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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


This model is applicableh4. Keys to Applicability
Can be applied to aany system of one or more [point particles/point particle] or [rigid objects|rigid object] subject to the influence of external [non-conservative forces]. (..implications of  internal-conservative forces) for which the [work|work] done by the [non conservative forces|non-conservative+force] is known. The non-conservative forces can be an external force on the system or an internal force as a result of the interactions between th eelemnts 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].
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Environment:   [External forces|external force] that do non-conservative work because these are one ofon the forces that can change the mechamical energy. (The internal non - conservative forces also change the mechanical energy).system. 

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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{~}_), (?the. {If the objects in the system interact with a spring constantthen the ofspring applicableconstant.)

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 non conservative forces (_F{_}{~}ext,k~{~}) or, alternately, the work done by the external forces on the system (here the internal non-conservative interactions are important- do we define them here?).

h4. Laws of Interaction

{latex}\begin{large}$ $\end{large}{latex}


h4. Laws of Change

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

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

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