Problem Solving in Physics
You may now be like many students a novice problem solver. The goal of this section is to help you become an expert problem solver. Effective, expert problem solving involves answering five questions:
- What's the problem about?
- What am I asked to find?
- What information am I to use? What principles apply?
- What do I know about similar situations?
- How can I go about applying the information to solve the problem?
- Does my solution make sense?
You, the expert, will decide, "this is an energy problem," or, "this is a Newton 2 problem." A novice is more likely to decide, "this is a pulley problem," or, "this is a baseball problem." The novice concentrates on the surface features of the problem while you concentrate on the underlying principle. You, an expert problem solver, will answer these questions, play around (briefly) with the problem, and make drawings and sketches (either in your mind, or even better, on paper) before writing down formulas and plugging in numbers. A novice problem solver, on the other hand, will try to write down equations and plug in numbers as soon as possible. A novice will make many more mistakes than you will when you become an expert.
In a physics course it's important to remember a couple of things about physicists and physics professors:
- A physicist seeks those problems that can be modeled or represented by a picture or
diagram. Almost any problem you encounter in a physics course can be described with a
drawing. Such a drawing often contains or suggests the solution to the problem.
- A physicist seeks to find unifying principles that can be expressed mathematically and that can
be applied to broad classes of physical situations. Your physics textbook contains many
specific formulas, but you must understand the broader Laws of Nature in order to grasp the
general overview of physics. This broad understanding is vital if you are to solve problems that
may include several different principles and that may use several different formulas. Virtually all
specific formulas in physics are combinations of basic laws.
General outline of how to approach a physics problem:
1. Read the problem. Look up the meanings of any terms that you do not know. Answer for yourself the question, "What's this about?" Make sure you understand what is being asked, what the question is. It is very helpful if you reexpress the problem in your own words or if you tell a friend what the problem is about.
2. Make a drawing of the problem. Even a poor drawing can be helpful, but for a truly good drawing include the following:
a. Give a title that identifies the quantity you are seeking in the problem or that describes the
b. Label the drawing, including the parameters or variables on which the solution depends and
that are given in the problem. Write down the given values of these parameters on the drawing.
c. Label any unknown parameters that must be calculated along the way or obtained from the
text in order to find the desired solution.
d. Always give the units of measure for all quantities in the problem. If the drawing is a graph, be
sure to give both the units and the scale of the axes.
e. Include on the drawing information that is assumed and not given in the problem (such as g,
the value of the acceleration due to gravity), and whether air resistance and friction are
3. Establish which general principle relates the given parameters to the quantity that you are
seeking. Usually your picture will suggest the correct techniques and formulas. At times it may be necessary to obtain further information from your textbook or notes before the proper formulas can be chosen. It often happens that further information is needed when the problem has a solution that must be calculated indirectly from the given information. If further information is needed or if intermediate quantities must be computed, it is here that they are often identified.
4. Draw a second picture that identifies the coordinate system and origin that will be used in
relating the data to the equations. In some situations this second picture may be a graph, free body diagram, or vector diagram rather than a picture of a physical situation.
5. Even an expert will often use the concrete method of working a problem. In this method you do the calculation using the given values from the start, so that the algebra gives numerical values at each intermediate step on the way to the final solution. The disadvantage of this method is that because of the large number of numerical calculations involved, mistakes are likely, and so you should take special care with significant figures. However this method has the advantage that you can see, at every step of the way, how the problem is progressing. It also is more direct and often makes it easier to locate a mistake if you do make one.
6. As an expert, you will more and more use the formal method of working a problem. In this method, you calculate the solution by doing as much as possible without using specific numbers. In other words, do as much of the algebra as you can before substituting the specific given values of the data. In long and complicated problems terms may cancel or expressions simplify. Our advice: gain experience in problem solving by substituting the numbers when you start physics, but gradually adopt the formal approach as you become more confident; many people adopt a compromise approach where they substitute some values but retain others as symbols (for example, "g" for the acceleration due to gravity).
7. Criticize your solution: Ask yourself, "Does it make sense?" Compare your solution to any available examples or to previous problems you have done. Often you can check yourself by doing an approximate calculation. Many times a calculation error will result in an answer that is obviously wrong. Be sure to check the units of your solution to see that they are appropriate. This examination will develop your physical intuition about the correctness of solutions, and this intuition will be very valuable for later problems and on exams.
An important thing to remember in working physics problems is that by showing all of your work you can much more easily locate and correct mistakes. You will also find it easier to read the problems when you prepare for exams if you show all your work.
8. In the AP examination, you may have to do problems under a strict time limitation. Therefore, when you are finished with a homework problem, practice doing it again faster, in order to build up your speed and your confidence.
When you have completed a problem, you should be able, at some later time, to read the solution and to understand it without referring to the text. You should therefore write up the problem so as to include a description of what is wanted, the principle you have applied, and the steps you have taken. If, when you read your own answer to the problem, you come to a step that you do not understand, then you have either omitted a step that is necessary to the logical development of the solution, or you need to put down more extensive notes in your write-up to remind you of the reasons for each step.
It takes more time to write careful and complete solutions to homework problems. Writing down what you are doing and thinking slows you down, but more important it makes you behave more like an expert. You will be well paid back by the assurance that you are not overlooking essential information. These careful write-ups will provide excellent review material for exam preparation.