# Extended Project

1. Aug 29, 2011

### FeDeX_LaTeX

Hello,

Next year I will possibly be starting something called an EPQ (Extended Project) where you pick a topic of interest and research it and write up a report of a minimum of 5000 words, including documented evidence and logs of each experiment done. It can be on any topic, from clay animation to the pyramids of Egypt.

I want to do something physics-related that has a lot of mathematics in it. The EPQ is effective in the UK when applying to universities as admissions tutors identify it as showing devotion and passion for a subject. I thought about doing one entirely on prime numbers, but I don't think I would be able to complete an entire 5000+ word report on that.

I was thinking that perhaps I could do an extension of the experiment that I did in this thread. I think I still have all the raw data for this coursework (index of refraction vs. wavelength). I liked this experiment because it was very easy to do practically and the relationship between refractive index and wavelength was very clear.

I would be open to doing an entirely different experiment, however. I don't have access to many resources; in my school they have power packs, ray boxes, tiny solar panels, magnets, glass blocks, etc. the standard things that a science department in a school would usually have. I don't have a full list, unfortunately.

If I have to buy materials they have to be fairly cheap and safe/easy to use (no building flamethrowers or firing guns). Some people have already suggested the double-slit experiment, the Doppler effect, etc. but I am not sure what to do. I don't really like 'fiddly' experiments where it takes a long time to set things up and it's likely I could get confusing or lots of anomalous results. I like particle physics but I'm not sure what kind of experiment I could do with that. I could do a mechanics-based project but I'm a bit unsure about this because I don't know a lot of mechanics. I've done some mechanics units at A-level already (stuff on moments, particle collisions, inclined planes, SHM, gravitation, projectile motion, centres of mass, work/energy/power, etc), but I don't know if I know enough to start a decent project that can be interesting as well as get me a top grade.

Does anyone have any ideas on what I could do? The work must be mostly theoretical and fairly interesting (enough for me to be able to work on for an entire year). I may be able to find the help of some friends to aid me with any experiments (if they're doing EPQs too, or if they're just willing to help). I have a basic knowledge of calculus topics (integration, differentiation, partial derivatives, calculating div/curl/grad).

Someone on another forum suggested I do an experiment on Special Relativity but I'm not sure how I would do this. I've started learning about the Lorentz transformation but that's about it. I am currently at the end of Year 11 (10th grade in US?) going into Year 12, and would be very appreciative of your ideas.

I also heard someone jokingly say on another forum (not in response to me) to do it about string theory. My understanding of string theory is not too great (in terms of the mathematics I know about it, pretty much nothing I think). I would like a report that involves a great deal of mathematics, and, though string theory is very mathematical, I don't yet possess the mathematical knowledge to make a decent report on it without it turning into a history essay or something.

Someone also said to do something cosmological where I look at secondary data from a range of sources and look for patterns, but I don't know where to start. It's not my strongest part of physics but I do like it. Any ideas?

The most recent maths/physics-related topic I've learned about are Fourier transforms/series. I know how to do some of the mathematics involving those topics but my physical understanding of them is not so great. What kind of experiment could I do involving them? Will it get too hard for me?

2. Aug 29, 2011

### A.T.

Well it depends if numbers count as words:

Report done.

3. Aug 29, 2011

### FeDeX_LaTeX

But I don't think I will get a very good grade with that...

4. Aug 29, 2011

### Dadface

Hi Fedex LaTex.To help you make a choice spend some time looking at the everyday things around you and try to see how physics principles can be applied to such things.I know a young lady who did her Nuffield A level physics project on absorbancy and amongst other things she measured how quickly water rises by capillary action up strips of paper towel.The most complicated piece of equipment she used was a clock.

5. Aug 29, 2011

### Studiot

A couple of suggestions

Get hold of the Open University book 'Electronic Materials' by Braithwaite and Weaver.

There are several idea along with lots of guidance in there.
The best is likely the chapter on transducers and in particular PZT (peizo electric transducers)

If you don't want anything to do with electricity you could try acoustics, either from an architectural (room acoustics) point of view or from a materials point of view (sound absorbancy etc)

Sticking with acoustics and thinking of your spectral analysis (Fourier) thoughts you could analyse sounds say from various combustion engines. Can you determine the number of cylinders from this?

Fluid mechanics also provides possible projects. I did one on smoke rings for my Nuffield 'A' level project bacK in the 1960s, although producing a machine to blow smoke rings was not easy.

In some areas local employers will support such projects financially or with (scrap) parts.

go well

6. Aug 29, 2011

### FeDeX_LaTeX

Thanks for the replies. I've been looking around and I still don't know what to do an experiment on. I only have a couple of weeks to decide and I was thinking of just doing refractive indices again, but that seems like cheating in a way, to do the same project but for a different course. It's unlikely they'd find out (different years, different examination board), but it might be risky to take that chance. I could do something similar with light I guess.

