PROBLEM SOLVING GUIDELINES

by D.D. Long

The ability to solve problems is not a skill with which most of us are born. It is an acquired skill. Developing a systematic, logical approach to solving even the simplest problems can greatly enhance your ability to tackle the difficult ones. The following procedure is one that many good problem-solvers find useful, and is the one that I expect you to follow in this class. Obviously, certain problems will require adapting this procedure to the given situation; however, you should adhere to these general guidelines for all problems.

1. Read the problem and form a mental picture of the situation.

2. Draw a simple diagram of the situation, and indicate what is given in the problem in terms of the symbols used for the quantities. (The problem statement may include information you don't need.)

3. Using the appropriate symbols, indicate what you are to find.

(Having done Steps 1 through 3, you have determined in your mind what the problem is. The rest should then be easier.)

4. Your solution should then include the following steps:

(a) If forces are involved, draw a free-body diagram. Otherwise draw a diagram indicating the essential features of the problem (or that part of the problem you're currently working on).

(b) Write down the relevant equation(s).

(c) Solve the equation(s) for the required unknown. Never substitute numbers into the equations until you have algebraically solved for the particular unknown in question. Many times certain quantities will cancel, leading to a greatly simplified calculation and, therefore, less chance of error. Furthermore, the algebraic equation will show you how the answer might change if the given numbers were changed.

(d) Substitute numerical values for the knowns, with units.

(e) Calculate the numerical answer and show that the input units lead to the desired units for the result. Correct units give a strong hint that you have done the problem right; incorrect units assure you that you've made a mistake.

(f) State the answer, with units, specified to the correct number of significant digits. Using the correct number of significant digits gives a good indication of how accurately you know the answer.

5. Look at your result and decide whether or not it is reasonable for the given situation. If not, recheck your calculation. If so, consider what the result tells you about the physical principles being illustrated.

6. Example: The problem below and its solution which follows illustrate the preceding guidelines.

A charged sphere of mass 0.30 g is suspended from a string. An electric force acts horizontally on the sphere so that the string makes an angle of 37° with the vertical when at rest. Find (a) the magnitude of the electric force and (b) the tension in the string. (From Halliday and Resnick, Ch.5.)