SciBlogs

Units – they just don’t go away Marcus Wilson May 24

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 One thing that’s become really clear to me in teaching physics is that dimensions and units are not straightforward concepts for students. I might hazard the assertion that they are ‘threshold concepts‘ – ones where grasping what they are about transforms you way of thinking. Most people at least half-understand the idea of units – if we measure a length, we can’t say it’s 26.5.  It’s 26.5 what? nanometres? kilometres? light-years? There’s big differences between them. 

There’s also this mathematical conundrum to through out which illustrates the idea of dimensions: "I have a cube. What length does the side of the cube need to be in order for its surface area to equal its volume? "

The algebra-happy student will have no problem with this question. If the side of the cube is x, then the area of one face is x^2 (that is, x squared), so the total surface area is 6 x^2 since there are six faces. The volume is obviously x^3 (x cubed).  So we have 6 x^2 = x^3 and we can cancel a factor of x^2 from left and right to give 6 = x, and so there’s our answer. Six. 

Six what?  Nanometres? kilometres? light-years? There’s a big difference. The solution of the conundrum is straightforward. You can never have the surface area equal to the volume (unless you have no cube at all – i.e. x is zero). Surface area and volume are fundamentally different things (dimensions).  In S.I. units, the former would have units metres squared, the latter metres cubed. So the question is ‘wrong’.

This afternoon I was talking with my students about the ‘electron-volt’ unit for energy. There’s clearly some difficulty in grasping this. Literally, it is a volt (which is a measure of energy per unit charge) times the charge on the electron.  The context in which it came up is with contact potentials in solid state physics. If I put a material with work function A, in contact with one of work function  B, then the contact potential is just (A-B)/e, where e is the charge on the electron. Work in electron volt units, eV, and it’s dead straightforward.  For example, if A is 7.0 eV, and B = 5.5 eV, then the contact potential is (7.0 eV – 5.5 eV) / e = 1.5 V.    On the numerator there’s the charge on an electron times a voltage, on the denominator there’s the charge on the electron, and so the charge on an electron cancels and we get a voltage. But many students felt that it couldn’t be that simple – they felt they needed to put in a numerical value for e rather than just cancelling it. 

Units and dimensions are tricky things. 

 

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What does electricity cost? Marcus Wilson May 21

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 I was at a local intermediate school this morning, talking to a group of students about energy. It’s a pretty broad topic, and they were very enthusiastic, meaning I only got through about half of what I wanted, but that’s OK. If it inspires them to go and find things out for themselves, then that’s a positive result.

I talked a little bit about measuring energy, and the unit of the ‘joule’, ‘kilojoule’, ‘kilowatt-hour’ and so on, as well as what power is (the rate of change of energy). At the end I asked the students how much they thought that a ‘unit’ (a kilowatt-hour) of electricity cost. That’s the cost of having a kilowatt of stuff running for one hour.  

Now, I didn’t really think that the students would have much idea. I mean, they aren’t the ones forking out every month for their power bills (ahem! that should be energy bill – remember a 100 W light bulb running for one hour will cost you the same as a 50 W light bulb for two hours – it’s energy that you pay for, not power). Estimates ran from 2 cents a kWh to ten dollars, mostly weighted to the several dollars end of the spectrum. I’m rather glad they’re not in charge of the power companies if they wish to charge that price!  I suggested that they ask their parents to look at an electricity bill (and compare a summer bill with a winter one). 

But I was a little surprised that the two teachers in the room had no idea either (or, if they did, they weren’t going to air it in front of their students). They knew what they paid roughly a month, but not what it cost, for (say) a light bulb for eight hours. One of them said that her parents told her that leaving a light bulb on for a few hours was equivalent to her week’s pocket-money (probably a good way of getting her to turn it off). I think they were being rather harsh on this one…

An incandescent light bulb, at 100 W (a bright one), will go through 800 W in eight hours (e.g. if you go out for the day). That’s 0.8 kWh, or 0.8 units. At current prices, of around 30 cents a unit (depends on what sort of contract you have of course) that gives about 24 cents cost. Withdrawing a week’s pocket money for this offence is a bit unreasonable! Leaving all the lights of the house on, while you go on holiday for a week, however, is a slightly different story. 

