# Thread: Model procedure for solving physics problems

1. 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.

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?

2. That is a nice succint guide to how to not only solve a problem but how to write up the solution so that someone else can follow the work.

It is rather standard for engineering calculations to be performed in a similar manner. This is in part due to the fact that engineering calculations are a piece of the overall technical package that goes with any product and they must be clear to a fairly wide audience.

Particularly for problems in mechanics the first step is what is called a "free body diagram" which is simply a diagram that isolates each rigid body and shows the forces that are imposed on each body. Of course contact forces are equal and opposite for any bodies that are in contact with one another.

3. Originally Posted by DrRocket
Particularly for problems in mechanics the first step is what is called a "free body diagram" which is simply a diagram that isolates each rigid body and shows the forces that are imposed on each body. Of course contact forces are equal and opposite for any bodies that are in contact with one another.
Good point. The display of forces is less obvious when you are covering more than just mechanics. I have editted my original post to mention forces explicitly.

4. Originally Posted by mvb
Good point. The display of forces is less obvious when you are covering more than just mechanics. I have editted my original post to mention forces explicitly.
I agree that the situation is a bit more straightforward when one is dealing with mechanics, but it is an important special case.

I must admit that I tend to try to draw a picture for almost any problem (no exceptions come to mind immediately). But on the other hand I think visually. I find that most other mathematicians think visually and I think that is the case with most scientists.

The important word above is "most". Not all mathematicians think pictorially. A friend of mine, a topologist, one visited with Dennis Sullivan. The very first question from Dennis was "Are you a pictures guy or a numbers guy?" The reason for the question is that Dennis is a pictures guy and did feel that he could communicate with anyone who was not. Different people think in different ways, and those ways can be effective.

So, I wonder what someone who does not think visually (a numbers guy) thinks of the strong recommendation (which I do endorse) that one begin to solve any problem by first drawing some sort of diagram. Thoughts ?

As an aside for someone who made not understand what it means to think visually, the notion of visualization need not be conventional pictures of what one might see with ordinary vision. Mathematicians have individual ways of visualizing higher dimensions, even infinite dimensions, for instance and gaining intuition from those visualizations that are later manifested in terms of rigorous logical arguments that may involve numbers (i.e. the visualization may not be at all apparent to the extent that therre may be no hint of it in the final paper or proof that presents the result). It is important to recognize this when one sees someone talk in visual terms about quantities in quantum mechanics.

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