PHYSICS PROBLEM SOLVING STRATEGY
Modified from material by Dr. Mark Hollabaugh
Normandale
Community College
Two factors can help make you a better physics problem solver.
- First of all, you must know and understand the
principles of physics.
Secondly, you must have a strategy
for applying these principles to new situations in
which physics can be helpful.
Physics problem solving can be learned just like you learned to drive a car,
play a musical instrument, or ride a bike. What can aid you more than anything
is to have a general approach to follow with each problem you encounter. You may
use different tools or tactics with differing areas of physics, but the overall
strategy remains the same. Most likely, you have already acquired some
problem-solving skills and habits from previous courses in physics, chemistry,
or mathematics. Like other areas of learning and life, some of these habits may
be beneficial and some may actually hinder your progress in learning how to
solve physics problems.
So, in learning this new approach, be willing to try new ideas and to discard
old habits that may in fact be hindering your understanding. As you mature as a
physics problem solver, you will find that the approach will become second
nature to you. You will begin automatically to do those things that will lead
you to construct an effective solution to the problem.
The strategy we would like you to learn has
five major steps:
Focus the Problem,
Physics Description,
Plan a Solution,
Execute the Plan, and
Evaluate the Solution.
Let’s take a detailed look at each of these steps and then do an sample
problem following the strategy. At this stage of our discussion, do not worry if
there are physics terms or concepts that you do not understand. You will learn
these concepts as they are needed.
Step 1: FOCUS the PROBLEM
Usually when you read the statement of a physics problem, you must
visualize the objects involved and their context. You need to
draw a picture and indicate any
given information.
- First, construct a mental image of the problem situation.
- Next draw a rough, although literal, picture showing the important
objects, their motion, and their interactions. An interaction, for example,
may consist of one object being connected to another by a rope.
- Label all known information. At this point, do not worry about assigning
algebraic symbols to specific quantities.
Sometimes the question being asked in the problem is not obvious. "Is the
rope safe?" is not something you can directly answer. Ask yourself, what
specifically is being asked? How does this translate into some calculable
quantity?
There are many ways to solve a physics problem. One part of learning how to
solve a problem is to know what principles of physics to use in your approach.
You will need to determine the concepts and principles you think will be useful
in solving the problem. We will be applying the principles of Electricity &
Magnetism in this class.
Frequently in situations involving thermal
physics or electromagnetism, the principle of Conservation of Energy is useful.
You may need to specify time intervals or distances over which the application
of each principle will be the most useful. It is important to
identify any constraints present in
this situation, such as "the electric field is zero at infinity."
Specify
any approximations or simplifications you think will make the problem solution
easier, but will not affect the result significantly. Frequently we ignore
frictional forces due to air resistance.
Your approach probably will be very consistent throughout a particular
section of the textbook. The challenge for you will be to apply the approach in
a variety of situations.
Step 2. DESCRIBE the PHYSICS
A "physics description" of a problem translates the given information and
a very literal picture into an idealized diagram and defines variables that can
be manipulated to calculate desired quantities. In a sense, you are translating
the literal situation into an idealized situation where you can then apply the
laws the physics. The biggest shortcoming of beginning physics problem solvers
is attempting to apply the laws of physics, that is write down equations, before
undertaking this qualitative analysis of the problem. If you can resist the
temptation to look for equations too early in your problem solution, you will
become a much more effective problem solver.
To construct your physics description, you must do the following:
- Translate your literal picture into an abstract diagram(s) which gives
only the essential information for a mathematical solution. In an idealized
diagram, people, cars, and other objects may become square blocks or points.
- Define a symbol for every important physics variable on your diagram.
Improper or incomplete variable definitions can lead to disasterous results.
- Usually you need to draw a coordinate system showing the + and -
directions.
If you are using kinematics concepts, draw a motion diagram
specifying the objects’ velocity and acceleration at definite positions and
times. In general it is best to take the direction of initial motion as the +
direction.
If interactions are important, draw free body diagrams.
When using conservation principles, draw "before", "transfer" (i.e.,
during), and "after" diagrams to show how the system changes.
- To the side of your diagram(s), give the value for each physics variable
you have labeled on the diagram(s) or specify that it is unknown.
- Then, using the question, your physics description and the approach you
have stated, you will need to identify a target variable. That is, you must
decide what unknown quantity is it that you must calculate from your list of
variables. Ask yourself if the calculated quantity answers the question. In
complex problems there may be more than one target variable or some
intermediate variables you will calculate.
- Now, knowing the target variable(s), and your approach, you can assemble
your toolbox of mathematical expressions using the principles and constraints
from your approach to relate the physics variables from your diagrams. This is
the first time you really begin to look
for quantitative relationships among the variables.
You are simply constructing a mathematical model of the physical situation you
have describe in the diagrams.
Step 3. PLAN the SOLUTION
Before you actually begin to calculate an answer, take time to make a
plan. Usually when the laws of physics are expressed in an equation, the
equation is a general, universal statement. You must translate this general statement into specific algebraic
equations that will enable you to calculate the target
variable.
- Determine how the equations in your toolbox can be combined to find your
target variable.
- Begin with an equation containing the target variable.
- Identify any unknowns in that equation.
- Find equations from your toolbox containing these unknowns.
- Continue this process until your equations contain no new unknowns.
- Number each equation for easy reference.
- Do not solve equations numerically at this time.
- Frequently expert problem solvers will start with the target variable and
work backwards to determine a path to the answer. Sometimes the
units will help you find the correct
path. For example, if you are looking for a velocity,
you know your final answer must be in m/s.
- You have a solution if your plan has the
same number of independent equations as there are
unknowns. If not, determine other equations or check
the plan to see if it is likely that a variable will cancel from your
equations.
- If you have the same number of equations and unknowns, indicate the order
in which to solve the equations algebraically for the target variable.
Typically, you begin your construction of the plan at the end and work
backwards to the first step, That is, you write down the equation containing
the target variable first.
Step 4. EXECUTE the PLAN
Now you are ready to execute the plan.
- Do the algebra in the order given by your outline.
When you are done
you should have a single equation with your target variable isolated on one
side and only known quantities on the other side.
- Substitute the values (numbers with units) into this final equation. A
major shortcoming of beginning problem solvers is inserting numbers much too
early in the solution of a problem.
Make sure units are consistent so that
they will cancel properly.
- Finally, calculate the numerical result for the target variable(s).
Make sure your final answer is
clear to the person who will evaluate your solution.
It is extremely important to solve the
problem algebraically before inserting any numerical values. Some unknown quantities may cancel out and you won’t need to actually
know their numerical value. In some complex problems it can be useful to
calculate intermediate numerical results as a check on the reasonableness of
your solution.
Step 5. EVALUATE the SOLUTION
Finally, you are ready to evaluate your answer. Here, you must use your
common sense about how the real world
works as well as those aspects of the physical world you
have learned in your physics
class.
- Do vector quantities have both magnitude and direction?
- Can someone else follow your solution?
- Is the result reasonable and within your experience? Remember, for
example, that cars don’t travel down the highway at 300 mi/hr. If you put a
cooler object into hot water, the water cools down and the object rises in
temperature.
- Do the units make sense? Velocity is not measured, for example, in kg/s.
- Have you answered the question?
Whenever possible, it is a good idea to read through the solution carefully,
especially if it is being evaluated by your instructor. If your evaluation
suggests to you that your answer is incorrect or unreasonable, make a statement
to that effect and explain your reasoning. This is
important for Partial Credit for the
solution.