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[Model Hierarchy]

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The root page Model Hierarchy could not be found in space Modeling Applied to Problem Solving.

Description and Assumptions

This model is [generally applicable] (assuming knowledge of the external forces and system constituents).

Problem Cues

This model is especially useful when describing the momentum of systems where external forces are absent (system momentum will be constant) or estimating the force in a process that occurs in a very short time interval as in collisions (impulse will be easier to determine than force).

Page Contents


Prerequisite Knowledge

Prior Models

Vocabulary


System

Constituents

The system must be effectively composed of point particles, though rigid bodies may be treated as point particles with positions specified by the center of mass positions of the rigid body when this model is used.

State Variables

Mass (m) and velocity (v) for each object or, alternately, the momentum (p) may be directly specified.


Interactions

Relevant Types

Only external forces need be considered, since internal forces do not change the system's momentum.

Interaction Variables

External forces (Fext) or, alternately, impulses may be specified (Jext). 


Model

Relevant Definitions

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\begin

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\begin

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& \vec

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= m\vec

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&\vec

^

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= \sum_

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\vec

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\end

\end

Laws of Change

Differential Form
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[ \frac{d\vec

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^{\;\rm sys}}

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= \:\sum \vec

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^

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]\end


Integral Form
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[ \vec

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^

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_

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= \vec

^

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_

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+ \sum \vec

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^

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= \vec

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^

_

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+ \int \sum \vec

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^

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\:dt ]
\end


Diagrammatical Representations


Relevant Examples

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RELATE wiki by David E. Pritchard is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.


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