Special-case Analysis allows you to make sense of a symbolic equation in physics. The objective is to choose a case that is special because the answer is obvious or the context becomes straightforward and check to see if your equation matches your intuition.
When you use Special-case Analysis, continue to follow the sensemaking steps you saw in Figure 1.7.1. Some particular things to keep in mind are listed below.
You will often need to identify an interesting special case. Good cases are special if they are easy to solve or if you have solved them before.
When you identify a good special case, you should quickly be able to write down the answer in that case. The answer you write down should be specific.
When you evaluate your answer in the special case, you will need to identify the value that a variable of interest takes on in the case and then evaluate your symbolic equation at that value. Sometimes the value may require you to take a limit!
At the end, you should compare your two answers; typically, this involves comparing two symbolic equations and checking if they are exactly equal!
ExercisesActivities
1.Practice with Special-case Analysis.
Recall Exercise 4.7.3 from the previous section. Use Special-Case Analysis to make sense of your original solution to this context. There are several possible special cases you might try here!
Remember that the goal is to find a case that is truly special in the sense that the answer seems obvious or intuitive. For example, if the kite string is horizontal, the force by the kite and the force by the father must directly cancel out if the wagon is to move at constant speed. (Angles often make good special cases--are there any other special angles here?)
