A Physics Problem-solving Framework

One of the main goals of this course is developing student competence in numerical problem-solving. “Plug-and-chug”and “pattern matching” problem-solving techniques will be discouraged. The following is a framework for organizinga solution to all numerical problems of this course [1][2].

This framework should make it clear what the graders will be looking for in your solutions. Fill out appropri-ately to obtain full credit. Use additional sheets as necessary, on which you should indicate the problem and the stepaddressed. You may also use your notebook sheets, as long as you clearly indicate which steps you are addressing, asshown in the following format.

Step 1 (6 points): Focus the problem (what is going on?)

This step is completed when you can put aside the problem text, and not have to look at it anymore until step5.

• Draw a picture of the situation

• Define useful quantities: identify what you know and don’t know

• State the question in terms of something you can calculate

Step 2 (6 points): Describe the physics (what does this have to do with physics?)

Here you go from something that mimics real-life situations (your problem) to an abstract and simplified situa-tion. You define the coordinate system (origin, axes, directions, etc.) and you identify and name the variables, inpreparation for working with equations.

• Draw any diagrams that might be useful

• Identify your target quantity

• State general principles that might be useful to approach this problem

• Give any constraints imposed by the situation

• State any approximations that might be useful

Step 3 (7 points): Plan a solution (how do I get out of this?)

Here you start to write equations. Simply transcribing generic equations from the equation sheet onto your an-swer sheet will not give you points, only applying them to your specific case (for your problem as shown in step 1, inthe coordinate system you defined in step 2, etc.) will give you credit. This step is not a memory test; if somethingyou need for your solution or happen to remember is not on the equation sheet, derive it starting from what you haveon the equation sheet.

• Translate the general principles into equations specific to the situation

• Construct a chain (or set) of equations linking your target to known quantities

• Check to see if you have sufficient equations

Step 4 (3 points): Execute the plan (let’s get an answer)

Here is the only mathematics, where you either manipulate your equations to obtain an expression for the vari-able you need or use a calculator to find its value for the numbers given in the problem. Defer calculating things untilyou have an algebraic expression for your answer. Variables often cancel out in the final expression, which makes thecalculation of what you are actually asked faster. Given the time constraints, remember what you look for (step 1),do not do things you don’t have to do.

• Follow your plan to calculate an answer

• Check your units

(over)

Step 5 (3 points): Evaluate the solution (can this be true?)

Always have units next to your answer. Check that the numerical answer makes sense for the specific numbersgiven in the problem. Also, check that the answer varies as expected as these numbers are varied (checking the“limits”). This, together with the units check in step 4, is a fast and useful diagnostic tool. To double-check that theanswer is complete, glance back at the actual problem text.

• Justify that your answer is not unreasonable

• Did you answer the question?

The problem-solving framework is a standard that will be applied equally to all students and will be used for allproblems, even though you have different backgrounds or interests and the problems vary in difficulty. Organize yoursolution to fit within this framework if you happen to be used to a different method. By doing this, you will not onlysolve a specific problem, but learn how to approach all problems in this course. You will find this more and moreuseful as problems become more complex.

Notes[1] As a rule of thumb, students should spend approximately two hours of independent study for each hour of class

or recitation. The 3 hours 20 min/week of instruction of this course translate into approximately 6-7 hours/week ofindividual study.

[2] From K. Heller and P. Heller, Cooperative Problem Solving in Physics, University of Minnesota. The coursetextbook also describes a problem-solving strategy on page 8 (2nd ed.), in which the second step (“develop”) approx-imately corresponds to steps 2 and 3 above. We will use the more detailed framework outlined above.