PROBLEM SOLVING PROCEDURES
1. MAKE A DIAGRAM
Make a diagram, if appropriate, of the problem situation. Define the meaning of the parameters to be used, the directions in which these parameters increase in magnitude, the origin and orientation of the chosen coordinate system, and anything else that will clarify the situation. Listing the known (given) and desired quantities for the problem is also helpful.
2. WRITE THE PERTINENT FUNDAMENTAL RELATIONSHIPS
Write the general mathematical relationships that describe the physics of the problem situation. Parameters that show up in these relations and in the diagram should be represented by the same letter. An attempt should be made to use commonly used letters for the parameters, such as "t" for time, etc. If two specific situations are being compared, be sure to subscript the appropriate parameters.
3. SIMPLIFY USING CALCULUS AND ALGEBRA
Perform any calculus operations and/or algebraically manipulate (simplify) the general relationships so as to isolate the desired quantity on one side of the equation.
4. SUBSTITUTE NUMBERS AND UNITS
Re-write the simplified relation substituting the numerical values and the units for each of the known parameters. If conversion of any of the units is necessary, the conversion factor(s) should be included at the appropriate point in the expression.
5. SIMPLIFY TO FINAL RESULT
Use the rules of arithmetic on the numbers, and simplify the units to arrive at the final numerical answer and the associated units.
6. CHECK SOLUTION
Does your answer make sense? Can you check the validity of your general solution (#3 above) by considering limiting or extreme cases?