Force And Laws Of Motion

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When two (or more) bodies act upon one another, their total momentum remains constant (or conserved) provided no external forces are acting.

Initial momentum = Final momentum

Suppose, two objects A and B each of mass m1 and mass m2 are moving initially with velocities u₁ and u₂, strike each other after time t and start moving with velocities v₁ and v₂ respectively.

Now,

Initial momentum of object A = m₁u₁

Initial momentum of object B = m₂u₂

Final momentum of object A = m₁v₁

Final momentum of object B = m₂v₂

So, Rate of change of momentum in A,

And Rate of change of momentum in B,

[From equations (i) & (ii)]

m₁v₁ – m₂v₂ = − m₂v₂ + m₂u₂

So, m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Thus, Initial momentum = Final momentum