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Newton’s Third Law of Motion

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Newton’s Third Law of Motion states that a given pair of bodies exert equal and opposite forces on each other. Newton’s Third Law of Motion is one of the basic laws of physics which is very useful in various aspects. Newton’s Third Law represents a specific symmetry in the nature of forces and explains how they always exist in pairs, and one body cannot exert a force on another without also experiencing a force.

It is one of three laws of motion given by Sir Isaac Newton. Newton’s third law of motion highlights a fundamental principle of symmetry in nature. It tells us that forces are always part of a mutual exchange: when one body exerts a force on another, it inevitably experiences an equal and opposite force in return. In simpler terms, you can’t push or pull something without that something pushing or pulling back on you with the same strength but in the opposite direction.

In this article, we will learn about Newton’s third law of motion, its definition, formula, derivation, and examples of third law of motion.

Isaac-Newton

What is Newton’s Third Law of Motion

Newton’s Third Law of Motion states that “When one body exerts a force on another, the first body feels a force equivalent in the opposite direction of the force exerted.” According to the above statement, every interaction involves a pair of forces exerted on the interacting objects. The magnitudes of the forces are equal, and the force on the first item is directed in the opposite direction as the force on the second item.

Let’s understand Newton’s Third Law of Motion more clearly with the help of the following examples:

  • While moving on the ground, we push the ground backward by our feet. The ground also exerts a forward force on our feet of equal magnitude in the opposite direction which makes us move forward.
  • A book when lying on a table. The book exerts a downward force due to its weight, but it does not fall down, therefore the net force on the book is zero. This is because the table exerts an equal and opposite force on the book in the upward direction.

Explanation of Newton’s Third Law of Motion

In both examples listed above, we can see that there are two forces that are acting on each body. In the first example, the force exerted by our feet on the ground is the action force and in response to that, the ground exerts an equal opposite force on our feet. In the second example, the force exerted by the weight of the book is the action force and the force exerted by the table on the book is the reaction force.

Action and Reaction Force

Now, let’s learn about two terms called Action and Reaction force, which are used in Newton’s third law of motion.

Action Force: The initial outside force exerted on the body is called the action force.

Reaction Force: The force the body exerts to respond to the active force in the opposite direction is called reaction force.

From the above case, Newton’s third law of motion can also be stated as:

If there is any interaction between two bodies (A and B), the force FAB (force applied by body B on body A) is equal to force FBA (force applied by body A on body B) but they are opposite in direction.

Note on Action and Reaction Forces

  • Action and Reaction forces are exerted by different bodies and not by the same body.
  • Action and Reaction always occur simultaneously, and they are always in pair.

Difference between Action and Reaction Force

Differences between action force and reaction force can easily be understood by the examples of action-reaction pairs as discussed below in the table.

Action Force

Reaction Force

Weight of the book lying on a table acting in the downward direction is action force. Force exerted by the table on the book in an upward direction is the reaction force.
Force exerted by the rocket on the burnt gases in the downward direction is action force. Force exerted by the gases on the rocket in an upward direction is the reaction force.
Force exerted by the gun on the bullet in the forward direction is action force. Force exerted by the bullet on the gun in the backward direction is the reaction force.

Newton’s Third Law of Motion Formula

Newton’s third law of motion formula or mathematical expression is given as follows:

Let’s consider two objects A and B, and A exerts a force FAB on ‘B’ then B will also exert a similar force on A as FBA in the opposite direction such that 

FAB = – FBA

OR 

FAB + FBA = 0

This tells us that the total force exerted by the system comprising both A and B is zero.

Examples of Action-Reaction Forces

Nature has a wide range of action-reaction pairings. Following are some examples listed below,

  • An example of an action-reaction pair is the movement of a fish through water. A fish’s fins are used to push water backward. This push serves to propel the fish ahead. The magnitude of the force on the water equals the magnitude of the force on the fish; the magnitude of the force on the water (backward) is opposite to the magnitude of the force on the fish (forwards).
  • The bird’s flight is an example of an action-reaction pair. The air is pushed downward by the bird’s wings. The bird is pushed higher by the air.
  • A swimmer pushes up against the water, and the water pushes him back.
  • Helicopters generate lift by forcing the air downward, resulting in an upward reaction force.
  • Climbers use their vertical rope to propel themselves upwards.
  • While walking on the ground, a person exerts a force on the ground in a backward direction with his feet (action force) and according to Newton’s third law of motion, the ground exerts an opposite and equal force in the forward direction as a reaction force, and so we can walk on the ground or on floor.

Newton’s Third Law of Motion Examples

There are various examples of Newton’s third law of motion in our daily life. Some of these examples are discussed as follows:

Firing a Bullet from a Gun

When a bullet is fired from a gun, the gun applies a force F to the bullet which can be considered as (action force) whereas simultaneously the bullet also applies the same force on the gun called the recoil of the gun which can be considered as the reaction force.

Catching a Ball

A fielder catching a ball experiences a force on its hand by the ball (action force) and the same amount of force is also observed by the ball (reaction force). The image given below shows a fielder catching a ball, when the fielder catches the ball it experiences the reaction force.