How would I analyse the sounds from combustion engines using Fourier series?

As for fluid dynamics -- I'd never thought about that before. I just read something about the Navier-Stokes equations; I saw this

$$\rho \frac{D\mathbf{v}}{Dt} = \nabla \cdot \mathbb{P} + \rho\mathbf{f}$$

but I've never worked with tensors before or 'substantive derivatives'. My understanding is that the equations state that changes in momentum of fluid particles are dependent only on the internal pressure and 'viscous forces'. I'm not sure that's a good idea though because I don't know if I can work with that equation (the tensor and that 'substantive derivative' D/Dt).

7. Aug 30, 2011

### Oldfart

I think it would be fun to measure the speed of light, having invented a way to do this with junkyard parts.

8. Aug 30, 2011

### FeDeX_LaTeX

That's an interesting idea; what would I be investigating though?

I think you can measure the speed of light if you put something in the microwave without the spinning plate, then measure the wavelength. The frequency is usually on the back.

9. Aug 30, 2011

### Oldfart

A historical angle on this would be interesting, many possibilities. For one of many, the year is 1000 AD, the Pope is angry about your scientific teachings, says OK, if you are so smart, prove it to me, show me within a year the velocity of light, or you will die. Meanwhile, during this year, I will support your study of this as you request. Now what?

As a much deeper project, determine the speed of gravity.

10. Aug 30, 2011

### Dadface

Fedex if you haven't already done so go to the web sites of your own and other exam boards(AQA Edexcel etc) and read up on the relevant information about the EPQ.Look at things such as examplar materials and marking criteria.Remember that the final choice of project will be made jointly with your supervisor and that anything requiring too many, or expensive extra resources is likely to be turned down.

11. Aug 30, 2011

### jbar18

I'm guessing you're from Britain, I am too, and I tried to do an extended project on a physics topic. I gave up after a couple of months due to the nature of the qualification (the actual content of the project doesn't count for much of the grade, it's all about citing sources and boring stuff like that). Plus you have to have to have some sort of controversial title, so that you can argue it from both sides and all the rest of it (I didn't want to it to turn into a history essay either, but you have to discuss the reliability of sources and argue both sides etc. to get any sort of decent grade). I found it particularly tiresome trying to come up with any title that related to the topics that I was thinking of that could be written in this way.

I originally was going to do it on chaos theory, but it wasn't particularly appropriate for the project and it included quite a lot of maths that I couldn't handle at the time. If you are determined/forced to do it, the best thing I could think of that was physics related was whether or not determinism is likely to be true. This is because determinism is quite an intuitive and logical idea (that if you could theoretically have enough information about anything you could predict it's future exactly), but things like Bell's theorem from quantum mechanics imply that this might not be the case. This is the most appropriate thing for the project that I could think of involving physics, you could pad it out with quite a lot about chaos theory and quantum theory etc. without any particularly difficult maths. If you want to find out more about it then there's plenty of it on these forums.

Like I said though, it's not much about what you actually write if I remember correctly. If you are planning to go to university, which seems likely if you are taking the EPQ, you may well get people telling you that it's a good qualification to have(as they did with me), all I can say to that is that currently no university which asks for grades accepts the EPQ as one of the grades, currently I believe it only counts for UCAS points. And if you do get weary of it (like me and many others taking the class did) and consider dropping it, make sure you don't write about it in your personal statement or anything like that, just in case. Lots of people I know wrote about what they were doing for the EPQ in their statement, and by the time they'd gotten an interview they had quit and found themselves in a bit of a pickle when the universities asked about it in the interview.

Sorry for the wall of text and all my personal bias against the qualification, I just had lots of teachers breathing down my neck for a long time trying to get me to do what I considered totally useless. The time I would've spent on the project ended up going into my other subjects and into researching things that I actually found interesting at my own pace. But like I said, if you are going to do it on something physics based, I would suggest determinism, it ticks all the boxes for what the project has to be about as I remember. And if you really wanted to you could slip a bit of maths in there without it getting too heavy.

Good luck :)

Last edited: Aug 30, 2011
12. Aug 30, 2011

### FeDeX_LaTeX

Hmm... there would be a lot to write about for this, I suppose. Where did you get the Pope story from?

I could determine the speed of gravity... but what I'm looking for is something more like "how does ____ affect ____"?

I looked at some exemplars -- a lot of them did indeed include a lot of citing of material. I couldn't find any maths or physics EPQ exemplars, unfortunately... mostly ones based on essay-type subjects (history, government and politics, sociology, etc).

