Fr. Wilfred's Suggested Problem Solving Strategy

The office next to mine for many years was occupied by Fr. Wilfred, who started teaching physics in 1955. This is the advice he gave students in his intro physics course.

Problem Solving Strategy

In a general physics course a student is asked to solve many problems. It is generally assumed that solving problems is the best way to clarify the concepts and principles of physics. This is true, provided that the student is able to make solving problems a real learning experience. It is possible that solving problems becomes only a routine: "How to discover the right equation". If a student approaches problem solving with the attitude that s/he only has to find the equation that will give the right answer, much time may be spent, but little learning of physics will take place. To make problem solving a more rewarding and profitable part of general physics, the following procedure should be kept in mind constantly.

  1. First read the problem carefully enough so that you can state in your own words what physical situation is being described.

  2. Whenever possible, draw some kind of a diagram or simple picture of the physical situation. This is essential to the understanding of most problems. Trying to solve a problem mentally or intuitively usually consumes much time with no results.

  3. Explicitly write down what principle or law you think you ought to apply to the problem. Should you use Newton's second law, the conservation of energy principle or the conservation of momentum principle?

  4. Write down an equation that you belive applies to the problem. Ask yourself if the equation definitely holds in this particular situation. Are you sure that the quantities given in the problem are the ones given in the equation? For example, an equation may have a symbol for average velocity, whereas the problem gives an instantaneous velocity.

  5. If you cannot find a single equation that enables you to find the unknown quantity or quantities, write down all the equations you think you must use.

  6. Rewrite the equation(s) in symbolic form in such a way the the unknown quantity or quantities are isolated. For example, suppose that in step 4 above you decided that the problem must be solved by Newton's second law:

    F = ma

    If the unknown quantity you are looking for is a, rewrite the equation as:

    a = F/m

  7. The numerical quantities that have been given in the problem should now replace their symbolic quantities in the equation. BE SURE THAT THE UNITS ARE CORRECT. For example, when the MKS system of units is used, the mass of a body must be entered in kilograms and the length must be entered in meters. Be sure that the correct sign (+ or -) is used, particularly for quantities where sign indicates direction. The average student wastes many hours because s/he has been careless about using the right units or proper sign.

  8. Calculate the unknown quantity. Does your answer appear reasonable--in magnitude and in units?

  9. Check your solution with the answer given in the text book.

  10. Go back to step 4 and see whether and how this problem clarified your understanding of a particular law or principle. Solving problems is only worthwhile if your knowledge of physics is deepened as a result.
The procedure outlined above will be applicable in many other situations, in the solutions of problems outside of physics and the other sciences. Most problems in business, medicine and scholarly research of any kind will be resolved more easily if a disciplined, orderly approach is developed.