A collision is called elastic if kinetic energy is also conserved along with the linear momentum. There is no transformation or loss of kinetic energy in this collision
Suppose two particles of masses m1 and m2 moving with velocities
and
respectively. They interact and their velocities after the collision become
and
respectively.
By conservation of the linear momentum,
Total linear momentum before collision = Total linear momentum after collision ,
or ... (1)
By conservation of kinetic energy,
Net kinetic energy before collision = Net kinetic energy after interaction
![618_Elastic collision7.png](https://www.expertsmind.com/../CMSImages/618_Elastic collision7.png)
or ... (2)
|
![2101_Elastic collision6.png](https://www.expertsmind.com/../CMSImages/2101_Elastic collision6.png)
|
and only for linear collision or head on collision
On solving the above equation (1) and (2),
... (3)
i. e. Relative velocity before collision = Relative velocity after collision.
Thus in elastic collision, the relative velocity of tends to of particles before collision is same to the relative velocity with which the particles recedes after collision. i.e. the value of relative velocity keeps the same, but the direction is reversed.
On solving the equation (1) and (3) we get
![883_Elastic collision10.png](https://www.expertsmind.com/../CMSImages/883_Elastic collision10.png)
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