Collision

Collision is an important fact in Natural life. In this article we are going to discuss the collision between Natural bodies in physical science major.

Let, 2 point objects say O₁, O₂ with mass m₁, m₂ respectively collide with initial velocity u₁,u₂ and final velocity v₁,v₂ with Coefficient of restitution α = (v₁ - v₂ ) / (u₂- u₁), the ratio of final and initial relative velocities.

Now we will have following 2 equations in hand :-
1.  α = (v₁ - v₂ ) / (u₂- u₁)
2.  m₁v₁ + m₂v₂ = m₁u₁  + m₂u₂ , The Conservation of Moments.

Now solving them we get

v₂  = v₀  + μ₂. α. ( u₂ - u₁)
v₁  = v₀  + μ₁. α. ( u₁ - u₂)

Where
v₀ = ( m₁u₁ + m₂u₂ ) / ( m₁ + m₂) , The velocity of the cm of the system.
μ₂ =   m₂ / ( m₁ + m₂) , Mass partition.

Now, if :-
1)  α = 0 then v₁ =  v_{2 ,}Totally inelastic collision.
2)  α = 1 then v₁ +  u₁  =  v₂ + u_2 ,Totally elastic collision.
3) Else, α ∈ (0,1) Natural Collision. :)

In only Natural and Inelastic collision Kinatic energy will be changed into other energy ( Heat , Internal energy etc ) For amount of mechanical energy loss just calculate

Q = 1/2 ( m₁v₁² + m₂v₂² - m₁u₁² - m₂u₂² )