## Three Tips for Solving Physics Problems

I spent quite some time this morning going over some coursework problems with my second-year Physics class. It’s quite a big course – about 100 students take it – but I mark all the coursework myself so as to get a picture of what the students are finding easy and what difficult. After returning the marked scripts I then go through general matters arising with them, as well as making the solutions available on our on-line system called *Learning Central*.

Anyway, this morning I decided to devote quite a bit of time to some tips about how to tackle physics problems, not only in terms of how to solve them but also how to present the answer in an appropriate way.

I began with the Feynman algorithm for solving physics problems:

- Write down the problem.
- Think very hard.
- Write down the answer.

That may seem either arrogant or facetious, or just a bit of a joke, but that’s really just the middle bit. Feynman’s advice on points 1 and 3 is absolutely spot on and worth repeating many times to an audience of physics students.

I’m a throwback to an older style of school education when the approach to solving unseen mathematical or scientific problems was emphasized much more than it is now. Nowadays much more detailed instructions are given in School examinations than in my day, often to the extent that students are only required to fill in blanks in a solution that has already been mapped out.

I find that many, particularly first-year, students struggle when confronted with a problem with nothing but a blank sheet of paper to write the solution on. The biggest problem we face in physics education, in my view, is not the lack of mathematical skill or background scientific knowledge needed to perform calculations, but a lack of experience of how to set the problem up in the first place and a consequent uncertainty about, or even fear of, how to *start*. I call this “blank paper syndrome”.

In this context, Feynman’s advice is the key to the first step of solving a problem. When I give tips to students I usually make the first step a bit more general, however. It’s important to *read the question* too.

The middle step is more difficult and often relies on flair or the ability to engage in lateral thinking, which some people do more easily than others, but that does not mean it can’t be nurtured. The key part is to look at what you wrote down in the first step, and then apply your little grey cells to teasing out – with the aid of your physics knowledge – things that can lead you to the answer, perhaps via some intermediate quantities not given directly in the question. This is the part where some students get stuck and what one often finds is an impenetrable jumble of mathematical symbols swirling around randomly on the page.

Everyone gets stuck sometimes, but you can do yourself a big favour by at least putting some words in amongst the algebra to explain what it is you were attempting to do. That way, even if you get it wrong, you can be given some credit for having an idea of what direction you were thinking of travelling.

The last of Feynman’s steps is also important. I lost count of the coursework attempts I marked this week in which the student got almost to the end, but didn’t finish with a clear statement of the answer to the question posed and just left a formula dangling. Perhaps it’s because the students might have forgotten what they started out trying to do, but it seems very curious to me to get so far into a solution without making absolutely sure you score the points. IHaving done all the hard work, you should learn to savour the finale in which you write “Therefore the answer is…” or “This proves the required result”. Scripts that don’t do this are like detective stories missing the last few pages in which the name of the murderer is finally revealed.

So, putting all these together, here are the three tips I gave to my undergraduate students this morning.

- Read the question! Some solutions were to problems other than that which was posed. Make sure you read the question carefully. A good habit to get into is first to translate everything given in the question into mathematical form and define any variables you need right at the outset. Also drawing a diagram helps a lot in visualizing the situation, especially helping to elucidate any relevant symmetries.
- Remember to explain your reasoning when doing a mathematical solution. Sometimes it is very difficult to understand what you’re trying to do from the maths alone, which makes it difficult to give partial credit if you are trying to the right thing but just make, e.g., a sign error.
- Finish your solution appropriately by stating the answer clearly (and, where relevant, in correct units). Do not let your solution fizzle out – make sure the marker knows you have reached the end and that you have done what was requested.

There are other tips I might add – such as *checking* answers by doing the numerical parts at least twice on your calculator and *thinking* about whether the order-of-magnitude of the answer is physically reasonable – but these are minor compared to the overall strategy.

And another thing is not to be discouraged if you find physics problems difficult. Never give up without a fight. It’s only by trying difficult things that you can improve your ability by learning from your mistakes. It’s not the job of a physics lecturer to make physics seem easy but to encourage you to believe that you can do things that are difficult.

So anyway that’s my bit of “reflective practice” for the day. I’m sure there’ll be other folk reading this who have other tips for solving mathematical and scientific problems, in which case feel free to add them through the comments box.

