Completely Inelastic Collision in 1D

Graphic - notesinelastic

A completely inelastic collision is one where, when two bodies collide, they stick together. Kinetic energy is transformed into some other form. The amount of kinetic energy lost is the maximum allowed by conservation of momentum.

Consider the situation above. The equation expressing momentum conservation is:

\[ m_1 v = (m_1 + m_2) V;\,\,\Rightarrow\, V = \frac{m_1v}{m_1 + m_2} \]

the final speed is always less than the initial speed.

A different reference frame

If we view the collision in the center of mass frame, the final state is obviously stationary with respect to the center of mass. In this reference frame, there is no kinetic energy left at all after the collision.