Conservation of linear momentum

 Conservation of Linear Momentum

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Introduction : Newton's first law and second law holds good with respect to law of conservation of linear momentum. As we know that linear momentum P is the product of mass and velocity, thus law of conservation is very useful in calculating  initial and final velocity of a system given one of the velocity as well as mass is known.

Statement: Law of conservation of linear momentum states that, when the resultant external force acting on a system is zero, the total linear momentum of the system of the body is conserved or constant.

Mathematical Expression :

Consider two sphere A and B making a head on collision. Sphere A and B have mass m₁ and m₂ with initial velocity u₁ and u₂ respectively. 

Before Collision

let u₁ > u₂

_{The total linear momentum (P) of the sphere before head on collision is given by}

_P1  = m₁ u_1 + m₂ u₂ -------(1)

During Collision

As u₁ > u₂ two sphere collide with each other and let 't' be the time of collision.By Newton's third law, The force is given by,

F_AB = - F_BA -------(2)

After Collision

 Let two sphere A and B separate and start moving in forward direction and their velocities becomes  V₁ and V₂ .After collision sphere A decelerate  and sphere B accelerate. i.e (V₁ < V₂)

_{The total linear momentum (P) of the sphere after head on collision is given by}

_P2  = m₁ v_1 + m₂ v₂ -------(3)

From Newtons Second Law,

 m₁ v_1 - m₁ u₁ = m₂ u_2 - m₂ v₂

m₁ u_1 + m₂ u₂ = m₁ v_{1 +} m₂ v₂

_{P1 = P2}

<<<Laws of Motion>>>│<<<Impulse>>>

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