Newton's Third Law of Motion

When you jump, you feel the gravitational force pulling you down towards the Earth. But did you know that at the same time, you are exerting an equal force on the Earth? This phenomenon is explained by Newton's Third Law of Motion.

Newton's Third Law of Motion is a foundational principle in physics, often referred to as the law of action and reaction. It plays a key role in countless everyday phenomena, from walking to rocket propulsion. This law highlights the inherent symmetry of forces, showing that forces always come in pairs—when one body exerts a force on another, it simultaneously experiences an equal and opposite force. Here, we will explore Newton's Third Law of Motion in detail, including its formula, examples, and practical applications.

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction.

⇒Newton’s Third Law of Motion states that when one object applies a force on another, the first object experiences a force equal in magnitude but opposite in direction to the applied force.

⇒According to the above statement, each interaction consists of 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 to the force acting on the second item.

⇒It is one of the three important laws of motion given by Sir Isaac Newton that directs the motion of any object in nature. This principle is also known as the Law of Action and Reaction.

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 F_AB (force applied by body B on body A) is equal to force F_BA (force applied by body A on body B) but they are opposite in direction.

Suppose, When a man pushes against a wall, the force he applies on the wall (F_AB) is equal in magnitude but opposite in direction to the force the wall applies on him (F_BA). Both forces act simultaneously, but the wall's force pushes the man back while the man pushes forward.

• 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

The differences between action force and reaction force can be clearly conclude through various examples of action-reaction pairs, as outlined in the table below.

Also Check, Law of Action and Reaction

Formula,

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

Let's consider two objects 1 and 2, and 1 exerts a force F₁₂ on '2' then 2 will also exert a similar force on 1 as F₂₁ in the opposite direction such that 

F₁₂ = - F₂₁

OR 

F₁₂ + F₂₁ = 0

⁛ This tells us that the total force exerted by the system comprising both 1 and 2 is zero.

Proof of Third Law of Motion (using Conservation of Momentum)

Momentum

Momentum is a measure of an object's motion and is defined as the product of its mass and velocity. It is a vector quantity, meaning it has both magnitude and direction.

p=mv

where:

p = momentum,

m = mass of the object,

v = velocity of the object.

In the International System of Units (SI), momentum is measured in kilogram meters per second (kg·m/s).

According to conservation of momentum a closed system with no external forces, the total momentum remains constant. This is expressed as:

Total Momentum=constant

Initial Momentum=Final Momentum

Consider the example of gun and bullet Interacting interacting with each other. Let them exert forces on each other during their interaction. The force that Gun exerts on Bullet F_{GB} and the force that Bullet exerts on Gun F_{BG}.

According to conservation of momentum:

Initial Momentum of Gun + Initial Momentum of Bullet = Final Momentum of Gun + Final Momentum of Bullet

→mass _gun ⨯ Initial Velocity _gun + mass _bullet ⨯ Initial Velocity _bullet = mass _gun ⨯ Final Velocity _gun + mass _bullet ⨯ Final Velocity _bullet

⇒ mass _gun ⨯ Initial Velocity _gun - mass _gun ⨯ Final Velocity _gun = mass _bullet ⨯ Final Velocity _bullet - mass _gun ⨯ Initial Velocity _gun

⇒ - (mass _gun ⨯ Final Velocity _gun - mass _gun ⨯ Initial Velocity _gun ) = mass _bullet ⨯ Final Velocity _bullet - mass _gun ⨯ Initial Velocity _gun

⇒ - mass _gun ⨯ (Final Velocity _gun - Initial Velocity _gun ) = mass _bullet ⨯ (Final Velocity _bullet - ⨯ Initial Velocity _gun)

Dividing both side by time,

⇒- mass _gun ⨯ (Final Velocity _gun - Initial Velocity _gun ) /t = mass _bullet ⨯ (Final Velocity _bullet - ⨯ Initial Velocity _gun)/t

- mass _gun ⨯ Acceleration _Gun = mass _bullet ⨯ Acceleration _bullet

⇒ -F_BG = F_GB

Where,

F_GB = Force on Bullet Exerted by Gun ( Action)

F_BG = Force on Gun Exerted by Bullet ( Reaction)

And the negative sign indicates the direction of -F_BG is opposite to F_GB

Note :

When two charged particles interact through electromagnetic force, they exert equal and opposite forces on each other, even though they don’t physically touch. These forces act at a distance, but they still come in action-reaction pairs as described by Newton's Third Law.

