A Logical Problem Solving
Strategy
(Summary
of this page)
Each profession has its own specialized knowledge
and patterns of thought. The knowledge and thought processes that you use
in each of the steps will depend on the discipline in which you operate.
Taking into account the specific nature of physics, we choose to label
and interpret the five steps of the general problem solving strategy as
follows:
A) Everyday language description:
In this step you develop a qualitative
description of the problem.
-
Visualize the events described in the problem
by making a sketch.
-
Write down a simple statement of what you
want to find out.
-
Write down verbal descriptions
of the physics ideas (the type of problem) which might be useful
in the problem and describe the approach you will use.
B) Physics description:
In this step you use your qualitative
understanding of the problem to prepare for the quantitative solution.
-
First, simplify the problem situation by describing
it with a diagram in terms of simple physical objects and essential physical
quantities. Make a physics diagram.
-
Define your variables (make a chart)
of know quantities and unknown quantities. Identify the variable
you will solve for.
-
Using the physics ideas assembled in A3
and the diagram you made in B1, write down general equations which
specify how these physical quantities are related according to the principles
of physics or mathematics.
C) Combine equations:
In this step you translate the physics
description into a set of equations which represent the problem mathematically
by using the equations assembled in step 2.
-
Select an equation from the list in
B3 that contains the variable you are solving for (as specified in B2).
-
Identify which of the variables in
the selected equation are not known.
-
For each of the unknown variables, select
another equation from the list in B3 and solve it for the unknown variable.
Then substitute the new equation in for the unknown quantity in
the original equation.
-
Continue steps 2 & 3 until all
of the unknown variables (except the variable you are solving for)
have
been replaced.
-
Solve for the target variable.
-
Check your work by making sure the
units
work out.
D) Calculate solution:
In this step you actually execute the
solution you have planned.
-
Plug in numerical values (with units)
into your solution from C5.
E) Evaluate the answer:
Finally, check your work.
-
Is it properly stated?
-
Is it reasonable?
-
Have you actually answered the question
asked?
Consider each step as a translation of the
previous step into a slightly different language. You begin with the full
complexity of real objects interacting in the real world and through a
series of steps arrive at a simple and precise mathematical expression.
The five-step strategy represents an effective
way to organize your thinking to produce a solution based on your best
understanding of physics. The quality of the solution depends on the knowledge
that you use in obtaining the solution. Your use of the strategy also makes
it easier to look back through your solution to check for incorrect knowledge
and assumptions. That makes it an important tool for learning physics.
If
you learn to use the strategy effectively, you will find it a valuable
tool to use for solving new and complex problems. After all, those
are the ones that you will be hired to solve in your chosen profession.
This page was adapted from
the University of Minnesota
Physics Education Research and Development Group with permision.