Archive for Physics

Power from Wind Problems

Posted in Cute Problems with tags , , on November 21, 2015 by telescoper

It has been a little while since I posted anything in the Cute Problems category so since today is quite a windy day I thought I’d give you this one, which leads to an extimate of the maximum power that can, in theory, be extracted from wind a windmill.

Assume that the wind far upstream and down-stream of the windmill has speed V and αV respectively, with 0≤α≤1, and let the wind speed at the sails of the windmill, which sweep out an area A, be v.

Now for the problems

(i) By equating the power absorbed by the mill to the rate of loss of kinetic energy of the wind, show that v/V=½(1+α).

(ii) Show that the power obtainable is proportional to AρV3 where ρ is the density of air.

(iii)  Show that the maximum power that can be extracted is 16/27 of the power available initially in the wind.

The final result is known as Betz’s Law and it works for any form of turbine, not just a windmill.




An Open Letter to the Times Higher World University Rankers

Posted in The Universe and Stuff, Education with tags , , , , , , , , on October 5, 2015 by telescoper

Dear Rankers,

Having perused your latest set of league tables along with the published methodology, a couple of things puzzle me.

First, I note that you have made significant changes to your methodology for combining metrics this year. How, then, can you justify making statements such as

US continues to lose its grip as institutions in Europe up their game

when it appears that any changes could well be explained not by changes in performance, as gauged by the metrics you use,  but in the way they are combined?

I assume, as intelligent and responsible people, that you did the obvious test for this effect, i.e. to construct a parallel set of league tables, with this year’s input data but last year’s methodology, which would make it easy to isolate changes in methodology from changes in the performance indicators.  Your failure to publish such a set, to illustrate how seriously your readers should take statements such as that quoted above, must then simply have been an oversight. Had you deliberately witheld evidence of the unreliability of your conclusions you would have left yourselves open to an accusation of gross dishonesty, which I am sure would be unfair.

Happily, however, there is a very easy way to allay the fears of the global university community that the world rankings are being manipulated: all you need to do is publish a set of league tables using the 2014 methodology and the 2015 data. Any difference between this table and the one you published would then simply be an artefact and the new ranking can be ignored. I’m sure you are as anxious as anyone else to prove that the changes this year are not simply artificially-induced “churn”, and I look forward to seeing the results of this straightforward calculation published in the Times Higher as soon as possible.

Second, I notice that one of the changes to your methodology is explained thus

This year we have removed the very small number of papers (649) with more than 1,000 authors from the citations indicator.

You are presumably aware that this primarily affects papers relating to experimental particle physics, which is mostly conducted through large international collaborations (chiefly, but not exclusively, based at CERN). This change at a stroke renders such fundamental scientific breakthroughs as the discovery of the Higgs Boson completely worthless. This is a strange thing to do because this is exactly the type of research that inspires  prospective students to study physics, as well as being direct measures in themselves of the global standing of a University.

My current institution, the University of Sussex, is heavily involved in experiments at CERN. For example, Dr Iacopo Vivarelli has just been appointed coordinator of all supersymmetry searches using the ATLAS experiment on the Large Hadron Collider. This involvement demonstrates the international standing of our excellent Experimental Particle Physics group, but if evidence of supersymmetry is found at the LHC your methodology will simply ignore it. A similar fate will also befall any experiment that requires large international collaborations: searches for dark matter, dark energy, and gravitational waves to name but three, all exciting and inspiring scientific adventures that you regard as unworthy of any recognition at all but which draw students in large numbers into participating departments.

Your decision to downgrade collaborative research to zero is not only strange but also extremely dangerous, for it tells university managers that participating in world-leading collaborative research will jeopardise their rankings. How can you justify such a deliberate and premeditated attack on collaborative science? Surely it is exactly the sort of thing you should be rewarding? Physics departments not participating in such research are the ones that should be downgraded!

Your answer might be that excluding “superpapers” only damages the rankings of smaller universities because might owe a larger fraction of their total citation count to collaborative work. Well, so what if this is true? It’s not a reason for excluding them. Perhaps small universities are better anyway, especially when they emphasize small group teaching and provide opportunities for students to engage in learning that’s led by cutting-edge research. Or perhaps you have decided otherwise and have changed your methodology to confirm your prejudice…

I look forward to seeing your answers to the above questions through the comments box or elsewhere – though you have ignored my several attempts to raise these questions via social media. I also look forward to seeing you correct your error of omission by demonstrating – by the means described above – what  changes in league table positions are by your design rather than any change in performance. If it turns out that the former is the case, as I think it will, at least your own journal provides you with a platform from which you can apologize to the global academic community for wasting their time.

Yours sincerely,


How to Solve Physics Problems

Posted in Cute Problems, Education with tags , , , , , , on September 18, 2015 by telescoper

It’s Friday afternoon at the end of Induction Week here at the University of Sussex. By way of preparation for lectures proper – which start next Monday – I gave a lecture today to all the new students in Physics during which I gave 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.

Richard-Feynman-cornellI began with Richard Feynman’s formula (the geezer in the above picture) for solving physics problems:

  1. Write down the problem.
  2. Think very hard.
  3. 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 key point is to write down the information given in the question and then try to think how it might be connected to the answer. To start with, define appropriate symbols and draw relevant diagrams. Also write down what you’re expected to prove or calculate and what physics might relate that to the information given.

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. The process of problem solving is not always linear. Sometimes it helps to work back a little from the answer you are expected to prove before you can return to the beginning and find a way forward.

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.

  1. Read the question! Some students give solutions to problems other than that which is 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.
  2. Remember to explain your reasoning when doing a mathematical solution. Sometimes it is very difficult to understand what students are trying to do from the maths alone, which makes it difficult to give partial credit if they are trying to the right thing but just make, e.g., a sign error.
  3.  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. In other words, finish with a flourish!