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November 2, 2012 at 1:06 pm

I’d say this about genuine research in theoretical physics: BACK yourself to crack it; think about it from as many different directions as possible, and don’t go bull-at-a-gate until you get a lead along one of those directions. (This is why a broad education across all of physics is vital – it gives you extra directions.) Keep pen/biro and paper handy because you will need to write down long formulae and doing that is a lot faster by hand; arguably all of the hand-eye-brain connections are relevant in problem-solving. (LaTeX is great but essentially for writing up.) In some problems, computer algebra can help. Test all general results with quick-and-easy special cases.

November 2, 2012 at 1:14 pm

I found that during my graduate studies my productivity as a researcher went up when I started to think more about what I was going to do before actually starting to do stuff. I learned this lesson by wasting weeks trying to solve a nasty numerical integral which turned out to be entirely irrelevant. Had I thought more before trying to the calculation I would have realised that was the case and not wasted so much time.

In undergraduate work I also get the impression that many students start playing around with the maths before really thinking about what the problem really means, which is what dictates the strategy a physicist should use for solving it…

November 2, 2012 at 1:46 pm

That story about the integral does rather explain why you once advised me that the job of a theoretical physicist was to come up with ways to avoid having to do integrals.

More on the topic, I believe a very clever physicist (Gell-Man? Schwinger?) once remarked that they never attempted a calculation they did not already know the answer to. I think this was a wise strategy.

November 2, 2012 at 1:53 pm

My first rule for doing integrals is “If possible, don’t”.

Quite a lot of questions in old textbooks use the phrase “Reduce the following problem to quadratures..”, which presumably means that it’s acceptable to avoid doing the actual integral.

November 2, 2012 at 1:49 pm

I wonder if this is a version of the story told about von Neumann, that he never attempted problems he found difficult, only problems that others found difficult.

November 2, 2012 at 2:07 pm

One might not be able to work out the entire answer in one’s head, but usually one can at least use dimensional analysis to obtain the form of the answer, perhaps preceded by a dimensionless factor. In astrophysics, for example, one can determine the gravitational binding energy, say, to be some multiple of GM^2/R – the factor has to be fixed by actually doing stuff.

November 2, 2012 at 2:24 pm

More fully, dimensional analysis allows you to say that there is a unique functional relation between all of the dimensionless multiplicative power-law combinations of variables that you guess are involved. If there is only one such dimensionless combination then it is equal to a constant, whose value is the only thing that is missing – effectively the constant of proportionality when one of the variables in that combination is expressed in terms of the others.

November 2, 2012 at 1:35 pm

I remember one problem in (I think) Pippard in which the solution came out in very few lines if you went against the usual wisdom and defined the *magnetic* field as the gradient of a scalar field (which was possible as it had zero curl in this problem).

November 2, 2012 at 1:17 pm

Teachers must be well equipped now to understand new physics beyond Einstein and modern quantum physics with the discovery of gravitoetherton in CERN. and the consequences of theories published by Durgadas Datta in year 2002.

November 25, 2012 at 4:05 am

[…] Three Tips for Solving Physics Problems […]

November 25, 2012 at 8:57 pm

I am a retiree with no math background. However as a little child a read about the astrologer seemingly humbly asking for a grain of whet doubled for each snare on a chess board, and took a pencil and paper and started doubling, had to switch to graph paper, and figure out how to add digest to correct occasional errors.

Also ten times is 1,024 and 1 millon also 1,+ and 1 billion also 1,+

the answer is now on the internet, and I think the same but the original answer must be long painted over in my childhood home.

MegaPenny visualizes 60 time with penneis

Anyway I recently collected visualizations of the world around us and had trouble finding visualizations of the very small.

Do you know of any?

Richard Kane RichardKanePA@aol.com,

http://lifeboat.com/blog/2012/11/visualizing-the-world-and-its-dangers

September 12, 2013 at 3:24 pm

Thanks a lot sir

October 8, 2013 at 4:29 pm

very insteresting tips , hope it will help all future aspirants just like me .i recentiy collected these three tips . thankyou for helping all the aspirants and me in this awesome way

February 11, 2014 at 3:23 pm

Inspiring and educative

July 1, 2014 at 3:20 pm

please ;provide me the shortcuts of solving numericals

July 1, 2014 at 3:21 pm

in physics

July 10, 2014 at 8:16 pm

PLS I NEED HELP ON TO TACKLE ANY PHYSIC PROBLEM.