
In general, solving a physics problem (and to a certain degree,
the exercises as well) involves taking a realistic situation and
constructing a simplified model that captures its essence. Often
the complicated details of a problem are deliberately suppressed
so it can be solved with simple physics principles. Creating a
model that is sufficient to describe the essence of a problem
without being overly complex is not an easy task. Doing this will
require practice.
The good news is that the
skills you refine here solving physics problems will be applicable
to other courses and other facets of life. And the reverse is
true as well, the problem solving skills you have from other experiences
will facilitate your physics problem solving. The reason for this
transfer is that problem solving, not matter the context, has
the same core elements.
Think of this the problem
solving as the basic scaffolding that will allow you to build
various masterpieces. At first this algorithm might feel awkward,
but trust me it will be beneficial in the long run. (The same
is true of other skills the proper grip on a tennis backhand
may at first feel uncomfortable, but you use an incorrect grip
your game will be limited.) Studies have shown that experienced
problem solvers (unlike novices) usually solve problems using
a framework that is independent of the problem or person.
What follows are some suggestions
for how to implement the general problem method to physics. In
each step, there is a list of questions that you may want to ask
yourself as you solve a physics problem, particularly, if you
get “stuck” along the way.
Problem
Solving Algorithm
 Understanding
the problem (Recognizing what is asked for.)
 Construct
a mental image of the objects and sequence of events
 Sketch
a picture
 Construct
diagrams or graphs to show important spatial and temporal relationships
 Define
all of the mathematical symbols
 What
objects are involved?
 Are
all the important objects known?
 The
important times, spatial relations, interactions and motions
known?
 Does
the question ask about a specific physical quantity? (If
not, can the question be reformulated so it does?)
 What
is the system of interest?
 What
are the known, and unknown, quantities?
 Creating
a plan (Responding to what is asked for.)
 State
principles and relationships that will likely be used.
 Select
one of the relationships to relate the desired unknown quantity
to known ones.
 If there
are multiple unknown quantities, additional relationships may
be necessary.
 If using
mathematical relationships (equations), combine so they allow
the target unknown quantity to be found.
 Which
physics principles are relevant?
 Are
any approximations necessary?
 What
reference frame or coordinate system would be most convenient?
 What
relationships and equations will follow from the selected
principles?
 Which
relationships relate the unknown quantity to the known ones?
 Are
there any restrictions on the relationships that may conflict
with the given information or principles?
 Are
there any quantities that cancel out when combining relationships?
 Executing
out the plan (Developing the result of the response.)
 Substitute
the numerical values and units for each quantity in the equations
and relationships.
 Calculate
the target quantity, both numerical value and units.
 If possible,
simplify the target quantity’s units so it is more readily
understandable.
 Which
values should be used for the variables?
 Do
the units need to be converted?
 Do
any units cancel?
 Reviewing (Checking. What does the result tell me? )
 Check
that the answer is reasonable. (If not, review the solution
and revise where necessary.
 Determine
if the answer is complete.
 Do
the units make sense?
 Do
vector quantities have both magnitude and direction?
 Does
the answer fit the mental picture of the situation?
 Do
the signs of the quantities agree with the chosen coordinate
system?
 Is
there a calculation mistake in the execution?
 Has
the question been answered?
 Could
somebody else read and follow the solution?
It’s
okay, if not beneficial to make mistakes within a solution. Everybody
does it. Just like solving a puzzle, nobody puts the pieces down
in the final position until after trying them in several other
places first. Expert problem solvers rarely solve a problem in
the linear, always perfect way textbooks present example solutions.
You shouldn’t feel as though you’re doing anything
wrong if you take a few wrong turns or lop back to previous steps
before moving to the next.
“Okay,…
so that’s how I solve a problem, but what do I turn in?”
Excellent question! ? After all, you’ll notice that most
of the problem solving occurs inside your head. Dr. Jeff can’t
very well scan your head with an MRI to see what you’re
thinking, but wouldn’t that be cool?
This is
where your documentation comes in to play. In order for Dr. Jeff,
or your supervisor later in life, to know that you solved the
problem you have to document your ideas. This is what is graded;
or, gets you promoted at work. The approach outlined here is based
on constructing a model of the situation described though three
different representations of the problem pictorial, conceptual and mathematical. In this way, you
can tap into three different modes of communication. A fourth
component, evaluating the answer or model, is also present.
