*This page written by
Dan Styer,
Oberlin College Physics Department;
http://www.oberlin.edu/physics/dstyer/WhyHowProblems.html.
last updated 6 August 2001.*

Why do I assign problems in physics courses? How can working these problems help you?

**Philosophy.** Listening to lectures,
reading books, running computer
simulations, performing experiments, participating in
discussions . . . all these are fine tools for
learning physics. But you will not *really* become
familiar with the subject until you get it under your skin by working
problems. The problems in a physics course
do not simply test your comprehension
of the material that you learned in the text. Instead they are
an important component of the learning experience, designed
to extend and solidify your grasp of the concepts and content of physics.
Solving problems is a more active, and hence more effective,
learning technique than reading text or listening to lectures.

In answering your homework (and exam) problems, you must
**show your work**. That is, you must present
your evidence and your reasoning as well as your final
conclusion. (This rule holds for all intellectual
discourse. For example, suppose you are asked in an
English Literature course to consider Melville's influence
on American literature.
You march off to the library and -- after considerable
reading and analysis -- conclude that
"Moby Dick changed
the entire landscape of the American novel." If you typed up
this single sentence and submitted it as your paper, your
professor would be unimpressed.) Exactly how much detail
should you give in presenting your reasoning? A good rule
of thumb is to present enough detail that you could reconstruct
your thought processes two or three months later, when
you're using your solutions to study for the final exam.

**Difficulty.** No one should expect to score 100% on homework.
Some of the problems are deliberately very challenging.
Everyone can use improvement, and the problems are a relatively
painless way for me to challenge you and show you how to improve.
I assign problems that will expose you to many fascinating
phenomena and useful devices.
The exams I set for you are much easier because they serve
an entirely different purpose. Homework is a way for *me* to
show *you* some of the many vistas of physics that you don't
know, whereas exams are a way for *you* to show
*me* the many aspects of physics that you do know.
Before each exam I will distribute a practice exam so that
you will have some idea of what to expect in terms of length and
difficulty.

**Warm up exercises.** A problem arises from my assigning
such interesting homework problems. They tend to be harder than
plodding, mechanical problems, and in particular, they tend to need
many steps in their solution. Hence I will, for
many assigned problems, suggest "warm up
exercises" that are more mechanical,
simpler, and involve fewer steps than the assigned problems. Working the
warm-ups is not required, and if you do work them you should not
hand them in. But if you find that a particular assigned problem is
too difficult, then try the associated warm-ups.
Working them should give you practice that will be directly relevant
in helping you solve the associated assigned problem.

**Model solutions.** I distribute model solutions to the homeworks
on the day that I collect them from you. My model solutions are only
that: models. You might have solved the problem in a completely
different way that is actually superior to the way I chose.
I urge you to scan the model solutions on the day I give them
out . . . the problems will be fresh in your mind and you'll learn from my
solutions more readily.
If you find that you solved the problem (correctly!) in a way different
from mine, then please do let me know about it.
One of the great joys I find in teaching is to learn from my
students, and it happens more frequently than you might think.

**Sample problem.** For concreteness, many of the tips below refer
to the following problem (Halliday, Resnick, and Walker,
*Fundamentals of Physics*, sixth edition **22**-9):

Two *free* point charges *+q* and *+4q* are a distance *L* apart.
A third charge is placed so that the entire system is in equilibrium.
(a) Find the location, magnitude, and sign of the third charge.
(b) Show that the equilibrium of the system is unstable.

**Explain.** When you write up solutions to problems, be sure
to explain your reasoning. Don't just give me the final
numerical answer or the end formula . . . I already know what it is!
Instead I'm interested in seeing how you overcome the roadblocks
that get in your way as you progress through the problem.
An appendix in the text by Halliday, Resnick, and Walker lists "Answers to
odd-numbered questions, exercises, and problems". Be aware that these
are merely skeleton answers, and I am interested in a full
solutions, like the model solutions that I hand out to you or that
you can find in the "sample problems" of the text.
The benefits that accrue from
active problem solving come only if you supply the reasoning yourself.
The "answers" at the end of the book will help you learn physics
if you work through the problem yourself and then use the skeleton
answer to check your reasoning. If you instead look up the answer
before attempting the problem, the "answers" section
will actually be an impediment to your learning.

