The following is from a web page I put up for my

introductory classes starting ages ago. I don't have

rigorous data on its usefulness, but my students liked

it, and those that used it seemed to work problems more

smoothly. I have since been told that my students were

better at working problems in subsequent courses than

students who went through the intro class after I

retired. See what you think:

1. Draw a diagram, if at all possible, even if it is so

simple-minded as to seem silly. For a problem involving forces,

draw all forces and show the body they are applied to.

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. Write down all the principles and equations which apply to

this kind of problem, whether or not it seems that you will use

them here. Write down too many. It is easier to ignore excess

information than to realize that you need something more. 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. You may need to look up

some standard constant in a table. 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 to determine as

many as possible of the unknowns. Substitute numbers into the

variables you can solve for and see if knowing their sizes

helps. Sometimes you discover at this point that you are not

working on the kind of problem you thought you were. If nothing

occurs to you in a reasonable amount of time, get help.

6. If necessary, add to your list of quantities any additional

ones 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 additional ones in the equations

you listed in step 4. Now is a good time to find any equations

you may have overlooked at step 4. Now is also a 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 your numbers are in consistent units.

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?