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I've spent most of today thinking Google's image-of-the-day is a wicket, but have just realized it is in honour of Alessandro Volta.



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In January I had a go at the 2014 Scholarship Physics Exam, as I've done for the last couple of years. Sam Hight from the PhysicsLounge came along to help (or was it laugh?) The idea of this collaboration is that I get filmed attempting to do the Scholarship paper for the first time. This means, unlike some of the beautifully explained answers you can find on YouTube, you get my thoughts as I think about the question and how to answer it. Our hope is that this captures some of the underlying thinking behind the answers - e.g. how do you know you're supposed to start this way rather than that way? What are the key bits of information that I recognize are going to be important - and why do I recognize them as such? So the videos (to be put up on PhysicsLounge) will demonstrate how I go about solving a physics problem (or, in some cases, making a mess of a physics problem), rather than providing model answers, which you can find elsewhere. We hope this is helpful. 

One of the questions for 2014 concerned friction. This is a slippery little concept. Make that a sticky little concept. We all have a good idea of what it is and does, but how do you characterize it? It's not completely straightforward, but a very common model is captured by the equation f=mu N, where f is the frictional force on an object (e.g. my coffee mug on my desk), N is the normal force on the object due to whatever its resting on, and mu (a greek letter), is a proportionality constant called the coefficient of friction. 

What we see here is that if the normal force increases, so does the frictional force, in proportion to the normal force. In the case of my coffee mug on a flat desk*, that means that if I increase the weight of the mug by putting coffee in it, the normal force of the desk holding it up against gravity will also increase, and so will the frictional force, in proportion.

Or, at least, that's true if the cup is moving. Here we can be more specific and say that the constant mu is called 'the coefficient of kinetic friction': kinetic implying movement.  But what happens when the cup is stationary? Here it gets a bit harder. The equation f=mu N gets modified a bit: f < mu N. In other words, the maximum frictional force on a static object is mu N. Now mu is the 'coefficient of static friction'. Another way of looking at that is that if the frictional force required to keep an object stationary is bigger than mu N, then the object will not remain stationary. So in a static problem (nothing moving) this equation actually doesn't help you at all. If I tip my desk up so that it slopes, but not enough for my coffee mug to slide downwards, the magnitude force of friction acting on the mug due to the desk is determined by the component of gravity down the slope. The greater the slope, the greater the frictional force. If I keep tipping up the desk, eventually, the frictional force needed to hold the cup there exceeds mu N, and off slides the cup. 

What this means is that we when faced with friction questions, we do have to think about whether we have a static or kinetic case. Watch the videos (Q4) you'll see how I forget this fact (I blame it on a poorly written question - that's my excuse anyway!). 


*N.B. I have just picked up a new pair of glasses, and consequently previously flat surfaces such as my desk have now become curved, and gravity fails to act downwards. I expect this local anomoly to sort itself out over the weekend. 

P.S. 17 February 2015. Sam now has the videos uploaded on physicslounge  

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Not so long ago, a tennis ball appeared in our garden. It's a rather distinctive red one. It doesn't belong to us. It was lying close by to the (low) fence between us and our neighbour, so I just chucked it back. 

Next morning, it was there again. I threw it back.

And, more or less immediately, it was back with us. Evidently, it didn't belong to next door. They were working on the assumption it belonged to us. The next-likely suspect was the house at the back of us, which has some rather energetic children. Over went the ball into their garden. 

Next day it was back with us. Not their ball, either. Suddenly, this ball has become highly mobile. It flits from garden to garden, and doesn't appear to be finding a home anywhere? Where did it come from?

I can't help thinking that this is a good analogy with conduction of electrons in n-type semiconductors. Although silicon underlies so much of modern electronics, it comes as a real surprise to many students to learn that silicon is really quite a lousy electrical conductor. That's unsurprising when you look at its structure - the silicon atoms are locked in a lattice, with each atom bonded by strong covalent bonds to four other atoms. There are no free electrons - all the outermost electrons that would contribute to conduction are tightly bound in chemical bonds. Without free, or losely bound, electrons, there's not going to be much electrical conduction. 

