Procedure For Solving Problems

1. Draw a diagram, if at all possible, even if it is so simple-minded as to seem silly. Only when you have worked a given type of problem so often that you automatically draw a mental diagram can you stop drawing one on paper.

2. Read the problem carefully, listing all quantities given and requested. (Leave room for more quantities you may need later).

3. Play with the situation either mentally or with models. Try to understand the behavior of the system qualitatively. Look for simpler special cases (zero angle, 90 degree angle, a zero length, a large mass, etc.) where the answer to the problem is obvious.

4. Decide what kind of problem you are working on (response to a force, energy conservation, equilibrium, etc.) Write down all principles and equations which apply to this kind of problem, whether or not it seems that you will use them in this particular problem. Write down too many. It is easier to ignore excess information than to realize that you need something that is not written down. Add to the list of quantities you made in part 2 any that are normally needed for this kind of problem but which are not specifically mentioned in the problem statement.

5. Determine whether or not the data given are adequate. If not, decide what is missing and how to get it. It may be necessary to look up some standard constant in a table or to make an assumption as to the value of some parameter. Work on the algebra to reduce the number of unknowns. When you have the same number of relevant, independent equations as you have unknowns, you probably have enough equations. Sometimes an unknown drops out, so when you have run out of ideas do some algebra even if it looks like you don't have enough equations. If you cannot find enough equations, determine as many as possible of the unknowns. Substitute numbers into the variables you can solve for and see if knowing their sizes helps. If nothing occurs to you in a reasonable amount of time, get help.

6. If necessary, add to the list of quantities you made at step 2 any additional quantities which you can compute but which were not asked for. Sometimes these additional quantities can be used to finish the problem. You can look for these quantities by examining the equations you listed in step 4. Now is also a good time to find any equations you may have overlooked at step 4. Now is also the time when you may have to change your mind about what kind of problem you are working on.

7. When you have an algebraic solution, put in numbers WITH UNITS. Be sure that all the numbers you use are in the same set of units.

8. CHECK

P lausibility [Algebra OK, numbers reasonable, signs correct?]

U nits [Are all consistent and appropriate?]

N otation [Vectors shown?]

S pecial cases [Does your solution obey those from step 3. If not, why not?]

9. When everything seems to be correct, write out a complete, logical solution (except when you are working an exam and your first version is intelligible). You will need this solution later to understand what you did. On homework problems, outline the method of solution in 2-3 lines or practice working through the solution quickly. If a similar problems occurs on an exam, you may have less time to think than you would like.

Adapted from Professor Maurice Barnhill at the University of Delaware

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