Principle of Conservation of Linear Momentum | Physics Grade XI

Linear Momentum

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Principle of Conservation of Linear Momentum | Physics Grade XI

Principle of Conservation of Linear Momentum

Principles of Conservation of Linear Momentum

Principle of law of conservation of linear momentum states, "if no external forces act on the system of colliding bodies then the vector sum of the linear momentum of each body will remain conserved and is not affected by the mutual interaction between them".

Let us consider a collision between two spheres A and B having masses of m1 and m2 respectively. Let u1 and u2 be the velocities of the spheres before collision such that u1>u2 and moving on the same straight line.

Let FA be the force exerted by body A on body B and FB be the force exerted by body B on body B during a collision. Let them collide for instant time ‘t’. 

After collision, let their velocities be v1 and v2 on the same straight line such that v2>v1.

According to the Newton’s third law of motion,

FA = -FB   ………...(i)
Where,
FA = change in momentum of B / time taken
     = m2 v2 – m2 u2 / t
FB = change in momentum of A / time taken
     = m1 v1 – m1 u1 / t
m2 v2 – m2 u2 / t = - (m1 v1 – m1 u1 / t)
m2 v2 + m1 v1 = m2 u2 + m1 u1

This proves that, the total momentum before collision is equal to the total momentum after a collision if no external forces act on them.

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