The model you build (not the number you get at the end of some
algebra) is the “answer.” With this view, algebraic
mistakes are not as significant as conceptual mistakes (making
incorrect assumptions for example). Essentially you are trying
to predict the system’s behavior with your model this is
what it means to do science.
It should
be pointed out that this sequence solve the problem first, then
create a final documentation explaining your ideas, is the way
to go. Just like an English paper, what you turn in is not a rough
draft or a sheet full of scratch marks, rather it is a final draft.
In other words, don’t try to work out your solution on the
same piece of a paper that you’re planning on turning in.
And, to motivate you to practice this… Any paper that is
full of scratch work, will loose points.
Problem Solving
Documentation
 Pictorial Representation
Draw
a picture that shows the essence of the situation. It does
not need to be a work of art. People can be stick figures,
cars can be squares; you’re just trying to get a feel
for the problem here. Be sure to indicate your coordinate
system. Is up the positive direction? Which way does the xaxis
point? Etc.
Also, this is a
good place to list known values & define variables. Choose
a naming convention that is easy to remember and understand.
For example, using subscripts can help to make sense of a
large number of variables.
 Conceptual or Verbal Representation
The
main point of this representation is to describe the situation
(& model) in words. You should be as complete as possible
describing the situation as well as the relevant physics concepts.
Here are a few more details:
 Identify the system. Are you looking for the force of the
table on the book or the book on the table?
 Indicate the fundamental physics principle or concept. Write
a sentence that describes the basic concept at play “Here
we see the conservation of momentum in a twobody collision.”
By identifying the principle early in the solution you can
help yourself stay on track.
 Identify any assumptions or simplifications. For example,
are you going to ignore air resistance? Making simplification
can make an apparently complicated problem much easier. Just
be careful that you retain the essence of the problem and
don’t oversimplify.
 Hypothesize what will be the solution or outcome. Often
you will be asked to predict the outcome “will the
car stay on the road as it takes the corner?” By stating
in words what you think will happen (by using your intuition)
you might be able to catch a mathematical error later in the
model. (“Given that the fact that the car isn’t
travelling very fast, I believe that it will stay on the road.”)
 Mathematical Representation
Here
is where you will set up and solve various equations that
model your situation. Notice that this is only one part of
a complete solution or model. Without the pictures and words
the equations are meaningless. Never forget that the equations
are merely one representation of the system.
When you write down
the equations make sure you begin with the fundamental principle
you identified before. ("Conservation of momentum implies
that P_{i}= P_{f}"). We want to let the
physics guide our math. Then solve the equations symbolically
for any unknown variables. This is the step where you will
be using your algebraic skills to rearrange the equations
to get something useful. You should also explain what you
are doing as you carry out each step "using equation
#2, substitute P_{i} into equation #3")
Finally, plug
in known values and calculate a numerical answer (if needed). Wait until the final step to plug in the numbers. A solution is much easier to follow if you use variables throughout
the solution.
 Evaluation
This
is not really another representation, rather this section
is where you make sure that your model and numerical results
match your reallife experience. You should check the answer
to any numerical calculation does the answer have the correct
units, sign, direction, etc.?
Make sure that you answer
the questions asked (if the question asks if a cheetah can
catch a gazelle, the answer is “yes” or “no”,
not 5.6 m/s) And finally, you should ask: Does the answer
make sense? Is the answer reasonable? How does it compare
to your hypothesis? This is where you try to reconcile your
intuition with your mathematics. If they differ, it would
be worth reviewing your model. Often even the “best”
problem solvers will get to this step and find that their
model and results do not match their reallife experience.
For example, cars cannot travel 3 x 10^{8} m/s. If
your equations produce this result, you should go back and
reexamine your model. When you perform this step, you will
largely be having a conversation with yourself. Document this
“conversation on your final paper; in other words, write
down your reasoning for believing that your model is reasonable.
I
should point our that our text also gives some good advice on
solving problems. Inside the front cover is a list of problemsolving strategies, or at least a list of where to find the strategies.

