Collision of Bodies
Let the two bodies 1 & 2 have momentum p1 & p2 before they collided with each other . After collision their momentum are p1 ’ and p2 ’ respectively .
By Newton ’ s Second law , F = dp / dt For 1 : F12 = ( p1 ’ – p1 ) / ∆t For 2 : F21 = ( p2 ’ – p2 ) / ∆t
By Newton ’ s Third law , F 12 = - F21 ( p1 ’ – p1 )/ ∆t = ( p2 ’ – p2 ) / ∆t ( p1 ’ – p1 ) = ( p2 ’ – p2 )
p1 ’ + p2 ’ = p1 + p2
Conclusion : Final momentum of the system = Initial momentum of the system
Problem : A railway truck A of mass 3 * 10 4 kg travelling at 0.6 m / s collides with another truck B of half its mass moving in the opposite direction with a velocity of 0.4 m / s . If the trucks couple automatically on collision , find the common velocity with which they move .