So how come silicon devices are at the heart of modern electronics? The key here (in the case of n-type silicon) is that extra electrons have been put into the lattice. This is done by adding impurity atoms with five, not four, electrons in their outer shell (e.g. phosphorus). These electrons aren't involved with bonding, and become extremely mobile, because none of the silicon atoms finds it favourable to take them on. They flit from atom to atom, finding a natural home nowhere, as does our tennis ball. Unlike a tennis ball, however, electrons are charged particles. Apply an electric field, and they have a purpose, and we suddenly have movement of electrical charge (which is simply what an electrical current is).

There's a second way to make silicon conduct, and that's the reverse. Rather than adding in electrons, we take them away. How does that work? Introduce now an atom into the lattice that only has three outer-shell electrons (e.g. boron). It is likely to grab one from a neighbour, to allow itself to make four covalent bonds. But now its neighbour is devoid of an electron. It will grab one from one of its neighbours. And so on. Now the 'lack of an electron', or 'hole', as its known in semiconductor physics, is what is mobile. Since electrons are positively charged, the lack of an electron (i.e., a hole) is positively charged. Apply an electric field and the hole moves - and we have electrical current again. This is 'p-type' silicon ('p' for positive, since conduction is through positively charged holes; contrast 'n' for negative, where conduction is through movement of negatively charged electrons). 

In our tennis ball analogy, the p-type lattice corresponds to a less desirable neighbourhood - someone on discovering that one of their tennis balls is missing makes up a complete set by sneaking round into the next-door garden to steal one, thus transferring the problem elsewhere. 

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"Doctor, Doctor, I keep seeing spots before my eyes"

"Have you ever seen an optician?"

"No, just spots".

The concept of seeing an optician floating across my field of view is a scary one indeed. However, the concept of seeing spots doing the same is one I'm coming to terms with. 

I had a talk to an opthamologist about this last week, as part of an eye check-up. He was very good, I have to say, and we discussed in detail some optical physics, particularly with regard to the astigmatism in my right eye (and why no pair of glasses ever seems quite right).  He also reassured me that seeing floaters is nothing, in itself, to be worried about. It's basically a sign of getting old. How nice. He did though talk about signs of a detached retina to look out for (pun intented) - and did some more extensive than usual examination. 

So what are those floaty things I see? To use a technical biological phrase, they are small lumps of rubbish that are floating around in the vitreous humour of the eye. They are real things - not an illusion - although I don't 'see' them in the conventional manner that I would see other objects. 

The eye is there to look at things outside it. Its lens focuses light from objects onto the retina, where light sensitive cells convert the image to electrical signals that are interpreted by the brain. But given that the floaters are actually between the lens and the eye, how am I seeing them?

There are a couple of phenomena going on. First of all, a floater can cast a small shadow onto the retina. You can see this effect by using a lens to put an image of something (e.g. the scene outside) onto a piece of card, and then put something between the lens and the image. Some of the light can't get to the card, and so part of the image is shadowed. The appearence of the shadow depends on how close the object is to the card - if its right by the lens there will be very little effect - but if close to the card there'll be a tight, well-defiined shadow. My experience is that these spots are definitely most noticable in bright conditions - presumably because the shadows on the retina then appear in much greater contrast than under dull conditions. 

Secondly, however, they can bend the light. Their refractive index will be different from that of the vitreous humour, and therefore when a light ray hits a floater it will bend, a little. The consequence is a defocusing of a little bit of the image, which wil be visible. If the floater stayed still, it would probably barely be noticable, but when it moves, the little bit of bluriness moves with it, and the brain picks up the movement rather effectively. 

The most interesting thing to me is that it just isn't possible to look at these things. When I try, my eyes move, and consequently these bits of rubbish flit out of view. Rather like quantum phenomena, you can't observe them without changing where they are and where they are moving to.  




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Alison has drawn my attention to this video. It demonstrates vibrational modes of a square plate by using sand. At certain frequencies, there are well defined modes of oscillation, in which parts of the plate 'nodal lines' are stationary. The sand will find its way to these parts and trace out some lovely pictures. 

