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Mechanical Energy and Non-Conservative Work

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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


h4. Vocabulary
*[System.|system]
*[Internal Forces.|internal+force]
*[External Forces.|external+force]
*[Conservative Forces.|conservative+force]
*[Non-conservative forces.|non-conservative+force]

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h2. Model Specification
h4. Keys to Applicability
Can be applied to any system for which the [work|work] done by the [non conservative forces|non-conservative+force] is known. The non-conservative forces can be anexternal externalforces forceexerted on the system or an internal forceforces as a result ofresulting from the interactions between ththe eelemntselements inside the system. It is specially useful for systems where the non-conservative work is zero. In this particular case the [mechanical energy|mechanical+energy] of the system is constant. 

h4. System Structure

Internal Constituents:  One or more [Point particles|point particle] or [rigid objects|rigid object]. \\

Environment:   [External forces|external force] that do non-conservative work on the system. (??? If I want to be consisten with all the model structure I should leave here only the external forces. My concern is that leaving it in this way may give the impression to the student that they only need to think about the external non conservative forces and forget the possible work done by internal non-conservative forces, what do you thin??)

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h4. Descriptors

Object Variables:  Mass or moment of inertia for each object about a given axis of rotation, (_m{_}{^}j^) or (_I{^}j{^}{~}Q{~}_). {(????If the objects in the system interact with a spring then the spring constant.)

State Variables:   Kinetic energy for each element of the system and the potential energy of the system. (? Or alternatively, linear speed or angular speed, (_v{_}{^}j^) or (_w{^}j{^}) for each object inside the system and the position of each of the objects in the system).

Interaction Variables:   External and internal non conservative forces, (_F{_}{~}NC,ext{~} and _F{_}{~}NC,int{~}) or, alternately, the work done by the external and forcesinternal onnon theconservative systemforces.

h4. Laws of Interaction
Here should go the possible type of forces, friction, tension, etcs
{latex}\begin{large}$ $\end{large}{latex}


h4. Laws of Change

{latex}
\begin
{large} $E_{f} = E_{i} + W_{i,f}^{NC} $ \end{large}{latex}\\

where _W{^}NC{^}{~}i,f{~}_ is the [work] done by the all the non-conservative forces on the system between the initial state defined by _E{~}i{~}_ and the final state defined by _E{~}f{~}_ and is givegiven by

{latex}\begin{large}$ W_{i,f}^{NC} = \int_{i}^{f} \sum \vec{F}^{NC} . d\vec{r}  $ \end{large}{latex}