| unmigratedcomposition-wiki-markupsetup |
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| Excerpt |
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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
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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).
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|
Photo courtesy U.S. |
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Force |
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Sgt. |
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Larry |
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A. |
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Simmons. |
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Consequences
During collisions,
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external
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forces
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are
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often
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neglected
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and
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it
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is
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assumed
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that
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momentum
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remains
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constant
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to
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a
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good
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approximation.
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A
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totally
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inelastic
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collision
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greatly
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simplifies
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the
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equations
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of
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momentum
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conservation
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for
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a
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collision,
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since
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in
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the
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final
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state
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only
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one
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object
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remains.
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For
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a
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two-body
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totally
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inelastic
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collision,
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the
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equation
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of
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momentum
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conservation
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becomes:
| Latex |
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}\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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