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.