Vibrational modes are often illustrated through waves on a guitar string. Here, the string is held stationary at both ends, but is free to vibrate elsewhere. There is a fundamental frequency of oscillation, where the distance between the ends of the string is half of a wavelength (this ensures the displacement of both ends of the string is zero since they are clamped).  Since wavelength is related to frequency (frequency = speed/wavelength) that means if the wavelength is 2 L where L is the distance between the ends of the string, we have frequency = speed/2L.  

But that's not the only possible mode. Another one would have L equal to a whole wavelength (equals two half wavelengths). Or one-and-a-half wavelengths (equals three half-wavelengths.) This gives us, rather neatly, frequency = n speed/2L, where n is an integer. We see that our 'harmonics' are just integer multiples of the fundamental frequency. Rather neat.

However, if you look at the frequencies given in the video, they appear to be all over the place. I challenge you to pull out the relationships between these (I've tried). There are a few reasons why the case shown on the video is considerably more complicated than the waves on the string. 

1. The boundary conditions. The edges of the plate aren't clamped in place. This makes it less straightforward to define the modes geometrically. 

2. The plate is square, giving rise to 'degeneracy' in the modes. This term refers to two or more distinct modes having the same frequency. You can see it rather well with the 4129 Hz mode. Basically, there are horizontal stripes shown. But equally, with the same frequency, you could get vertical stripes. Why don't the two occur together? They do. You can see the effect of having a little bit of vertical stripe most clearly at the far end of the plate, where the pattern becomes more square-like. Also, with a square, you can get two completely different types of mode with the same frequency. This occurs because what matters are the sums squares of pairs of integers. Broadly speaking (at least for a square clamped on the edges, which I must point out this ISN"T), our modes follow the relationship:

f = C sqrt(n^2 + m^2)

where C is a constant, 'sqrt' means square-root, and n^2 is n-squared. So, for example, not only is 50 equal to 5-squared plus 5-squared, it is also equal to 1-squared plus 7-squared (or 7-squared plus 1-squared). This gives us three  modes all competing to appear at exactly the same time. What happens then isn't easy to tell. 

3. Non-linear effects. This a physicist's code-word for 'it's all too difficult'. That's not quite true - arguably most of the interesting physics research happening in the world is looking at non-linear effects. What this really means is that, if A and B are both solutions of a problem, then some combination of A and B is NOT a solution. A lot of physics IS linear - Maxwell's equations in a vacuum is a good example - but a whole lot isn't. With waves, the speed of the wave usually depends on frequency (i.e. is not constant) which means we lose the nice, integer-multiple relationship of our waves-on-a-string mode.

So, enjoy the video for what it is, and don't try to analyze it TOO closely. 



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I'm sure many readers will know that one of the hats I wear is the treasurer of the New Zealand Institute of Physics. NZIP is the professional organization for physicists within New Zealand. Its aim is to promote the interests of physics and physicists, at all levels, within the country. In addition to counting the beans, the role comes with a position on the council, and therefore I have a significant responsibility for looking after the institution.

With that in mind, I had the dubious pleasure of travelling to Wellington shortly before Christmas to represent NZIP at a meeting of council members of New Zealands 'science' societies at the Royal Society of New Zealand. I use 'science' in a very broad context here.  It was one of those ten-degrees-with-horizontal-rain summer days in the captial*, though that didn't matter too much as the day was spent inside RSNZ's rather nice new building. The day was actually very useful, as we talked through some of the common issues facing our science societies. 

One clear issue that many societies are facing (NZIP included) is dwindling membership. With dwindling membership comes dwindling income, making it harder for the society to do useful things. A great many socieities can't afford paid staff and so run on volunteers who necessarily need to prioritize their time elsewere.  Dwindling income basically means loss of services that can be offered to members, such as travel grants, teaching materials, careers advice, prizes and so forth.  It's a vicious cycle. 

