Statement
To every action there is always an equal and opposite reaction
To every action there is always an equal and opposite reaction
Proof
Consider about two moving bodies in an isolated system. Masses of the bodies are M1 and M2. Velocities are V1 and V2.
Consider about two moving bodies in an isolated system. Masses of the bodies are M1 and M2. Velocities are V1 and V2.
Due to interaction, their velocities change. Consequently there will be change in their momenta in time ∆t. Suppose, change in momentum of the first body = ∆p1 and change in momentum of the second body = ∆p2.
From the law of conservation of linear momentum, we know that
∆p1 + ∆p2 = 0
∆p2 = -∆p1
Now, dividing both sides by ∆t
∆p2/∆t = - ∆p1/∆t
Take limit both sides when ∆t tends to zero.
dp2/dt = - dp1/dt
F2 = - F1
Force acting on M2 = - Force acting on M1
Action = - Reaction
To every action there is always an equal and opposite reaction. Proved.
This represents Newton's third law of motion.
∆p2 = -∆p1
Now, dividing both sides by ∆t
∆p2/∆t = - ∆p1/∆t
Take limit both sides when ∆t tends to zero.
dp2/dt = - dp1/dt
F2 = - F1
Force acting on M2 = - Force acting on M1
Action = - Reaction
To every action there is always an equal and opposite reaction. Proved.
This represents Newton's third law of motion.
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