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.
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. Then put
the examples aside and work this problem without further help. Write
down all 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.
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.
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 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.
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 (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 problem occurs on an exam, you may have less
time to think than you would like.