But it's not all bleak, so long as we are prepared to accept the message that is coming from the research in this area. A recent report from the Australasian Society of Association Executives [which I'm afraid I can't find openly on their website, so no link I'm afraid - you might have to pay membership fees for it ;-)  ] talks about the changing face of membership. The report is rather pessimistically and not entirely accurately  titled 'Membership is Dead'. It talks about the difference in expectations that a 'Generation Y' person has from the Baby-boomer (I so hate those stereotyping terms - but the report uses them). What particularly got my attention is that the very things that Generation Y values [clearly defined value to them, responsiveness (which means hours or minutes or instant, not days or weeks), innovations, accessibility] are things that baby-boomer-dominated councils see as low priority, because they themselves don't value them. In other words, the expectiations of Generation Y and Council members when it comes to what a science society is and does are vastly different. A Baby-boomer may happily pay their membership fees year-on-year because they feel it's part of their duty as a professional to belong - a Y-er is less likely to take that generous line. If they can't see the value to them, they don't cough up. (For the record, I'm an X-er). It encourages institutions to work hard and getting younger people onto councils, by actively targeting undergraduate students, for example by giving them opportunities to assist with conference organization, website development and maintenance, tweeting on behalf of the society, etc. Then step back and let the younger people run it in a way that the younger people (=future members) want it run. 

So membership isn't actually dead. Instead, we just need to accept that 'membership' is going to mean something different to our younger people and adapt to account for it. Because, if we don't, our societies will dwindle away, to be replaced by something rather different. 

*Maybe I'm a bit harsh here. On our return from the South Island after our Christmas Holiday, the ferry Aratere (with full a complement of screws (propellors) and a fully-functional electrical system) took us across a flat Cook Strait and into a beautifully calm and sun-kissed Wellington harbour. As they say, you can't beat Wellington on a fine day...



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In the last couple of weeks, I've been using Hermite Polynomials in my work. I won't go into what they are (look them up here if you like) suffice to say that they are one of many contributions to mathematics from Charles Hermite (1822-1901), who was himself one of  many french mathematicians whose work has laid a foundation for much of modern theoretical physics. A physicist would generally know these polynomials (when modulated by a gaussian function ) as the solutions to the 1-dimensional quantum harmonic oscillator, although that's not why I'm using them. 

The 1-dimensional quantum harmonic oscillator problem is a textbook problem that gets inflicted on generations of students. I remembering suffering the algebra that went with it. At the University of Waikato, we save our second year students the algebra by just talking about the solutions, but then spring it on them in third year. For those who like that kind of thing, it's an interesting analysis, but for those that don't, it really is quite horrible. 

Perhaps that is what motivated Paul Dirac to come up with (in my opinion) a really elegant complementary approach to solving the 1-dimensional quantum harmonic oscillator problem. While his approach is easily found in text-books, what I haven't been able to track down is a description of how he came up with it. The same seems to be true of many of the analyses that get wheeled out to students. While they look clean and tidy when presented now, I'm left with the question "How did they come up with this?". That tends to be overlooked in favour of the end product. Did Dirac spend weeks pondering over this, thinking "there must be a better approach - the symmetry between p and x in this equation should surely be exploitable somehow...", was it a sudden revelation, did he try twenty different approaches till something worked, or what? My text books don't say. 

What Dirac did was to reformulate the problem in terms of 'raising' and 'lowering' operators. He realized the problem as a ladder of energy-levels, and showed rather elegantly that these energy levels were equally spaced. Moreover, some rather neat operators, that he defined, could move a quantum state 'up' or 'down' the ladder. That's a very creative way of looking at the problem, and has been taken much further since then. For example, when analyzing problems with many electrons (which generally means just about anything electronic) we can now formulate the problem in terms of operators that create and destroy electrons. Whether electrons really are being created and destroyed is a moot point, but the formulation is a neat one that helps us to analyze what is going on. Theoretical physicists consider it a really useful 'tool' of the trade, even though the history behind its construction tends to be overlooked when we teach it. 

So what is the point of me telling you this? Well, it's about teaching. Just how do you teach creativity, especially in something that is, on the face of it, as tedious as physics. Physics isn't actually tedious (if it were I wouldn't be sitting here writing this) but we do tend to make it unnecessarily so at times. I wonder whether that's because that's the easiest path to take for undergraduate teaching. At PhD level and beyond, there's some really creative research going on, but do our undergraduates really see this? Likewise, from what I've seen at school science fairs, there's some great creativity at primary and intermediate school level, but that then vanishes late in secondary school in favour of 'content'. Somehow, we tend to smother out creativity and elegance in favour of 'something-that-gets-the-job-done.'  But truly great physicists, Dirac included, have never 'just-got-the-job-done'. 

