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A model is a simplified description of a complex entity or process. Models often highlight some particular feature of the modeled entity or process while blatantly ignoring others. For example some scale models of a particular airplane (e.g. an SR-71) are faithful in appearance, but can't fly. Other models of that same plane can fly but don't look very much like an SR-71. Still other models are not tangible, e.g. computer models of the supersonic air flow over the wings and into the air inlets for the engines of the SR-71. As George Box (an industrial statistician) once said, "All models are wrong. Some are useful."
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This WIKI aims to enable you to apply these models to the physical world. It therefore adds another category: what are the key restrictions and requirements about the system and its interactions, and the typical physical cues, that trigger the mind to recognize that a particular model applies.
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- One-Dimensional Motion with Constant Acceleration
- Simple Harmonic Motion
- Mechanical Energy, External Work, and Internal Non-Conservative Work
- Point Particle Dynamics (applying Σ F = m a to a point particle)
For a formal organization of these models, see Hierarchy of Models.
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Description: What separates this model from the others.Problem Cues: Common physical situations where model is a good approximation to reality.
Compatible Systems: The restrictions needed to ensure a given system can be adequately described by the model.
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A Models Hierarchy for Mechanics is used to help the learner understand that there are only four basic conceptual domains in Newtonian mechanics:
- Motion
- Momentum
- Mechanical Energy
- Angular Momentum
and that each domain has an associated class of relevant interactions (the class of interactions that cause evolution of the principle quantity)
- Motion is altered by acceleration, or equivalently, net force.
- Momentum is altered by external forces.
- Mechanical Energy is altered by non-conservative work.
- Angular Momentum is altered by external torque.
Pedagogical Usefulness
The key pedagogical reason for using models is to provide a framework within which students can organize the many facts and procedures they learn in introductory physics into a small number of useful models. They can then relate these models to the few overall theories that underlie the material, and think about the real world by recognizing situations or simplifications where these models apply. This leads to an understanding of the world through the ability to simplify and model physical situations that are new. From an expert/novice perspective models organize the many formulae and graphs on the novice's formulae sheet into a much smaller number of "chunks" of related things that are of reflective of nature's organization.
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