Life Examples of Newton’s Third Law of Motion

Newton’s Third Law can be observed in common activities. The following examples explain how this law works in life.

1. Walking on the Ground

Walking is one of the examples of Newton’s Third Law.

When you walk your foot pushes the ground backward. In response the ground exerts a frictional force on your foot helping you move forward.

On a surface walking becomes difficult because your foot cannot get enough friction to push effectively against the ground.

• Action: Your foot pushes the ground backward.

• Reaction: The ground pushes your foot forward.

This interaction helps explain how people walk without falling backward.

2. Swimming in Water

A swimmer moves forward by pushing water with their hands and feet.

According to Newton’s Third Law the water exerts a force on the swimmer. This force helps propel the swimmer

• Action: The swimmer pushes water backward.

• Reaction: The water pushes the swimmer forward.

This principle is also important in understanding the movement of animals and water-propelled devices.

3. Rocket Launch

Rocket propulsion is an example of Newton’s Third Law.

A rocket engine burns. Expels exhaust gases at high speed through its nozzle. The rocket pushes the gases backward. The gases exert a forward thrust on the rocket.

This thrust can accelerate a rocket upward when it is large enough to overcome gravity and other opposing forces.

• Action: The rocket pushes exhaust gases backward.

• Reaction: The gases exert a force on the rocket.

A rocket does not need air to push against. It can produce thrust in the vacuum of space because the engine expels exhaust gases.

4. Firing a Gun

When a gun fires a bullet the gun exerts a force on the bullet. At the time the bullet exerts an equal and opposite force on the gun.

This causes the gun to move backward a phenomenon known as recoil.

• Action: The gun pushes the bullet forward.

• Reaction: The bullet pushes the gun backward.

Although the forces have magnitudes the bullet and the gun generally experience different accelerations because their masses are different.

5. Jumping from the Ground

When a person jumps their feet push the ground downward. The ground exerts a force on the person.

This upward force helps accelerate the person into the air.

• Action: The person pushes the ground downward.

• Reaction: The ground pushes the person upward.

The ground’s upward force is a part of the process that allows a person to jump.

6. Rowing a Boat

When a person rows a boat the oars push water backward. The water then exerts a force on the oars and boat in the direction.

This forward force helps the boat move through the water.

• Action: The oars push water backward.

• Reaction: The water pushes the boat forward.

Rowing demonstrates how forces can be used to move an object through a fluid.

7. Pushing a Wall

When you push a wall your hand applies a force to it. The wall applies an opposite force to your hand.

Even if the wall does not move the forces still exist. The wall remains stationary because the forces acting on it including those supported by the building structure prevent it from accelerating.

• Action: Your hand pushes the wall.

• Reaction: The wall pushes your hand.

This example shows that a force does not always produce movement.

8. A Balloon Releasing Air

Inflate a balloon and release its opening without tying it. Air escapes in one direction. The balloon moves in the opposite direction.

The balloon pushes air outward. The escaping air produces an opposing force on the balloon.

• Action: The balloon pushes air outward.

• Reaction: The air exerts a force that moves the balloon in the direction.

This is an experiment that demonstrates the basic principle of rocket propulsion.

9. Kicking a Football

When a player kicks a football the foot exerts a force on the ball. Simultaneously the ball exerts an opposite force on the players foot.

The force on the ball can change its velocity while the force on the foot can be felt as an impact.

• Action: The foot pushes the football.

• Reaction: The football pushes the foot in the direction.

Newton’s Second Law helps explain the ball’s acceleration while Newton’s Third Law explains the paired forces during the kick.

10. Two People Pushing Each Other on Skateboards

Suppose two people stand on skateboards and push each other. Each person exerts a force on the other causing them to move apart if the forces and other conditions allow.

The interaction forces have magnitudes and opposite directions but the two people may have different accelerations because their masses differ.

This is a demonstration of Newton’s Third Law in a classroom or science activity.

Solved Numerical Examples of Newton’s Third Law

Newton’s Third Law primarily describes pairs of forces. Numerical questions often ask you to determine the magnitude and direction of a reaction force. Some problems combine this law with Newton’s Second Law.

Example 1: Calculate the Reaction Force

Question: Object A pushes object B with a force of 30 N towards the right. Calculate the force exerted by object B on object A.

Given:

Force exerted by A on B = 30 N to the right.

Principle:

The reaction force has the magnitude and the opposite direction.

Solution:

Reaction force = 30 N to the left.

Answer: Object B exerts a force of 30 N towards the left, on object A.

Example 2: A Person Pushes a Trolley

A person pushes a trolley with a force of 50 N. The trolley has a mass of 10 kg and there is a horizontal force of 50 N acting on it. Figure out the acceleration. Find the reaction force.

Given:

The net force on the trolley is 50 N.

The mass of the trolley is 10 kg.

Step 1: Figure out the acceleration using Newton’s Second Law.

Formula:

a equals F divided by m

Put in the numbers:

a equals 50 divided by 10

a equals 5 meters per squared

Step 2: Find the reaction force.

The trolley pushes back with a force of 50 N in the direction as part of the interaction.

