- A (perfectly) elastic collision is one that retains 100% of its initial total KE.
- As a result, the two bodies always separate from each other at the same speed as they approached each other. (see proof here)
- The outcome of an elastic collision can therefore be calculated through the equations:

- and

–

- Depicted below are the momentum and KE variations during a head-on
**(perfectly) elastic**collisions of two equal masses*m*with equal initial speed*u*.

- For simplicity, we assume a constant contact force during the collision.
- Note that the total momentum remains constant (at zero)
**throughout**the collision. - The total KE drops to zero at one point during the collision, but returns to 100% by the end of the collision.
- The two masses approach and separate from each other at relative speed of 2
*u*.

–

- Depicted below are the momentum and KE variations during a head-on
**(perfectly) elastic**collision of two equal masses*m*, one of them with initial speed of*u*, and the other initially at rest.

- For simplicity, we assume a constant contact force during the collision.
- Note that the total momentum remains constant (at
*mu*)**throughout**the collision. - The total KE drops to 50% at one point during the collision, but returns to 100% by the end of the collision.
- The two masses approach and separate from each other at relative speed of
*u*.