Example
A bullet is fired from a gun. If the force on the bullet by the gun is F, the force on the gun by the bullet is – F, according to the third law. The two forces act for a common interval of time Δt. According to the second law, F Δt is the change in momentum of the bullet and – F Δt is the change in momentum of the gun. Since initially, both are at rest, the change in momentum equals the final momentum for each.
Thus if pb is the momentum of the bullet after firing and pg is the recoil momentum of the gun,
pg = – pb i.e. pb + pg = 0. That is, the total momentum of the (bullet + gun) system is conserved.
Thus in an isolated system (i.e. a system with no external force), mutual forces between pairs of particles in the system can cause momentum change in individual particles, but since the mutual forces for each pair are equal and opposite, the momentum changes cancel in pairs and the total momentum remains unchanged.
The total momentum of an isolated system of interacting particles is conserved.
This law can be applied for two bodies in collision.Consider two bodies A and B, with initial momenta pA and pB. The bodies collide, get apart, with final momenta p′ A and p′ B respectively. By the Second Law
which shows that the total final momentum of the isolated system equals its initial momentum. Notice that this is true whether the collision is elastic or inelastic.Related posts :
Newton's First law of motion
Newton's second law of motion
Newton's third law of motion
Concept of momentum
Uniform circular motion
Projectile motion
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