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h2. Description and Assumptions

{excerpt:hidden=true}*System:* Any system that does not undergo significant changes in [internal energy]. --- *Interactions:* Any interactions that can be parameterized as mechanical work.  Notable exceptions include heat transfer or radiation.{excerpt}

If we ignore processes like heat transfer, radiative losses, etc., then we arrive at a model involving only [mechanical energy] which changes due to the application (or extraction) of the [work|work] done by [non-conservative forces|force#nonconservative] The non-conservative forces can be external forces exerted on the system or internal forces resulting from the interactions between the elements inside the system. 

h2. Problem Cues

The model is especially useful for systems where the non-conservative work is zero, in which case the [mechanical energy] of the system is constant.  Since friction is a common source of non-conservative work, problems in which mechancial energy is conserved can often be recognized by explicit statements like "frictionless surface" "smooth track" or in situations where only gravity and/or springs ([conservative forces|force#nonconservative] that can be represented by [potential energy]) are involved.

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h1. Prerequisite Knowledge

h4. Prior Models

* [Point Particle Dynamics]

h4. Vocabulary

* [system]
* [force]
* [work]
* [kinetic energy]
* [rotational kinetic energy]
* [gravitational potential energy|Gravitation]
* [elastic potential energy|Hooke's Law]
* [mechanical energy]

h1. Compatible Systems

One or more [point particles|point particle] or [rigid bodies|rigid body], plus any interactitons that can be accounted for as [potential energies|potential energy] of the system.

h1. Relevant Interactions

All [non-conservative forces|force#nonconservative] that perform [work] on the system must be considered, _including_ [internal forces|internal force] that perform such work. [Conservative forces|force#nonconservative] that are present should have their interaction represented by the associated [potential energy] rather than by the [work].
{note}Occasionally it is easier to consider the work of conservative forces directly, omitting their potential energy.
{note}


h1. Model

h3. Relevant Definitions

\\
{latex}\begin{large}\begin{alignat*}{1} & E = \sum_{\rm system} K + \sum_{\rm system} U \\
 & K = \frac{1}{2}mv^{2} + \frac{1}{2}I\omega^{2}\\
 &W = \int_{\rm path} \vec{F} \cdot d\vec{s}
\end{alignat*}\end{large}{latex}

The system potential energy is the sum of all the potential energies produced by interactions between system constituents.  Even when there are two system constituents involved (for example in a double star) each *interaction* produces only one potential energy.
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h3. Law of Change
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{latex}
\begin{large}\[ E_{f} = E_{i} + \sum_{\rm non-cons} W \] \end{large}{latex}
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h1. Diagrammatic Representations

* [Initial-state final-state diagram|initial-state final-state diagram].
* [Energy bar graph|energy bar graph].

h1. Relevant Examples

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