Define conservation of momentum in brief ?

Question

Answer

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the total momentum of a body remains constant if No external force acts on the system.

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Answer

The law of conservation of momentum states that the total momentum before collision is equal to the total momentum after collision.

For eg, Suppose two balls of masses m1 and m2 collide with each other with an initial velocity of u1 and u2 respectively.

Before collision,

momentum of ball of mass m1= m1u1 {momentum= mass x velocity}

momentum of ball of mass m2= m2u2

total momentum before collision = m1u1 + m2u2

Force = F1=m1 (v1-u1/t) { Force= mass x acceleration=m(v-u/t}

After collision,

let their final velocity be v1 and v2 respectively.

momentum of ball of mass m1= m1v1

momentum of ball of mass m2= m2v2

total momentum after collision = m1v1 + m2v2

force = F2= m2(v2-u2/t)

Newton's second law of motion states that every action has an equal and opposite reaction.

Therefore, F1= -F2

m1 (v1-u1/t) = m2 (v2-u2/t)

m1( v1-u1) = -m2 (v2-u2)

m1v1 - m1u1 = m2v2 - m2u2

m1v1 + m2v2 = m1u1 + m2u2

Hence, total momentum before collision = total momentum after collision.

-Proved