The Three-Step Approach to Problem Solving
The Three-Step Approach to Problem Solving
The systems we will look at in this chapter won’t test your knowledge of obscure formulas so much as your problem-solving abilities. The actual physics at work on these systems is generally quite simple—it rarely extends beyond Newton’s three laws and a basic understanding of work and energy—but you’ll need to apply this simple physics in imaginative ways.
There are three general steps you can take when approaching any problem in mechanics. Often the problems are simple enough that these steps are unnecessary. However, with the special problems we will tackle in this chapter, following these steps carefully may save you many times over on SAT II Physics. The three steps are:
  1. Ask yourself how the system will move: Before you start writing down equations and looking at answer choices, you should develop an intuitive sense of what you’re looking at. In what direction will the objects in the system move? Will they move at all? Once you know what you’re dealing with, you’ll have an easier time figuring out how to approach the problem.
  2. Choose a coordinate system: Most systems will only move in one dimension: up and down, left and right, or on an angle in the case of inclined planes. Choose a coordinate system where one direction is negative, the other direction is positive, and, if necessary, choose an origin point that you label 0. Remember: no coordinate system is right or wrong in itself, some are just more convenient than others. The important thing is to be strictly consistent once you’ve chosen a coordinate system, and to be mindful of those subtle but crucial minus signs!
  3. Draw free-body diagrams: Most students find mechanics easier than electromagnetism for the simple reason that mechanics problems are easy to visualize. Free-body diagrams allow you to make the most of this advantage. Make sure you’ve accounted for all the forces acting on all the bodies in the system. Make ample use of Newton’s Third Law, and remember that for systems at rest or at a constant velocity, the net force acting on every body in the system must be zero.
Students too often think that physics problem solving is just a matter of plugging the right numbers into the right equations. The truth is, physics problem solving is more a matter of determining what those right numbers and right equations are. These three steps should help you do just that. Let’s look at some mechanical systems.
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