Open-ended projects are a way to go (and we manage to some extent to do this with our engineering students), but, as many readers know, we run into trouble with time, the need to prepare students for exams, fitting in with timetabling requirements, and so forth. The problem may go much deeper than we think - indeed, does the whole secondary and tertiary education structure smother-out creativity from students (at least in physics)? 

And with that, have a creative Christmas, and Happy New Year to you all!  I'll be heading southward next week to the Canterbury hills - a part of the country I haven't been to before. 



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I've been reading a paper by Majorie Darrah and others (full reference below) on the use of 'virtual labs' in Undergraduate Physics. At Waikato (along with lots of other universities) our first year physics students carry out laboratory sessions to help them learn physics concepts and practical skills. If you are someone who has run a first-year laboratory class, you'll be well aware that these things are costly and time-consuming. If they're not done well, they become an expensive way of wasting everyone's time. 

Recently, there's been a lot of work on 'virtual' laboratories. These are laboratory sessions that aren't 'hands-on', but simulated on a computer. There are some pretty sophisticated ones out there. At our last NZ Institute of Physics conference, David Sokoloff, one of our keynote speakers, talked about some of these. The computer software allows a student to do pretty-much whatever would be done in a laboratory, but without the university having to purchase, set-up and maintain the expensive equipment. (And, from the student's perspective, they are not constrained as to when they carry out the 'lab'). 

So, do they work? I don't mean does the software work, but does the virtual lab give the same benefit to the student as undertaking a real lab. In other words, do the students achieve the same learning outcomes? To test this, Darrah and her colleagues worked with 224 students at two universities. They were put into three groups - one group did the traditional hands-on labs in a laboratory, one group did the hands-on labs AND the virtual labs, and the third group did just the virtual labs. Their learning was tested with a quiz after the lab , an assessment of the student's written lab report, and  tests. 

So what was the result? They found no difference between the groups. One of the universities conveniently carried out a test assessment both before and after the lab sessions and found that all groups improved as a result of the labs, be they real or virtual. That is certainly an encouraging result for the likes of Sokoloff, and those budget-pressed universities with lots of students to push through first year university physics. The problem of doing laboratory work has been one of the reasons why MOOCs for science and engineering have been fairly slow to get going, However, it may be reasonable to do away with this, if good virtual labs can be prodcued. 

But, there is a but. It's a big but in my opinion, and one that, surprisingly, the authors fail to comment on. Their post-lab assessment of learning was based on a written test of the physics theory concepts that were covered in the lab. In other words, they were testing how well the laboratory (real or virtual) supplemented the teaching of physics theory done in lectures and elsewhere. What they weren't testing were practical laboratory skills (e.g. how to wire up a circuit, track down problems with the apparatus, carry out experiments in a controlled manner, etc.) These are all important skills for a physicist. If universities as a whole shifted towards virutal labs in first year, where does that leave students in learning these other skills? The paper doesn't comment. What I'd like to see is the same study done, but the students afterwards given a laboratory test - put them in a real lab and get them to do a real experiment, assessing some practical learning outcomes. Then what happens? It would be nice to try it out - but it will take a bit of organizing (not least acquiring some virtual labs and convincing my colleagues that it is a good idea.) So don't expect a response from me soon.

Darrah, M., Humbert, R., Finstein, J. Simon, M. & Hopkins, J. (2014). Are virtual labs as effective as hands-on labs for undergraduate physics? A comparitive study at two major universities. Journal of Science Education Technology 23:803-814. doi 10.1007/s10956-014-9513-9 


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Benjamin has recently acquired a 'new' book from Grandma and Grandad: Mr Archimedes' Bath (by Pamela Allen - here's the amazon link - the reviews are as interesting as the content). The story-line is reasonable guessable from the title. Mr Achimedes puts water into his bath, gets in, and the water overflows. What's going on? So we've been doing some copycat experiments - not by filling the bath right up and having it slosh all over the bathroom floor (Waipa District Council - you can rest easy about water usage)  but filling up rather more sensible-sized containers and dropping objects in.

