During the course of the collision the colliding objects become attached to form a single rigid body. (Also often called a perfectly or a completely inelastic collision.)
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Motivation for Concept
Often real-world collisions involve objects sticking together. When a projectile like a bullet or a baseball reaches its target, it is often embedded in the target or caught by the target. When two people or two animals collide, they often become entangled (accidentally or on purpose).
Consequences
During collisions, external forces are often neglected and it is assumed that momentum remains constant to a good approximation. A totally inelastic collision greatly simplifies the equations of momentum conservation for a collision, since in the final state only one object remains. For a two-body totally inelastic collision, the equation of momentum conservation becomes:
\begin
[ \vec
_
+ \vec
_
= \vec
_
]\end
or, in terms of the masses of the initial objects:
\begin
[ m_
\vec
_
+ m_
\vec
_
= (m_
+m_
)\vec_
_
]\end
These equations are easily generalized to more objects.