State and Explain the Law of Conservation of Linear Momentum

Statement:

According to the law of conservation of linear momentum, for an object or system of objects, the total momentum of the system is always conserved if no external force acts on them

The unit of kg.m.s-1 and the dimensional formula is MLT-1. The mathematical representation of the law of conservation of linear momentum is given as:

m1u1 + m2u2 = m1v1 + m2v2

Proof:

Consider collision between two balls. The momentum of these two balls before collision is given as:

P1i = m1u1

P2i = m2u2

The total momentum of the balls before the collision is given as:

Pi = P1i + P2i

Pi = m1u1 + m2u2

F12 is the force exerted by the m1 during the collision on m2.

F21 is the force exerted by the m2 during the collision on m1.

Therefore, F12 = F21

There is a change in the velocity of these balls after the collision which is given as:

P1f = m1v1

P2f = m2v2

The total momentum of the balls after the collision is given as:

Pf= P1f + P2f

Pf= m1v1 + m2v2

From Newton’s second law:

Force = Change in momentum / time interval

F12 = m2v2 – m2u2 / t

F21 = m1v1 – m1u1 / t

From Newton’s third law:

F12 = F21

Therefore, we get:

m1u1 + m2u2 = m1v1 + m2v2

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