- A (perfectly) inelastic collision is one that retains the
**minimum**amount of its initial total KE. - As a result, the two bodies will always “stick together” and travel at a common speed after the collision.
- The outcome of an elastic collision can therefore be calculated using the PCOM equation:

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- Depicted below are the momentum and KE variations during a head-on
**perfectly inelastic**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. - To conserve momentum, both masses must come to rest after the collision, losing 100% of the initial KE.

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- Depicted below are the momentum and KE variations during a head-on
**perfectly inelastic**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. - To conserve momentum, both masses must travel at a common speed of 0.5
*u*after the collision, losing 50% of the initial total KE. - (Note that it is not possible to lose more than 50% because of momentum conservation)