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During |
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the |
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course |
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of |
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the |
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collision |
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the |
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colliding |
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objects |
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become |
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attached |
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to |
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form |
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a |
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single |
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rigid |
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body. |
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(Also |
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often |
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called |
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a |
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perfectly |
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or |
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a |
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completely |
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inelastic |
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collision.) |
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Motivation for Concept
Often real-world
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collisions
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involve
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objects
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sticking
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together.
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When
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a
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projectile
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like
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a
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bullet
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or
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a
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baseball
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reaches
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its
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target,
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it
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is
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often
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embedded
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in
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the
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target
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or
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caught
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by
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the
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target.
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When
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two
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people
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or
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two
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vehicles collide,
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they
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often
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become
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entangled
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(accidentally
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or
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on
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purpose).
|
Photo courtesy U.S. Air Force |
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:
| Latex |
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h2. 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: {latex}\begin{large}\[ \vec{p}_{1,i} + \vec{p}_{2,i} = \vec{p}_{f} \]\end{large}{latex} |
or,
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in
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terms
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of
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the
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masses
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of
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the
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initial
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objects:
| Latex |
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}\begin{large}\[ m_{1}\vec{v}_{1,i} + m_{2}\vec{v}_{2,i} = (m_{1}+m_{2})\vec_{v}_{f} \]\end{large}{latex} |
These
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equations
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are
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easily
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generalized
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to
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more
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objects.
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