Description and Assumptions
[Model Hierarchy]
This model is applicable to a point particle (or to a system of objects treated as a point particle located at the system's center of mass) when the external forces are known or needed. It is a subclass of the model [Momentum and Impulse] defined by the constraint dm/dt = 0.
Problem Cues
This model is typically applied to find the acceleration in cases where the forces will remain constant, such as an object moving along a flat surface like a ramp or a wall. It is also useful in combination with other models, such as when finding the normal force exerted on a passenger in a roller coaster at the top of a loop-the-loop (in which case, it would be combined with [Mechanical Energy and Non-Conservative Work]).
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Assumptions and Limitations
Prior Models
Vocabulary
Model Specification
System Schema
Constituents: Point particle, or a system of constant mass that is treated as a point particle located at the system's center of mass.
Interactions: External forces must be understood sufficiently to draw a free body diagram for the system. Internal forces will always cancel from the equations of Newton's 2nd Law for the system and can be neglected.
Descriptors
[State Variables]: Mass (m) (must be constant in this model).
[Interaction Variables]: External forces Fextk (k = 1,2,...,N where N is the number of external forces acting), acceleration (a).
Model Equations
Mathematical Statement of the Model
\begin
[ \sum_
\vec
^
_
= m\vec
] \end
As with all vector equations, this Law of Interaction should really be understood as three simultaneous equations:
\begin
[ \sum_
F^
_
= ma_
]
[ \sum_
F^
_
= ma_
]
[\sum_
F^
_
= ma_
]\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 |
