Question

Prove the law of conservation of momentum. Mathematically.​

Answer 1

हिंदी में खोजेंगणितीय गति के संरक्षण के कानून साबितTotal momentum of the system of two balls after collision, pf = p1f +p2f = m1v1 + m2v2. Also from Newton"s Second Law: Total momentum before collision = Total momentum after collision. Hence this equation implies that if no external force acts on the system of two colliding balls, the total momentum is conserved.

Answer 2

Consider a body of mass m1 moving with velocity U1, striking against another body of mass m2 moving with velocity U2.

Let the two bodies remain in contact with each other for a small interval "delta t".

Let F12 be the average force exerted by mass m1 on m2, and let F21 be the force on m2 due to m1.

Let v1 and v2 be the velcoities of two bodies after collision.

Momentum of mass m1 before collision=m1u1

Momentum of mass m2 after collision=m2u2

Momentum of mass m1 after collision=m1v1

By using the definition of impulse, change in momentum of mass m1 is,

(refer figure).