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Problems: When approaching a problem the most important thing is to change your objective from “Find the Answer” to Plan the Solution. That is, concentrate on the process of solving it – what principles did you apply and why? Very valuable is a retrospective look at what one or two sentences of advice would have enabled you to solve the problem more quickly – this is what you really learned by doing the problem.
Role of this WIKItextBook
Conceptual Organization
This WikiTextBook arranges the core concepts and their associated conditions of validity and equations of change into about a dozen models. The models are then arranged into categories that depend on the type of system and its interaction. Thus determining the system and interactions present in a problem hints at the category of models that can solve it. Within each category, the models are arranged in a hierarchy to make it clear that some are simply special cases of the one(s) above suitable for a restricted set of circumstances (e.g. that the force does not change with time).
The SIM Approach
If you are a novice skier, your teacher will say something like “Bend your knees and put equal weight on both skis.” as you are about to start down the slope. The teacher would not need to tell this to an experienced skier, who would naturally do this. In the same way, this WIKI will ask you to begin each problem with a prescribed, conceptual rubric. This rubric has been carefully designed to teach steps that every expert problem solver goes through when approaching a mechanics problem, even if they don't always mention the steps explicitly. This rubric is at the heart of your transition from a formula hunter to expert who starts problem solving from fundamental principles.
Our S.I.M. Problem Solving Approach asks you to think in terms of the system and its Interactions (forces) in your problem, rather than to key on the superficial features like “inclined plane” or “pulley” or “collision problem”. The system and interaction serve as a guide to your selecting the best Model from the hierarchy. This will then lead to a graphical approach or an equation of change that will provide the best route to the solution.
Here is an expanded description of the components of the S.I.M. Approach:
System: Specify the object or objects whose motion you are describing and state whether they will be considered as point particles or rigid bodies.
Interactions: Specify the forces that act on the system and classify these forces as internal vs. external, conservative vs. non-conservative, and/or torque-producing vs. non torque-producing.
Model: A selection from the Hierarchy of Models provided to you. The model that you choose to deploy is an idealized mathematical representation of the problem.
When you review example problems or work problems on your own, it is important to keep SIM in mind. What and why was that particular system employed? Review the forces and ask which one is the least obvious. Finally, why was the successful model selected? Did the problem contain several pieces that required different models – either in time or in space? (You should also look for tricky constraints, e.g. from pulleys, geometry, etc.)
This approach is used in all the worked examples presented in this WIKI.