Description and Assumptions
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 just the work done by non-conservative forces 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.
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 that can be represented by potential energy) are involved.
[Model Hierarchy]
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Prerequisite Knowledge
Prior Models
Vocabulary
- system
- force
- work
- kinetic energy
- rotational kinetic energy
- [gravitational potential energy]
- [elastic potential energy]
- mechanical energy
System
Constituents
One or more point particles or rigid bodies, plus any interactitons that can be accounted for as potential energies of the system.
State Variables
Mass (m) and possibly moment of inertia (I) for each object plus linear (v) and possibly rotational (ω) speeds for each object, or alternatively, the kinetic energy (K) may be specified directly.
If non-conservative forces are present, each object's path of travel (s) must be known throughout the time interval of interest unless the work done by each force is specified directly.
When a conservative interaction is present, some sort of specific position or separation is required for each object (height h for near-earth [gravity], separation r for universal gravity, departure from equilibrium x for an elastic interaction, etc.) unless the relevant potential energy (U) is specified directly.
Alternately, in place of separate kinetic and potential energies, the mechanical energy of the system (E) can be specified directly.
Interactions
Relevant Types
All forces that do [non-conservative] work on the system must be considered, including internal forces that perform such work. Conservative forces that are present should have their interaction represented by the associated potential energy rather than by the work.
Occasionally it is easier to consider the work of conservative forces directly, omitting their potential energy.
Interaction Variables
Relevant non-conservative forces (FNC) or the work done by the non-conservative forces (WNC).
Model
Relevant Definitions
\begin
\begin
& E = K_
+ U_
& K_
= \sum_
\left(\frac
mv^
+ \frac
I\omega^
\right)
&W^
= \int_
\vec
^
\cdot d\vec
& W^
_
= \sum_
W^
\end
\end
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.
Law of Change
\begin
$E_
= E_
+ W^
_
$ \end
Diagrammatical Representations
- Initial-state final-state diagram.
- [Energy bar graph].
Relevant Examples
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RELATE wiki by David E. Pritchard is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License |
