A Logical Problem Solving Strategy

A) Everyday language description:

In this step you develop a qualitative description of the problem.
1. Visualize the events described in the problem by making a sketch.  The sketch should indicate the different objects involved and any changes in the situation (e.g. changes in force applied, collisions, etc.)  First, identify the different objects that are relevent to finding your desired category.  Next, identify whether there is more than one stage (part) to the behavior of the object during the time from the beginning to the end that is relevent for what you are trying to find out.  Things that would indicate more than one part would include key information about the behavior of the object at a point between start and end of movement, collisions, changes in the force applied or acceleration of an object.
2. Write down a simple statement of what you want to find out.  This should be a specific physical quantity that you could calculate to answer the original question.
3. Write down verbal descriptions of the physics ideas (the type of problem).    Identify the physics idea for each stage of each object.  If the physics idea is a vector quantity (motion, force, momentum, etc.) identify how many dimensions are involved.

B) Physics description:

In this step you use your qualitative understanding of the problem to prepare for the quantitative solution.
1. 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.  You will need a diagram for each physics idea for each object, and possibly one for each stage and for each dimension.
2. Define your variables (make a chart) of know quantities and unknown quantities.  Identify the variable you will solve for.  Make sure variables are defined for each object, stage, idea and dimension.  Pay attention to units, to make sure you have the right kind of units for each type of variable.
3. 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.  You should write down at lleast one equation for each (object)x(stage/physics idea)x(dimension--if vector idea).

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.
1. Select an equation from the list in B3 that contains the variable you are solving for (as specified in B2).
2. Identify which of the variables in the selected equation are not known.
3. 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.
4. Continue steps 2 & 3 until all of the unknown variables (except the variable you are solving for) have been replaced or eliminated.
5. Solve for the target variable.
6. Check your work by making sure the units work out.

D) Calculate solution:

In this step you actually execute the solution you have planned.
1. Plug in numerical values (with units) into your solution from C5.

E) Evaluate the answer:

Finally, check your work.
1. Is it  properly stated?
2. Is it reasonable?
3. Have you actually answered the question asked?

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.