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.

To illustrate the advice I’ve given I used this problem, which I leave as an exercise to the reader. It is a slightly amended version the first physics problem I was set as tutorial work when I began my undergraduate studies way back in 1982. I think it illustrates very well the points I have made above, and it doesn’t require any complicated mathematics – not even calculus! See how you get on…


Quantum Madness

Posted in The Universe and Stuff with tags , , on September 18, 2015 by telescoper

A very busy day lies in store so I only have time for a quick morning visit to the blog. If you enjoyed the recent guest post on the “hidden variables” interpretation of Quantum Mechanics, then you will probably enjoy reading a paper that recently appeared on the arXiv with the abstract:

Motivated by some recent news, a journalist asks a group of physicists: “What’s the meaning of the violation of Bell’s inequality?” One physicist answers: “It means that non-locality is an established fact”. Another says: “There is no non-locality; the message is that measurement outcomes are irreducibly random”. A third one says: “It cannot be answered simply on purely physical grounds, the answer requires an act of metaphysical judgement”. Puzzled by the answers, the journalist keeps asking questions about quantum theory: “What is teleported in quantum teleportation?” “How does a quantum computer really work?” Shockingly, for each of these questions, the journalist obtains a variety of answers which, in many cases, are mutually exclusive. At the end of the day, the journalist asks: “How do you plan to make progress if, after 90 years of quantum theory, you still don’t know what it means? How can you possibly identify the physical principles of quantum theory or expand quantum theory into gravity if you don’t agree on what quantum theory is about?” Here we argue that it is becoming urgent to solve this too long lasting problem. For that, we point out that the interpretations of quantum theory are, essentially, of two types and that these two types are so radically different that there must be experiments that, when analyzed outside the framework of quantum theory, lead to different empirically testable predictions. Arguably, even if these experiments do not end the discussion, they will add new elements to the list of strange properties that some interpretations must have, therefore they will indirectly support those interpretations that do not need to have all these strange properties.

You can download a PDF of the full paper here. It’s a short piece, but with a very good list of references for further reading.

Widening Participation in Physics

Posted in Education with tags , , , , on September 9, 2015 by telescoper

Following on from a provocative post I wrote a couple of weeks ago on this blog (which was subsequently reblogged by the Times Higher), I was contacted by Paul Crowther who sent me a copy of the slides used by Peter Main of the Institute of Physics in a talk in May 2015 on the subject of Widening Participation in Physics. With Peter Main’s permission I’m sharing those slides here as a service to the Physics community. There’s a lot of interesting information in these slides, which I think many UK physicists would be interested in.

Have we reached Peak Physics?

Posted in Education, The Universe and Stuff with tags , , , , on August 17, 2015 by telescoper

One of the interesting bits of news I picked up concerning last week’s A-level results is a piece from the Institute of Physics about the number of students taking A-level physics. The opening paragraph reads:

Although there was an overall rise of 2% in the number of A-level entries, the number taking physics fell to 36,287 compared with 36,701 last year – the first time numbers have fallen since 2006. The number of girls taking physics rose by 0.5%, however.

The decline is slight, of course, and it’s obviously too early to decide whether we’ve reached Peak Physics or not. It remains the case however that Physics departments in UK universities are competing for a very small pool of students with A-levels in that discipline. With some universities, e.g. Newcastle, opening up physics programmes that they had previously closed, competition  is going to be intense to recruit students across the sector unless the pool of qualified applicants increases substantially.

The article goes on to speculate that students may be put off doing physics by the perception that it is harder than other subjects. It may even be that some schools – mindful of the dreaded league tables – are deliberately discouraging all but the brightest pupils from studying physics in case their precious league table position is affected.

That’s not a line I wish to pursue here, but I will take the opportunity to rehearse an argument that I have made on this blog before. The idea is one that joins two threads of discussion that have appeared on a number of occasions on this blog. The first is that, despite strenuous efforts by many parties, the fraction of female students taking A-level Physics has flat-lined at 20% for over a decade. This is the reason why the proportion of female physics students at university is the same, i.e. 20%. In short, the problem lies within our school system. This year’s modest increase doesn’t change the picture significantly.

The second line of argument is that A-level Physics is simply not a useful preparation for a Physics degree anyway because it does not develop the sort of problem-solving skills, or the ability to express physical concepts in mathematical language, on both of abilities which university physics depends. Most physics admissions tutors that I know care much more about the performance of students at A-level Mathematics than Physics when it comes to selecting “near misses” during clearing, for example.

Hitherto, most of the effort that has been expended on the first problem has been directed at persuading more girls to do Physics A-level. Since all universities require a Physics A-level for entry into a degree programme, this makes sense but it has not been successful.

I now believe that the only practical way to improve the gender balance on university physics course is to drop the requirement that applicants have A-level Physics entirely and only insist on Mathematics (which has a much more even gender mix at entry). I do not believe that this would require many changes to course content but I do believe it would circumvent the barriers that our current school system places in the way of aspiring female physicists. Not all UK universities seem very interested in widening participation, but those that are should seriously consider this approach.

I am grateful to fellow astronomer Jonathan Pritchard for pointing out to me that a similar point has been made to drop A-level Physics as an entry requirement to  Civil Engineering degrees, which have a similar problem with gender bias.

Physics Graduation, according to Private Eye

Posted in Education, The Universe and Stuff with tags , , on August 11, 2015 by telescoper

Very busy day today, what with one thing and another (and another, and another…) so in lieu of a proper post I thought I’d just post this rather excellent cartoon I saw in last week’s Private Eye

Physics Graduation


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