Editing Collision (section)

===Perfect inelastic collision===
[[Image:Inelastischer stoß.gif|a completely inelastic collision between equal masses]]

In a perfect [[inelastic collision]], i.e., a zero [[coefficient of restitution]], the colliding particles [[Coalescence (physics)|coalesce]]. Using conservation of momentum:
::<math>m_a \mathbf v_{a1} + m_b \mathbf v_{b1} = \left( m_a + m_b \right) \mathbf v_2,</math>
the final velocity is given by
::<math>\mathbf v_2 = \frac{m_a \mathbf v_{a1} + m_b \mathbf v_{b1}}{m_a + m_b}.</math>
The reduction of total kinetic energy is equal to the total kinetic energy before the collision in a [[center of momentum frame]] with respect to the system of two particles, because in such a frame the kinetic energy after the collision is zero. In this frame most of the kinetic energy before the collision is that of the particle with the smaller mass. In another frame, in addition to the reduction of kinetic energy there may be a transfer of kinetic energy from one particle to the other; the fact that this depends on the frame shows how relative this is.
With time reversed we have the situation of two objects pushed away from each other, e.g. shooting a [[projectile]], or a [[rocket]] applying [[thrust]] (compare the [[Tsiolkovsky rocket equation#Derivation|derivation of the Tsiolkovsky rocket equation]]).