The explanation does not need to be terribly long or detailed, but it must exist if you are to earn full credit. For example, in the sample problem the third charge must be located on the axis: Otherwise the total force on the first two charges would have a vertical component and hence could not equal zero. You can get away with a statement as simple as "The equilibrium position is on the axis", but you can't just omit it.

**Map out the logic.** This point is similar to the one above.
If you are using Coulomb's law to find the force between two
particles of charge *+q* and *+4q* separated by a distance *L*,
then you might say
"*F = k q _{1}q_{2}/r^{2} =
k 4q^{2}/L^{2}*",
or "From Coulomb's law,

**Diagrams and definitions.** In almost all cases, the first step
in solving a problem is to draw a diagram showing the geometry of
the situation. The diagram will organize your work and point out
ways to proceed.

The diagram is often a good place to define variables that you will
need as well. Using the sample problem as an example again,
remember that you need to find the location of the third charge.
Saying *x = L/3* is not an answer unless you have first defined *x* to be
the distance from the charge *+q* rather than the distance from
the charge *+4q*. The easiest way to do this is through a diagram.

**Do full problem for full credit.** The sample problem has two parts.
Part (a) is clearly the main part of the
problem, but it's not the *only* part of the problem! For
full credit, you must do part (b) as well. If a problem asks you
to derive an equation and discuss the result in the limit that
the charge vanishes, then you have to supply the discussion to
get full credit. Sentences count just as much as equations and numbers!

**Do partial problem for partial credit.** If you can't solve
a problem completely, then hand in a start. If you have a plan
for solving the problem but can't execute it, then hand in the
plan. If you can't
find the magnitude of the electric field but can find its direction,
then tell me the direction. If a problem has two variables *x* and
*y*, and you can solve it only in the case that *x = 2y*, then
hand in the solution for the special case that you have solved.
You will even get some points for saying nothing more than "This problem can
be solved using Coulomb's Law, but I can't figure out the details."
In the world of physics research, it often happens that the
questions change as you work on the answers, and you can
use the same philosophy in this course.
(If you follow this advice and solve a problem related to but different
from the one that I assigned, then please point this out explicitly
in your solution.)

**Citation.**
If you use a specialized result from your text, then cite it.
No need to cite momentum conservation, but there is a need to cite an
equation giving the final velocity of the target particle in a
one-dimensional elastic collision with the target initially
stationary . . . now there's a specialized result!

**If you can't solve the problem** then at least do something:
sketch the situation and define a few relevant variables.
State a relevant principle. If you come up with a silly result
(e.g. a negative kinetic energy), then tell me that it's silly
and you've earned a point (or two). If you run out of time,
then write a sentence about how you would solve the problem
if you did have time. Writing down your thoughts can clarify them
and lead you to your goal. If nothing else, they might earn you points.

**Mechanics.** The problem sets are graded by a student working under
my close supervision. I have the final say on your homework
grade, so if you feel that the grader has been unfair or arbitrary or wrong,
then see me and I might change your grade. (In practice, however,
I rarely do so because I give the grader very detailed instructions.)
Sometimes I will
ask the grader to look at only about half the problems that I
assign to you. This way, he or she can go through the sets quickly
and get your solutions back to you soon enough that you can learn
effectively from them.

Your solutions do not need to be obsessively neat, but they do need to be legible . . . particularly your name! One former grader for this course said "If I can't read it, I can't give you credit." I know of no one (certainly not myself) who can solve the problems in this course on the first shot: you'll need to work the problems first in rough draft and then copy out a version to submit for grading. The copying out is not just for neatness. It helps you consolidate your thoughts and brings the logic of your solution into focus. Please staple your problems together, for otherwise the pages are likely to become separated from each other and you will get credit for only the first page of your answers.

The problems in a physics course are not dry appendages designed to keep you indoors on sunny days. They are exciting, dynamic, and central to the course structure. Enjoy them!