The S.I.M. Approach to Problem Solving
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A preview of one of the most important and novel features you will encounter here. The S.I.M. strategy is a systematic, conceptual approach to starting mechanics problems. |
- S. Choose a system to consider.
In every mechanics problem, you will choose to focus on the motion of one or more objects. These objects will make up the system under consideration. Sometimes this choice will be easy. For problems involving the motion of a single car or baseball or box, the car or baseball or box will be the system. Other times, the choice can be hard. When two boxes collide, you may want to focus on only one of the boxes, or both independently, or you may want to consider them together as one system. Or you may decompose the system into intervals where first one and then another treatment is best.
- I. Describe the interactions this system experiences.
Interactions are influences that change the motion of the system. The most common way to describe interactions is to think of them as forces and represent them using a free body diagram, but later you will become familiar with energy and torque as alternate descriptions. There are only a few types of interactions that we will study in this course, including gravity, contact forces (pushes, pulls, friction, etc.) and spring forces. It is important to recognize that interactions always occur between two objects. For instance, if your system is subject to a gravitational interaction, it must be near another object (often the earth). If your system is subject to a contact force, there must be another object nearby to do the pushing or pulling.
- M. Choose a model from the hierarchy that will help you to solve the problem.
Models summarize the important physical content of the course, and each has certain allowed interactions and contains an associated equation of change. For example, if you know that your system experiences a constant acceleration, the equations of change describe the system’s position and velocity as functions of time. To help you get a big picture overview of the course, we have organized the most important models that you will learn into a hierarchy of models.
Strategy and the S.I.M.
When starting problems using the S.I.M. approach, it is important to understand that you cannot think of this as a “1, 2, 3” prescription for success. Choosing the most advantageous system when solving a problem will usually require you to understand the interactions in the problem. Choosing an appropriate system and model will always require a good understanding of the interactions. The way that you describe the interactions will require you to think about the model you want to employ. These relationships are fundamental to a strategic approach to problem solving.
Using the S.I.M.
We want you to begin every problem with the S.I.M., so it is important that it be brief.
- Describing your system can be a sentence or two, or perhaps just clear labels on a picture showing what is inside and outside the system.
- Describing the interactions is the most important part, but it should be possible to be clear in one paragraph. It will often help to draw free body diagrams. Briefly discuss the interactions that are relevant to the system and the model, and what objects are participating in the interactions (remember, there are always two objects participating in any interaction).
- Choosing the model is as simple as picking one of the models from the hierarchy.
To get a sense of how these specifications work in practice, please have a look at the worked examples in this WIKI, which all use the S.I.M. approach.