write the law of conservation of momentum and prove it
Answers
The law of momentum conservation can be stated as follows. For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.
Law of conservation of linear momentum :- when there is no any external force applied on a system of particles then , momentum of system of particles will be conserved or you can say that if external force is zero. Then momentum of system of particles in intially = momentum of system of particles in finally.
Mathematically,
From Newton's second law,
Fext = dP/dt
If Fext = 0, ∫ dP =∫ 0.dt
Means dP = 0
e.g., Pi = Pf
Let two bodies A and B of masses m₁ and m₂ are moving with velocities u₁ and u₂ , after collision velocities of bodies are v₁ and v₂ respectively.
Then, initial momentum of bodies ,Pi= m₁u₁ + m₂u₂
Final momentum of bodies, Pf = m₁v₁ + m₂v₂
Because external force doesn't apply here, so, linear momentum will be conserved .
e.g., Pi = Pf
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