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h2. Description

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{td:align=center|bgcolor=#F2F2F2}*[Model Hierarchy]*
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h2. Assumed Knowledge


h4. Prior Models

* [Point Particle Dynamics]
* [One-Dimensional Motion with Constant Acceleration|1-D Motion (Constant Acceleration)]

h4. Vocabulary

* [system]
* [force]
* [impulse]
* [momentum]
* [acceleration]

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h2. Model Specification


h4. Keys to Applicability


Can be applied to any system for which [external forces|external force] are known, especially useful for systems where they are absent (momentum conserved for that system) or act only for a short time (Impulse) as in collisions.

h4. System Structure

Internal Constituents:  System is composed of [Point particles|point particle].
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Environment:   Only [external forces|external force] need be considered, since [internal forces|internal force] do not change the system's momentum.
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h4. Descriptors

Object Variables:  Mass for each object (_m{_}{^}j^), unless momentum is given directly.

State Variables:   Velocity (_v{_}{^}j^) or momentum (_p{_}{^}j^) for each object inside the system.

Interaction Variables:   External forces (_F{_}{~}ext,k~) or, alternately, impulses may be specified (_J{_}{~}ext,k~).  They may act on any or all particle(s) in the system.


h4. Laws of Interaction

{latex}\begin{large}\[ \frac{d\vec{p}_{\rm system}}{dt} = \:\sum_{k=1}^{N_{F}} \vec{F}_{ext,k} \]\end{large}{latex}
where the system momentum is the vector sum of the constituent momenta:
{latex}\begin{large}\[ \vec{p}_{\rm system} = \sum_{j=1}^{N} \vec{p}^{j} \]\end{large}{latex}
where _N_ is the number of system constituents.  The integral form involves

<B>Impulse<\B>&nbsp; *Impulse:*

{latex}\begin{large}\[ \vec{J}_{ext,k} = \int \vec{F}_{ext,k}\:dt \]\end{large}{latex}

h4. Laws of Change

{latex}
\begin
{large}\[ \vec{p}_{\rm system,f} = \vec{p}_{\rm system,i} + \sum_{k=1}^{N_{F}} \vec{J}_{ext,k} \]\end{large}
{latex}\\

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h2. Relevant Examples

{contentbylabel:example_problem,momentum_force|showSpace=false|showLabels=true|excerpt=true|operator=AND|maxResults=50}
{contentbylabel:example_problem,constant_momentum|showSpace=false|showLabels=true|excerpt=true|operator=AND|maxResults=50}
{contentbylabel:example_problem,impulse|showSpace=false|showLabels=true|excerpt=true|operator=AND|maxResults=50}

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