Motion of a Boat in Water

How a boat move in water is the best way to explain Newton’s Third Law of Motion. If we observe a boatman rowing the boat we see that when the boatman pushes the water backward with his oar (action force) the water pushes the boat forward (reaction force) and in this way, a boat moves in the water.

Newton's Third Law of Motion Examples

 

Statement Validation of Newton’s Third Law of Motion

All of Newton’s Laws of Motion are only valid in inertial frames. So it is safe to assume that Newton’s Third Law of Motion is also only valid in the inertial frame of reference. The frame of reference is a situation in which the observer observes the surroundings. So, a frame of reference in which either the body is at rest or moving with a constant velocity or zero acceleration in a straight line is an inertial frame

Applications of Newton’s Third Law of Motion

Newton’s Third Law of Motion is one of the most applicable laws in our daily life. We use this law intuitively without even thinking about it if we got disbalance our bodies try to apply force in the opposite direction so that we won’t fall on the ground. Some more applications of Newton’s third law are discussed in detail as follows:

Rockets and Thrust

Rocket Propulsion is another example of the use of Newton’s Third Law of Motion. According to this theory,

”A rocket is launched into space using the upthrust created by releasing the hot gases from its exhaust.” Here in the image given below a rocket goes up with acceleration ‘a’ when the force applied is ‘F’ but an equal amount of reactive force is also experienced by the exhaust gases of the rocket.

A rocket accelerating

The working of rocket propulsion is the same as the action-reaction pair in Newton’s Third Law. In this situation, the burning of fuel and the release of hot gases from the engine of the rocket is the action and the upthrust created by it is the reaction that sends the rocket into space.

Swimming

Swimming is also an example of action and reaction forces. When a person swims and pushes the water backward with the help of his hands and feet, the water exerts an equal force on the person in the forward direction. The action in swimming is the person pushing the water, and the reaction is the water pushing the person.

Resources related to Newton’s third law,

Solved Examples on Newton’s Third Law of Motion

Example 1: A man pushes a wall with a force of 100N towards the north. What force does the wall exert on the man?

Solution:

Given,

Action force, F is 100 N.

According to Newton’s third law of motion,  

Action force = – Reaction force

Therefore, the reaction force = -100 N  

That is, the reaction force is equal to 100 N towards south.

Example 2: A cricket ball of mass 500 g travelling at 20 m/s is hit by a cricket bat to return it along its original path with a velocity of 10 m/s. Calculate the change of momentum that occurred in the motion of the cricket ball by the force applied by the cricket bat.

Solution:

Given,

Mass of the hockey ball, m is 500 g = 0.5 kg.

Initial velocity of the ball, u is 20 m/s. 

Final velocity of the ball after hitting, v is 10 m/s.

Change in momentum = Final momentum – Initial momentum

                                     = mv – mu

                                     = m (v – u)

                                     = 0.5 kg × (20 m/s – 10 m/s)

                                      = 0.5 kg × 10 m/s

                                      = 5 kg m/s

Therefore, change of momentum of the cricket ball by the force applied by the cricket bat is 5 kg m/s.

Practice Problems on Newton’s third law of Motion

1. If you push a book on a table with a force of 10 N to the right, what is the reaction force exerted by the table on the book?

2. When a swimmer pushes water backward with their legs, what is the reaction force that propels the swimmer forward?

3. A rocket engine expels exhaust gases backward with a force of 1,000 N. According to Newton’s Third Law, what is the force that propels the rocket forward?

4. If you stand on a bathroom scale and exert a downward force of 600 N on it, what force does the scale exert on you?

5. When you row a boat by pushing water backward with an oar, what is the reaction force that moves the boat forward?

FAQs on Newton’s Third Law of Motion

1. State Newton’s Third Law of Motion.

According to newton’s third law of motion “Every action, has an equal and opposite reaction.”

2. Is Newton’s third law important for class 9?

Yes, Newton’s third law of motion is very important for class 9. Infact, all the three laws of motion are very important.

2. Give an example of Newton’s Third Law of Motion.

There are various condition in our daily life where we observe Newton’s third law in action. Some of the examples explaining Newton’s third law are,

  • A rocket going upward pushes the hot gases downwards.
  • Recoil is observed when we fire a bullet from the gun.
  • While moving forward we push the ground backward with our feet.

3. What are the Contact force & Non-contact force?

There are two different types of forces

  • Contact Force: The force which act only when two bodies are in contact are called Contact Forces. Example: Friction, etc.
  • Non-Contact Force: The force which act on two bodies without being them in contact is called Non-Contact Forces. Example: Electrostatics Force, Magnetic Force, etc.

4. What are Third-Law-Force pairs?

The Action-Reaction pair is called the Third-law-force pair. Such pair include,

  • Firing of bullet and Recoil of gun
  • Rocket going upward and hot gases going downword

5. If the Astronaut wanted to Move Upward, in Which Direction should he Throw the Object? Why?

If the astronaut wanted to move upward, he should throw the object downward as the downward force creates a upword reaction force which move the astronaut upward.

6. Do Weight and Normal Force act on a block placed on a flat surface called Action-Reaction pair?

Yes, weight and normal force acting on a block placed on a flat surface are action-reaction pairs. Here the weight of object acts downward and normal force acts upward and both force cancel out each other resluting in no acceleration.



Last Updated : 04 Feb, 2024
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