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:

Example 1: 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.

Example 2: Hitting on the Jaw

In boxing, when a boxer delivers a punch to an opponent's jaw, it serves as a clear example of Newton's Third Law of Motion. When the boxer's fist makes contact with the opponent's jaw, the fist exerts a force on the jaw (action force). According to Newton's Third Law, the opponent's jaw exerts an equal and opposite force on the boxer's fist (reaction force). 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.

Example 3: 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.

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

Practical Applications of Newton's Third Law of Motion

Newton's Third Law of Motion states, "For every action, there is an equal and opposite reaction." This principle is incredibly applicable in our daily lives, often guiding our actions without us even realizing it. Here’s a more effective breakdown of how this law comes into play in various situations:

Rockets and Thrust

Rocket propulsion demonstrates Newton's Third Law of Motion. When a rocket burns fuel, it expels hot gases downward (action), creating an equal and opposite upthrust (reaction) that propels the rocket upward. The force applied to the rocket is 'F' causing it to accelerate with 'a.' This action-reaction pair is essential for the rocket to overcome gravity and launch into space. The expulsion of exhaust gases and resulting upthrust is the key mechanism behind rocket propulsion.

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.

Sports

In sports, understanding the third law of motion by Newton helps improve performance. Athletes use this knowledge to enhance their techniques in activities like running, jumping, and throwing.

Driving a Car

When a car’s wheels push backward on the road, the road pushes the car forward with an equal and opposite force. This is why a car accelerates when the engine applies force to the wheels.

Jumping

When you push down on the ground to jump, you apply a force in the downward direction. In response, the ground pushes you upward with an equal and opposite force, allowing you to lift off the ground.

Misconceptions about Newton's Third Law of Motion

Misconception 1: Forces Cancel Each Other

A common misconception is that the action and reaction forces cancel each other out. While they are equal and opposite, they act on different bodies and thus do not cancel out.

Misconception 2: Only Large Objects Exhibit These Forces

Newton's Third Law applies to all objects, regardless of their size. Even microscopic particles experience these forces.

Solved Examples

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

Change in momentum = mv - mu

Change in momentum = m (v - u)

Change in momentum = 0.5 kg × (20 m/s - 10 m/s)

Change in momentum = 0.5 kg × 10 m/s

Change in momentum = 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.

Example 3 :A rocket expels gases at a speed of 3000 m/s. If the mass of the gases expelled per second is 500 kg/s, calculate the thrust (reaction force) produced.

Solution:

Given:

• Speed of gases = 3000 m/s
• Mass flow rate = 500 kg/s

Using the formula for thrust:

Thrust (F)=mass flow rate×velocity of gases

F=500kg/s×3000m/s=1,500,000N

The thrust produced is 1,500,000 N.

Example 4 : Two ice skaters are standing on a frictionless ice surface. One skater, A, pushes against skater B with a force of 50 N. What is the force exerted by skater B on skater A, and what will be the effect on the motion of both skaters?

Solution:

According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. This means that the force exerted by skater A on skater B will be equal in magnitude but opposite in direction to the force exerted by skater B on skater A.

• Force exerted by skater A on skater B = 50 N
• Force exerted by skater B on skater A = -50 N (negative because it's in the opposite direction)

Practice Problems

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?

Conclusion

Newton's Third Law of Motion states that for every action force, there is an equal and opposite reaction force. In other words, when one object applies a force on another, the second object applies a force of the same magnitude but in the opposite direction on the first object. These forces always occur in pairs and act on separate objects. This principle highlights the mutual interaction between two objects and is fundamental about the motion of bodies.

Also, Read

• Newton's laws of Motion
• Newton's Second Law of Motion
• Newton's First Law of Motion
• Laws of Conservation of Momentum