Question

State law of conservation of momentum? Derive a mathematical expression for it?​

Answer 1

வாழ்க தமிழ் வளர்க தமிழ்

Answer:

For two or more bodies in an isolated system acting upon each other, their total momentum remains constant unless an external force is applied. Therefore, momentum can neither be created nor destroyed.

Law of conservation of momentum is an important consequence of Newton's third law of motion.

Derivation:-

Consider two colliding particles A and B whose masses are m₁ and m₂ with initial and final velocities as u₁ and v₁ of A and u₂ and v₂ of B. The time of contact between two particles is given as t.

A = m₁ (v₁−u₁) (change in momentum of particle A)

B= m₂ (v₂−u₂) (change in momentum of particle B)

F BA =−F AB (from third law of motion)

F BA = m₂ x a₂ = m₂(v₂−u₂)t

F AB = m₁ x a₁

        = m₁ (v₁−u₁)t x m₂(v₂−u₂)t

        =−m₁(v₁−u₁)t x m₁u₁+m₂u₂

        =m₁v₁+m₂v₂

Therefore, above is the equation of law of conservation of momentum where m₁u₁+m₂u₂ is the representation of total momentum of particles A and B before collision and m₁v₁+m₂v₂ is the representation of total momentum of particles A and B after a collision.

Answer 2

Newton's third law states that for a force applied by an object A on object B, object B exerts back an equal force in magnitude, but opposite in direction. This idea was used by Newton to derive the law of conservation of momentum. ... B=m_{2}(v_{2}-u_{2}) (change in momentum of particle B)