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
you can stop drawing one on paper.
Read the problem carefully, listing all quantities given and
requested. (Leave room for more quantities you may need later).
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.
Decide what kind of problem you are working on (response to a
force, energy conservation, equilibrium, or what have you). Use
examples from your notes and text to help with the decision and with
the general techniques used to solve problems of this type.
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.
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 are needed to finish the problem.
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?]
When everything seems to be correct, write out a complete,
logical solution. Watch for the correct number of significant digits in the
numerical answers.
On homework problems, outline the method of
solution in 2-3 lines or practice working through the solution
quickly. If a similar problem occurs on an exam, you may have less
time to think than you would like.