Answer:

• The acceleration of the trolley is 5 meters per second squared in the direction of the force.

• The reaction force that the trolley applies on the person is 50 N in the direction.

The persons acceleration can't be found with this information because we don't know their mass or the other forces acting on them.

Example 3: Two Objects Exert Forces on Each

Question: Object A applies a force of 80 N on object B towards the north. What is the force that object B applies on object A?

Solution:

According to Newton’s Third Law the forces are the same in size. Opposite in direction.

Force that B applies on A is 80 N towards the south.

Answer: 80 N towards the south.

Example 4: Find the Acceleration of Two Interacting Objects

Question: A 4 kg object and a 2 kg object push against each other on a horizontal surface. The 4 kg object applies a force of 12 N on the 2 kg object. Assuming this is the horizontal force on the 2 kg object calculate the acceleration of each object due to the interaction.

Step 1: Calculate the acceleration of the 2 kg object.

Using Newton’s Second Law:

a equals F divided by m

a equals 12 divided by 2

a equals 6 meters per squared

The 2 kg object speeds up in the direction of the force from the 4 kg object.

Step 2: Calculate the acceleration of the 4 kg object.

The 2 kg object applies a force of 12 N in the direction on the 4 kg object.

A equals F divided by m

a equals 12 divided by 4

a equals 3 meters per squared

The 4 kg object accelerates in the opposite direction.

Answer:

• The acceleration of the 2 kg object is 6 meters per squared.

• The acceleration of the 4 kg object is 3 meters per second squared in the direction.

This example shows that the forces between interacting objects are equal. However the accelerations can be different because the masses are different.

Why Do Action and Reaction Forces Not Cancel Each Other?

One of the asked questions about Newton’s Third Law is why the equal and opposite forces do not cancel.

The answer is simple: the action and reaction forces act on objects.

For example when you push a trolley you apply a force on the trolley. The trolley applies an opposite force on you.

When you look at the trolley’s acceleration you only look at the forces acting on the trolley. The force that the trolley applies on you does not cancel the force on the trolley because it acts on your body.

Forces can cancel when they are equal and opposite and act on the object. However an action–reaction pair from Newton’s Third Law acts on two objects.

Difference Between Newton’s Second and Third Laws

Newton’s three laws explain different parts of movement.

Newton’s First Law of Motion: An object stays at rest. Moves in a straight line at a constant speed unless a net external force acts on it. This is also known as the Law of Inertia.

Newton’s Second Law of Motion: The net external force causes an object to accelerate. For a mass the formula is F equals mass multiplied by acceleration.

Newton’s Third Law of Motion: Every interaction has forces that're equal in size and opposite in direction acting on two different objects.

For example when a football is kicked:

• The First Law explains why the ball is still until it starts moving.

• The Second Law explains how the net force makes the ball move.

• The Third Law explains why the ball pushes back on the player’s foot.

Together these three laws give a base for understanding mechanics.

Applications of Newton’s Third Law in Daily Life

Newton’s Third Law is used in daily actions, engineering, transport and technology.

•. Running: The force from the feet and the ground helps move

• Swimming: Pushing water backward helps the swimmer move forward.

• Rocket movement: Expelling gases helps the rocket move forward.

• Car movement: Tires push the ground. The ground pushes back on the tires.

• Sports: Balls and bats push each other during contact.

•. Ships: Propellers push water back to move forward.

• Industrial machines: Parts push each other while working.

• Space travel: Rockets move forward without needing air to push against.

These uses show that Newton’s Third Law is important for both complex systems.

Frequently Asked Questions (FAQs)

1. What is Newton’s Third Law of Motion?

Newton’s Third Law says that for every action force there is an opposite reaction force. The two forces act on objects.

2. What is the formula for Newton’s Third Law?

The formula is:

F equals negative F

This means that the force from object A on object B is equal in size and opposite in direction to the force from object B on object A.

3. Give five examples of Newton’s Third Law.

Five examples are walking on the ground, swimming, rocket launch, gun recoil and rowing a boat.

4. Why does a rocket move forward?

A rocket pushes gases backward. The force creates a push on the rocket so it can move when the net force is in the forward direction.

5. Why does a gun move back when fired?

The gun pushes the bullet forward. The bullet pushes back on the gun. This backward movement is called recoil.

6. Do action and reaction forces cancel each other?

No. They act on objects so they do not cancel when looking at the net force on one object.

7. Can an object feel a force without moving?

Yes. An object can stay still if the forces on it balance. For example a wall can push on your hand while staying still.

8. Are action and reaction forces always equal?

Yes. For the action the forces are the same in size but opposite in direction. The effects on the two objects can be different because the objects might have masses or other forces acting on them.

9. Who came up with Newton’s Third Law of Motion?

Sir Isaac Newton created the three laws of motion. Wrote about them in his 1687 book Philosophiæ Naturalis Principia Mathematica.

10. What is the difference between Newton’s Third Laws?

Newton’s Second Law connects force with acceleration using F equals mass multiplied by acceleration for constant mass. Newton’s Third Law talks about forces that're equal and opposite acting on two different objects.