13. Aug 30, 2011

### FeDeX_LaTeX

Thanks, this was a really helpful post. I have my interview tomorrow, so about 12 hours to decide; with sleep, that's about 2 hours. It seems as though a lot of people say that the EPQ is not what I think it would be; that it's about citing sources and whatnot.

You mentioned chaos theory and determinism; these do seem like very interesting topics, but I don't know what kind of mathematics I could use with them. I'm a bit concerned about choosing these because I don't know any QM (well, nothing really advanced). What kind of mathematics was involved in chaos theory? I can't find much on it... also, I seem to get the impression that the focus is more on an essay/argument-style piece rather than an actual investigation. Does this mean that it can't have the same format as, say, a scientific paper, with lots of heavy mathematics involved? Does it actually have to be accessible to every audience?

What kind of controversial title do you have to choose? Is it one of those titles that is usually a question?

Determinism does sound very interesting, but I'd really like to have a fair bit of mathematics in there. My worry is that I don't know if I can understand that mathematics in at most a couple months time.

Thanks for telling me about the personal statement. If I hadn't known any better I might have included it.

Thanks for your post, it was very helpful.

14. Aug 30, 2011

### Oldfart

I made up the Pope story.

If you can determine the speed of gravity, that should be good for a Nobel and a full scholorship to Oxford...

15. Aug 30, 2011

### jbar18

I'm glad to help. The more accessible it is the better, since it doesn't necessarily get marked by a mathematician or a physicist (unless you know otherwise).

It does pretty much have to be a title in the form of a question, and it does pretty much have to be an essay styled argument. You pretty much just need a project that will have more than one opinion on the matter, so that you can explain both sides and then say where you stand and why.

You sound like you are itching to get maths heavily involved, and while you wouldn't have to include it in determinism, you easily could. You would probably want to talk about Bell's theorem and the uncertainty principle, when you combine these things with chaos theory (just systems being very sensitive to starting conditions) you get a pretty convincing argument against determinism. But then at the same time, it can't be ruled out, so there's your controversy.

As far as the maths of chaos theory, I remember taking one look at some of the actual maths and I never went back. It's quite unnecessarily complex at this sort of level for what can be summarised very easily with words. If you are determined to involve maths, you could possible just find some of the chaotic functions and explain how they work, but I get the feeling most of your maths will probably come from talking about QM. Even if you do include a hefty portion of maths, the project will still be mainly you explaining the arguments and justifying your point of view. And unfortunately, at least an equivalent amount of the project will be about citing sources.

As for the QM, most of your project will probably involve explaining key concepts in a basic and non-technical way that gets the basic point across, and how it all relates to your overall question. If you do some research into the relevant topics that shouldn't be too difficult.

If you are worried about getting the maths, it can seem pretty daunting at first, but from the sound of it you would be more than capable of doing some of the basic maths in QM, the difficulty is more getting used to the notation and what it all means. There are some really good podcasts on iTunes of lectures from oxford on quantum mechanics to break you in, and the guy explains it all pretty clearly. I would suggest you read up a little on some QM concepts first just to get used to it. Some things to get familiar with on a conceptual level would be the uncertainty principle, Bell's theorem, local and non-local (hidden) variables, the EPR thought experiment, and some other bits and bobs like entanglement, tunneling, and particle-wave duality, just for laughs (if you aren't already familiar with this stuff). ZapperZ and DrChinese on these forums have links to pages which explain in a very clear way the uncertainty principle and Bell's inequality respectively, in particular ZapperZ highlights a few of the misconceptions about the uncertainty principle which don't seem to be made clear anywhere else. Both of them show how the theories were derived and their implications.

I'm not really sure exactly how you could get the maths in in a way that would be relevant, since determinism is more a philosophical debate. My only suggestion right now would be to compile all of the arguments for and against, the arguments for determinism will be more based in logic while the arguments against will be based more in science and actual evidence, and you should be able to slip in a bit of maths there when you are talking about the actual experiments and so on. You will be able to find most of what you need on these forums and wikipedia to be honest, but for the purpose of the project you will have to find other sources where you can say you got the information from as you need a diverse range of sources for a good grade :P (silly, isn't it?)

Good luck, again.

Last edited: Aug 30, 2011
16. Aug 30, 2011

### Pythagorean

chaotic systems are generally a system of deterministic ordinary differential equations (or iterative mapping equations).

They can be relatively simple systems, like the Lorenz system:
http://en.wikipedia.org/wiki/Lorenz_attractor

or they can be complicated, like a network of Hodgkin Huxley neurons (each neuron adds four dimensions to the system).

The test to see whether a system is chaotic is to measure it's lyapunov exponent, to see if two initial conditions very close to each other (infinitesimally close, ideally) will diverge wildly away from each other in their future.

http://en.wikipedia.org/wiki/Lyapunov_exponent

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