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Introduction to the Model

Description and Assumptions

Excerpt
hiddentrue

System: Any. — Interactions: Any. — Note: Linear momentum evolves separately from angular momentum, so all system constituents are treated as point particles in this model.


This model is generally applicable (assuming knowledge of the external forces and system constituents). The 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 such as collisions (impulse will be easier to determine than force).

Learning Objectives

Students will be assumed to understand this model who can:

Relevant Definitions


Latex
\begin{large}\[ \vec{p} = m\vec{v}\]\end{large}

S.I.M. Structure of the Model

Compatible Systems

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.

Relevant Interactions

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

Laws of Change

Mathematical Representation
Section
Column
Differential Form


Latex
\begin{large}\[ 
}{composition-setup} {table:rules=cols|cellpadding=8|cellspacing=0|border=1|frame=void} {tr:valign=top}{td:width=355px|bgcolor=#F2F2F2} {live-template:Left Column} {td} {td} h1. Description and Assumptions {excerpt:hidden=true}*System:* Any. --- *Interactions:* Any. --- *Note:* Linear momentum evolves separately from angular momentum, so all system constituents are treated as [point particles] in this model.{excerpt} This model is [generally applicable|generally applicable model] (assuming knowledge of the external forces and system constituents). h1. 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 || | {toc:style=none|indent=10px|maxLevel=3} | h1. Prerequisite Knowledge h3. Prior Models * [Point Particle Dynamics] h3. Vocabulary * [system] * [force] * [impulse] * [momentum] * [velocity] h1. Compatible Systems The system must be effectively composed of [point particles|point particle], 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. h1. Relevant Interactions Only [external forces|external force] need be considered, since [internal forces|internal force] do not change the system's momentum. h1. Model h3. Relevant Definitions \\ {latex}\begin{large}\[ \vec{p} = m\vec{v}\]\end{large}{latex} h3. Laws of Change {section} {column} h6. Differential Form {latex}\begin{large}\[ \sum_{\rm system}
\frac{d\vec{p}}{dt} = \sum
_{\rm external}
 \vec{F}^{\rm ext}\]\end{large}
{latex} {column} {column} h6. Integral Form {latex}
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width40px

Column
Integral Form


Latex
\begin{large}\[ 
\sum_{\rm system}
\vec{p}_{f} = 
\sum_{
\
rm system}\
vec{p}_{i} + \sum
_{\rm
 
external}
\vec{J}
= \sum_
^{\rm 
system}
ext}_{fi} = \vec{p}_{i} + \int_{t_{i}}^{t_{f}} \sum
_{\rm external}
 \vec{F}^{\rm ext}\:dt  \]
\end{large}
{latex} {column} {section} h1. Diagrammatic Representations {contentbylabel:representation,momentum|showSpace=false|showLabels=false|excerpt=true|operator=AND|maxResults=50} h1. Relevant Examples h4. {toggle-cloak:id=const} Examples Involving Constant Momentum {cloak:id=const}{contentbylabel:constant_momentum|showSpace=false|showLabels=true|excerpt=true|maxResults=50}{cloak} h4. {toggle-cloak:id=imp} Examples Involving Impulse {cloak:id=imp}{contentbylabel:impulse|showSpace=false|showLabels=true|excerpt=true|maxResults=50}{cloak} h4. {toggle-cloak:id=oned} Examples Involving 1-D Collisions {cloak:id=oned}{contentbylabel:1d_collision|showSpace=false|showLabels=true|excerpt=true|maxResults=50}{cloak} h4. {toggle-cloak:id=twod} Examples Involving 2-D Collisions {cloak:id=twod}{contentbylabel:2d_collision|showSpace=false|showLabels=true|excerpt=true|maxResults=50}{cloak} h4. {toggle-cloak:id=elas} Examples Involving Elastic Collisions {cloak:id=elas}{contentbylabel:elastic_collision|showSpace=false|showLabels=true|excerpt=true|maxResults=50}{cloak} h4. {toggle-cloak:id=all} All Examples Using this Model {cloak:id=all}{contentbylabel:constant_momentum,momentum_force,impulse|showSpace=false|showLabels=true|excerpt=true|operator=OR|maxResults=50}{cloak} ---- {search-box} \\ {td} {tr} {table} {live-template:RELATE license} \\
Diagrammatic Representations

Relevant Examples

Toggle Cloak
idconst
Examples Involving Constant Momentum
Cloak
idconst
falsetruetrue50constant_momentum
Toggle Cloak
idimp
Examples Involving Impulse
Cloak
idimp
falsetruetrue50impulse
Toggle Cloak
idoned
Examples Involving 1-D Collisions
Cloak
idoned
falsetruetrue501d_collision
Toggle Cloak
idtwod
Examples Involving 2-D Collisions
Cloak
idtwod
falsetruetrue502d_collision
Toggle Cloak
idelas
Examples Involving Elastic Collisions
Cloak
idelas
falsetruetrue50elastic_collision
Toggle Cloak
idinel
Examples Involving Totally Inelastic Collisions
Cloak
idinel
falsetruetrue50totally_inelastic
Toggle Cloak
idflux
Examples Involving Continuous Momentum Flux
Cloak
idflux
falsetruetrue50momentum_force
Toggle Cloak
idall
All Examples Using this Model
Cloak
idall
falsetruetrueOR50constant_momentum,momentum_force,impulse

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