Elastic collision

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An elastic collision is a collision in which the total kinetic energy of the colliding bodies after collision is equal to their total kinetic energy before collision. Elastic collisions occur only if there is no conversion of kinetic energy into other forms.

Consider two particles A and B had elastic collision. Let the x component of velocity before the collision vA1 and vB1 and those after the collision vA2 and vB2.

From conservation of kinetic energy.

Total kinetic energy is the same before and after the collision, hence:

1/2 mAvA1^2 +1/2 mBvB1^2=1/2mAvA2^2+1/2 mBvB2^2,

and conservationb of momemtum gives

mAvA1+mBvB1=mAvA2+mBvB2

if the masses mA and mB and the initial velocities vA1 and vB1 are known, these two equations can be solved simultaneously to find the two final velocities vA2 and vB2.