Problem Solving Strategy

 

  1. Focus:  Translate the words of the problem statement into a visual representation:
    1. Sketch the situation, noting on the sketch the important quantities, known and unknown.
    2. Identify the specific question(s) that must be answered.
    3. Identify the general approach you will use, the physical principles involved.
    4. Identify any assumptions that you will have to make.
    5. Identify the known and unknown quantities and the constraints.

 

  1. Physical Description:  Translate the problem into the terms and tools of physics.
    1. Construct idealized diagrams with labeled coordinate systems for each quantity of interest.
    2. Assign symbolic names to the relevant known and unknown quantities.
    3. Assemble the relevant fundamental equations that relate the known and unknown quantities (some you may not end up using.)
    4. Identify your Target quantitie(s).

 

  1. Mathematics:  Translate the physical description into a series of mathematical actions.
    1. Numberless Algebra (plugging numbers in too early obscures your reasoning and hides mistakes)

                                                               i.       Start with an equation that includes the target variable. 

                                                             ii.      If there is another unknown in addition to the target variable, identify another equation that includes this variable.  Solve the new equation for this unknown and substitute this solution into the previous equation.  

                                                            iii.      Repeat this process until the only unknown quantity is your target.

                                                           iv.      Solve the resulting equation for the target quantity.

    1. Substitute the numeric values (along with their units) into the final equation and compute the numeric solution.  Simplify the units (ex. m/(m2*Hz) = 1/(m*Hz) = 1/(m*1/s) = s/m.)

 

  1. Check and Evaluation:  Algebra errors are as easy to detect as they are to make.
    1. Check completeness:  Did you answer all the questions posed by the problem?
    2. Check units:  The units should be appropriate for the target quantity (ex. if you solved for a speed, but got the units of m/s3 instead of m/s, something went wrong.)
    3. Evaluate answer:  Are the sign and magnitude of the answer reasonable (ex. if you find that the speed of sound is 3,344 m/s when the air temperature is 40C, something went wrong.)