h4. Introduction to the Model
h5. Description and Assumptions
This [model|model] is applicable to a [point particle] (or to a [system|system] of objects treated as a [point particle|point particle] located at the system's [center of mass]) when the [external forces|external force] are known or needed. It is a subclass of the model [Momentum and External Force] defined by the constraint _dm/dt_ = 0.
h5. Learning Objectives
Students will be assumed to understand this model who can:
* State and explain the significance of Newton's Laws of Motion.
* Define [normal force] and describe its relationship to [weight].
* Discriminate between [static|static friction] and [kinetic|kinetic friction] friction.
* Explain the role of the [coefficient of friction] in both the [kinetic|kinetic friction] and [static|static friction] cases.
* Construct a [free body diagram] for an object subject to [contact forces|contact force], [gravity|gravity (near-earth)], [elastic forces|Hooke's Law for elastic interactions], and/or [tension forces|tension].
* Construct and solve a system of equations describing the dynamics of more than one object that interact with one another.
h4. S.I.M. Structure of the Model
h5. Compatible Systems
A single [point particle|point particle], or a system of constant mass that is treated as a point particle located at the system's center of mass.
h5. Relevant Interactions
[External forces|external force] must be understood sufficiently to draw a [free body diagram] for the system. [Internal forces|internal force] will always cancel from the equations of Newton's 2nd Law for the system and can be neglected.
h4. Law of Change
h5. Mathematical Representation
{latex}\begin{large} \[ \sum \vec{F}^{\rm ext} = m\vec{a} \] \end{large} {latex}
{note}As with all vector equations, this Law of Interaction should really be understood as three simultaneous equations:\\
{latex}\begin{large}\[ \sum F^{\rm ext}_{x} = ma_{x}\]
\[ \sum F^{\rm ext}_{y} = ma_{y}\]
\[\sum F^{\rm ext}_{z} = ma_{z}\]\end{large}{latex}{note}
h5. Diagrammatical Representations
* [Free Body Diagram|free body diagram]
h4. Relevant Examples
h6. {toggle-cloak:id=vec} Examples Involving Vector Components
{cloak:id=vec}
{contentbylabel:dynamics,vector_components|showSpace=false|showLabels=true|maxResults=50|exerpt=true|operator=AND}
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h6. {toggle-cloak:id=norm} Examples Involving Normal Force
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{contentbylabel:dynamics,normal_force|showSpace=false|showLabels=true|maxResults=50|excerpt=true|operator=AND}
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h6. {toggle-cloak:id=appw} Examples Involving Apparent Weight
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{contentbylabel:dynamics,apparent_weight|showSpace=false|showLabels=true|maxResults=50|excerpt=true|operator=AND}
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h6. {toggle-cloak:id=tens} Examples Involving Tension
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{contentbylabel:dynamics,tension|showSpace=false|showLabels=true|maxResults=50|excerpt=true|operator=AND}
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h6. {toggle-cloak:id=incl} Examples Involving Inclined Planes
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{contentbylabel:dynamics,inclined_plane|showSpace=false|showLabels=true|maxResults=50|excerpt=true|operator=AND}
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h6. {toggle-cloak:id=stat} Examples Involving Static Friction
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{contentbylabel:dynamics,static_friction|showSpace=false|showLabels=true|maxResults=50|excerpt=true|operator=AND}
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h6. {toggle-cloak:id=kin} Examples Involving Kinetic Friction
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{contentbylabel:dynamics,kinetic_friction|showSpace=false|showLabels=true|maxResults=50|excerpt=true|operator=AND}
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h6. {toggle-cloak:id=cen} Examples Involving Centripetal Acceleration
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{contentbylabel:dynamics,centripetal_acceleration|showSpace=false|showLabels=true|maxResults=50|excerpt=true|operator=AND}
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h6. {toggle-cloak:id=all} All Examples Using this Model
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{contentbylabel:dynamics,example_problem|showSpace=false|showLabels=true|maxResults=50|excerpt=true|operator=AND}
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