Conservation Of Linear Momentum In Collision

Let two bodies 1 and 2 collide against each other. They exert mutual impulsive forces on each other during the collision time ∆t. The change produced in momentum of the two bodies will be

∆P₁ = F₁₂∆t and ∆P₂ = F₂₁∆t

Where, F₁₂ is force exerted by 2 on 1

and F₂₁ is force exerted by 1 on 2.

Now, According to Newton’s third law of motion, We have

F₁₂ = – F₂₁

Multiplying both side by ∆t

F₁₂∆t = – F₂₁∆t

F₁₂∆t + F₂₁∆t = 0

∆P₁ + ∆P₂ = 0

∆(P₁ + P₂) = 0

P₁ + P₂ = Constant

Hence, The total linear momentum is conserved at each instant during collision.

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