[Model Hierarchy]
Description and Assumptions
This model is [generally applicable] (assuming knowledge of the external forces and system constituents).
Problem Cues
This model is especially useful when describing the momentum of systems where external forces are absent (system momentum will be constant) or estimating the force in a process that occurs in a very short time interval as in collisions (impulse will be easier to determine than force).
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Prerequisite Knowledge
Prior Models
Vocabulary
System
Constituents
The system must be effectively composed of point particles, though rigid bodies may be treated as point particles with positions specified by the center of mass positions of the rigid body when this model is used.
Variables and Parameters
Mass (mj) and velocity (vj) for each object or momentum (pj) for each object inside the system.
Interactions
Relevant Types
Only external forces need be considered, since internal forces do not change the system's momentum.
Interaction Variables
External forces (Fextk) or, alternately, impulses may be specified (Jextk).
Model
Relationships Among State Variables
If not directly given, momenta can be obtained using the definition:
\begin
[ \vec
_
= m_
\vec
_
]\end
The relationship implied by the model is most easily expressed in terms of the system momentum, which is the vector sum of the constituent momenta. For a system composed of N point particles:
\begin
[ \vec
_
= \sum_
^
\vec
_
]\end
The number of point particle constituents in the system is not necessarily fixed. A totally inelastic collision, for example, could be viewed as a process where two separate system constituents exist in the initial state, but only one is present in the final state.
Laws of Change
Differential Form
\begin
[ \frac{d\vec
_{\rm sys}}
= \:\sum_
^{N_{F}} \vec
^
_
]\end
Integral Form
\begin
[ \vec
_
_
= \vec
_
_
+ \sum_
^{N_{F}} \vec
^
_
= \vec
_
_
+ \int \sum_
^{N_{F}} \vec
^
_
\:dt ]
\end
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 |
