Do Physics!

As I was organizing myself for the start of this term I thought that I must have created a framework for 'Do Physics' at some point in the past. Remarkably it appears that I have only documented this process on various final exam problems but not in any other place. Time to rectify that oversight!

I would note that 'Do Physics' is not really about physics. It is about the process of what is called 'expert problem solving'.

Form of a 'Do Physics' Problem:

'Real' problems in physics and engineering come with some context usually but often are incompletely defined. The questions/answers that might be desired are sometimes apparent and sometimes not. The setting is typically one that does not overlap cleanly with particular problems you have done in the past for any number of reasons. You will find that such problems are also called authentic or context rich or open ended problems. They are typical of graduate school problems and industrial research and development.

Phase 1: Contemplate the Problem: Getting Clarity

Spend some time with the problem. Explore what you visualize the situation to be. Make sketches of various parts to clarify your understanding of the problem. Don't worry that this understanding may be incomplete at this point. That's normal.

Look for features or clues in the description of the problem that suggest which physics tools might be useful. Consider, for each physics tool, whether you have some or all of the information needed to put the tool to use. Write down the basic form of the tool and assess the knowns and unknowns.

What features of the problem setting might suggest data you can add to the problem statement. Is gravity a player? What planet? Might friction be a player? Do you have some sense of the mass or density of objects in the problem? As you experience more areas of physics and engineering you will find many more potential features to consider like boundary conditions, periodic motion, fields, currents, or potential maps. The breadth of your experience will constantly grow as will the variety of problems you address. That's why this phase of the problem solving is so critical.

Are there any features of the problem for which you can set limits based on your experience? Maximum plausible velocities or sizes? As the breadth of your knowledge grows so will you sense of these limits.

Simplifying assumptions: What simplifying assumptions will you make to start with? It is possible to oversimplify and the problem disappears but that just tells you that you went too far. There may be several initial simplifications that you will come back and remove as you get deeper into the problem.

Articulate as clearly as possible the question or questions that you will address first.

Phase 2: Frame the Physics: Refine your Understanding

For each physics tool that seems relevant there are frameworks that we have learned to use. These include freebody diagrams, energy bar charts, tables of components, or momentum bar charts. This often involves drawing new sketches and annotating the various points of interest. Write down the mathematical statement of the physics tool so the data you need is apparent. This will help clarify what quantities need to be labelled at this stage.

This is the part where you label and name everything in the problem that seems to need a label. Unlike standard problems, where the labels are often given to you, these problems will need you to make many choices. Use standard symbols where appropriate to avoid confusion like μ for friction and use subscripts liberally to identify important points in the process. Do not be surprised if you wad up your first attempt and throw it in the trash. I go through a lot of paper in these first two steps as I come back to totally restart really fun problems.

Start building a list of the features of the problem that you want to determine. In standard classroom problems the text or the instructor tells you what to look for. In more realistic settings you have to make this identification. It will seem odd in the beginning but learning what questions might be of interest is a skill you can develop. There are likely to be several or many and it is not always clear what comes first. In the next phase of problem solving you will start the process of actually setting up and making calculations.

At this point you should be able to explain the problem clearly to another classmate along with the questions about the setting that you have identified.

Phase 3: Planning/Executing: Calculating

Problem solving is often presented as a planning stage followed by an execution stage. In my experience this only works when you recognize the problem you are solving and already have a successful approach. Most of the really fun and challenging problems involve a certain amount of trying, failing, and coming at it from a new direction.

Having written down potentially relevant physics tools in an earlier phase of problem solving now is a good time to see if any of the tools are easy to solve for a single unknown. Even if you're not sure it's totally relevant it can lead to new insights. If there are multiple unknowns consider each one individually and whether there is a separate pathway to determining a value for it. As always, count unknowns and equations so the extent of the challenge is understood.

This is a good place to make any numerical estimates that you can. Estimates are not full calculations.

Keep track of units everywhere and note what the units of each 'answer' should be.

Keep your calculations symbolic so it is easier to update them as your understanding of the setting evolves.

Follow through on any potential calculations and then reassess your situation.

Phase 4: Evaluation: Check Yourself

Did the units work out correctly?

Is the answer reasonable at some level? Check against any estimates of limits that you established in the previous phase.

Regardless of whether your answer aligns with your estimate or not take one last look to make sure it all makes sense.

Back to Phase 2 and see what else you can determine now..

Disclaimer: This is a first draft of the Do Physics process so please provide feedback for improving this framework.