Archimedes principle is actually a little more involved than simply saying that putting an object in the water will raise the water level. It says that the weight of water displaced is equal to the force of buoyancy acting on the object.  This picture summarizes it. That is, if an object of 2 kg floats, then 2 kg of water will be displaced. If an object is unable to displace enough water for this to be the case, it will sink. That still should be pretty easy to get, especially if you've done some experimenting. However, it can still be the basis of some really hard questions. I had one in my third year  physics exams at Cambridge. In our 'paper 3', as it was called then, the examiners had free reign to ask about ANYTHING that was on the core curriculum from any of our years of study - plus ANYTHING that was considered core knowledge for entry into the degree (which meant basically anything at all you were taught in physics or general science from primary school upwards). This paper was feared like anything - it was basically impossible to revise for*. 

Here is a question then, as I recall it from the exam.

An ice cube contains a coin. The ice completely surrounds the coin. The cube is floating in a container of water.  The cube melts. Does the water level rise, fall, or stay the same? 

Think carefully before answering. 

Now, the icecube melting question is one that is often banded about. A floating icecube will displace its own mass of water (so says Mr Archimedes). When it melts, this water will occupy the 'space' that is displaced by the cube. Consequently, the water level will stay the same. A practical example of this is in the estimation of sea-level rises due to global climate change. When the ice floating on the Arctic Ocean melts, it does not cause a sea-level rise, since it is already displacing its own weight. However, the icecap on Greenland will cause a sea-level rise as it melts, since it is currently not displacing any of the sea (since it is sitting on land.) 

However, that is not the question that is asked. Our icecube has a coin inside it. What difference does it make? Well, the icecube-and-the-coin will still displace its weight of water since it floats. However, when the icecube melts, the coin sinks and no longer displaces the same amount of water as it did when it was frozen into the cube. Therefore the water level falls. That's quite a subtle application of Archimedes principle. After the exam, a group of us sat arguing about it, till we collectively worked out what the right answer was (see - exams can be good learning experiences!). Unfortunately, at this point I realized my answer was wrong. Even still, I managed to get out of the degree with a first-class honours, so I couldn't have done too badly on this exam overall.

*The other question I remember from this paper is 'What is Cherenkov Radiation?' I didn't have a clue what Cherenkov radiation was when I sat the paper - I made up some waffly words and wrote them down and almost certainly received zero for the question.'  Later, one of my friends found a single, incidental sentence in a handout that was given out by our nuclear physics lecturer that identified what it was. That's how nasty this exam was. 

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Today the University of Waikato is hosting a group of local secondary physics teachers. We've had an entertaining morning, with some sharing of ideas. As part of this, Rob Torrens, who teaches our large first-year engineering papers, talked a bit about life as a first-year engineering student. How does the school to university transition work? (or not.)   On a non-technical front, he talked about the need for students to begin to take some responsibility for their own learning. If you fail to submit an assignment, it might be a little while before it's noticed and acted on.  At university there's no 'bell' to tell you that you need to be at your next lecture - there may indeed be no-one even telling you to get out of bed in the morning. It's easy fall off the radar if you're not motivated. 

On a technical front, Rob talked about some of the skills developed at university that are new to many students. Mathematical modelling is one. He used the example of 'mass balance' in an industrial process. If you are drying grain, you put damp grain into your drier and extract dry grain from the end; this is achieved by drawing in dry air from outside, heating it up, passing it over the grain, and expelling the damp air. Mass balance says that mass isn't created or destroyed in the process. But how is that represented for this particular process. There isn't a 'grain-drying mass-balance'  formula in most engineering text books. Students need to work it out for themselves. The mass of what goes in must equal the mass of what goes out, so:

M_grain_in + M_air_in = M_grain_out + M_air_out

We have an equation that we've constructed, just by thinking about the physical principles involved. Throw in some more consideration about the amount of water air can hold (and therefore what M_air_out - M_air_in can be, and we can find out useful things, like how much air we need to draw into the machine for each tonne of grain that goes through it. We've started the process of mathematical modelling. 

This is a skill aligned well with what the Physics Scholarship exam is about - where students need to think carefully through physics concepts before drawing from mathematical equations. 

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