Newtons Third Law of Motion, Law of Conservation of Momentum

Newtons Third Law of Motion:

According to Newton’s Third Law of Motion, if a body exerts a force on some other body, then the second body exerts a force of the same magnitude but in opposite direction on the first body. Newtons Third Law of Motion may be stated as follows-

To every action, there is an equal and opposite reaction.

For the illustration of Newton’s Third Law of Motion, consider the following examples-

A ball thrown against a hard surface (action) rebounds with equal and opposite force (reaction).
A bullet fired from the gun (action) pushes the gun backward (reaction).
While walking on the ground, we exert a force over it by our foot (action), and our body is pushed forward by the ground (reaction).
When an athlete takes a jump, he presses the ground backward (action) and the ground throws him forward (reaction).
Due to the escaping gases from its rear end (action), the rocket moves upwards (reaction).

Law of Conservation of Momentum:

Let us discuss the change in momentum when two bodies moving in the same direction collide.

Consider two bodies A of mass m₁ and B of mass m₂ moving in the same direction with velocities μ₁ and μ₂ respectively. Let these bodies collide for a short time t and acquire the velocities ν₁ and ν₂ after the collision. Let the force experienced by A be F_A and by B be F_B during the time of the collision. Then-

According to Newton’s second law of motion,

F_A = Force on body A = m₁ (ν₁ – μ₁) / t

F_B = Force on body B = m₂ (ν₂ – μ₂) / t

According to Newton’s third law of motion, the force F_A should be equal and opposite to the force F_B.

Therefore, F_A = – F_B

or m₁ (ν₁ – μ₁) / t = -m₂ (ν₂ – μ₂) / t

or m₁ (ν₁ – μ₁) = -m₂ (ν₂ – μ₂)

or m₁ν₁ + m₂ν₂ = m₁μ₁ + m₂μ₂

Thus, the total momentum before the collision (m₁μ₁ + m₂μ₂) is equal to the total momentum after the collision. This shows that there is no change in the momentum of the system due to the action and reaction of the bodies A and B forming the system. This may be generalized by saying that the total momentum of the system is conserved when no external force acts on the system. This is called the law of conservation of momentum.