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 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.
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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
Compatible Systems
One or more point particles or rigid bodies, plus any interactitons that can be accounted for as potential energies of the system.
Relevant Interactions
All non-conservative forces that perform 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.
Model
Relevant Definitions
\begin
\begin
& E = \sum_
K + \sum_
U
& K = \frac
mv^
+ \frac
I\omega^
&W = \int_
\vec
\cdot d\vec
\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_
+ \sum_
W ] \end
Diagrammatic Representations
- Initial-state final-state diagram.
- [Energy bar graph].
Relevant Examples