Collision

Collision The striking of one particle with other particle or an interaction between them is called collision.

Elastic Collision: In this type of collision both the momentum and the kinetic energy of the system remain conserver.

Inelastic Collision: In this type of collision both the momentum of the system remains conserver but the kinetic energy doesn’t remain conserved.

Elastic Collision in one dimension: Since the momentum remains conserved m1u1 + m2u2 = m1v1 + m2v2 Since the Kinetic Energy remains conserved (1/2)m1u12 + (1/2)m2u22 = (1/2)m1v12 + (1/2)m2v22 u1 - u2 = - (v1 - v2) Relative velocity before collision = Relative velocity after collision.

Velocity of the particle A = v2 = u1 – u2 + v1 v1 = [(m1 – m2) / (m1 + m2)] u1 + [(2m2) / (m1 + m2)] u2 Velocity of the particle B = v1 = u2 – u1 + v2 v2 = [(2m1) / (m1 + m2)] u1 - [(m1 – m2) / (m1 + m2)] u2 Case 1: If m1= m2 Then v2 = u1 and v1 = u2 The velocities of the particles get interchanged. Case 2: If the second particle is at rest u2 = 0 Velocity of the particle A = v2 = u1 – u2 + v1 v1 = [(m1 – m2) / (m1 + m2)] u1 Velocity of the particle B = v1 = u2 – u1 + v2 v2 = [(2m1) / (m1 + m2)] u1 also, if m1= m2 then v2 = u1 and v1 = 0. I.e. after collision the 1st particle will come to rest and the 2nd particle starts moving with the velocity of the 1st particle. Case 3: If m2 << m1, mass m2 is negligible compared to mass m1 then v2 = 2u1 and v1 = u1. Thus if a heavy body collides with a stationary body, the heavy body continues to move with the same velocity whereas the other body starts moving with twice the velocity of the heavy body. ______________________________________