 

 

 

 

 

 

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The bubble raft and lattice defects Marcus Wilson May 16

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 After doing the washing up a few days ago, I returned to the sink to find a raft of bubbles had formed on the surface of the water. All the bubbles were roughly equal size, and they had aligned themselves into a close-packed lattice, as the photo shows. (Sorry about the quality of the photo – the bubbles were small and the light was poor – and I didn’t have a tripod – but I did my best. )

bubble_raft.jpg

 

Look closely, however, and you’ll see some defects on this lattice. If you follow a row of bubbles, you’ll see in places that a row ends abruptly or another one is inserted. This is a ‘dislocation’. Also, you’ll see single point defects (a bubble missing) and grain boundaries – where parts of the raft with different directions of the bubble rows meet.

All these defects are found in real materials – though of course in a real crystal there is a third dimension which complicates things a bit more. For example, there is a ‘screw dislocation‘ that can occur in a 3d lattice which has no analogue in 2d. 

Making a bubble raft is a good way of teaching about crystal structure and crystal defects – the tricky bit is getting all the bubbles about the same size. I’m not sure how it happened in this case, but it was worth grabbing the camera and having a closer look. 

 

 

 

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You know you are having a bad day when… Marcus Wilson May 09

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This morning I turned up to give my solid state physics lecture and I realised I was in the wrong place. I’d gone to the lecture room where the Friday lecture is held, not the Thursday one. The trouble is, I had absolutely no recollection of where the Thursday lecture was. 

Not being a smart-phone owner, I couldn’t go to the online timetable easily and check. After some racking of my brain, I vaguely recalled giving a lecture somewhere in the I,J,K complex on campus. Couldn’t remember exactly where though. I had to walk along the main I,J,K corridor looking in more-or-less every lecture room till I found my students.  

What was impressive was that I still beat half my students to the lecture! 

I’ve turned up at a lecture with the wrong course notes before, and I’ve turned up at the wrong time before (fortunately at 9am when the lecture was 10am, not the other way around), but this was the first time I’d had a complete location failure. 

Am I tired or am I just getting old?

 

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Don’t miss the eclipse (hee hee) Marcus Wilson May 08

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Friday is the last opportunity to view a solar eclipse in New Zealand for a long time (till 2021 – or 2025 if you don’t count anything of a few percent or lower). I say ‘view’, but the reality is that such a smidgen of sun is going to be covered that you’re going to have to look carefully at the right time. And that’s only for us northerners – most  in the South Island are going to miss out. (Details for this eclipse are here). 

For Hamilton, the eclipse hits its maximum coverage (a mere 5%) at 11:49 am. 

But it’s not all bad news – an eclipse famine is followed by an eclipse bonanza – three total and three annular eclipses visible from New Zealand between 2028 and 2045. Worth looking forward to. I’ll be into my seventies for the last one of these. Ouch. 

 

11:51am, Friday 10th May. Just caught a glimpse of the sun in a clear patch between the clouds. Can I detect any ‘nibble’ out of it. Nope. I thought 5% was a bit of an unlikely viewing situation.

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The sleep machine Marcus Wilson May 06

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I came across this paper while doing a bit of reading about the applications of transcranial magnetic stimulation (TMS). A TMS machine applies pulses of magnetic field to the brain. The rapidly-varying magnetic field induces an electric field (Faraday’s law) and this in turn influences neural activity (but just how and where is an open question).  A team of leading sleep researchers (Marcello Massimin, Guilio Tononi and Reto Huber)  has probed the state of the brain using TMS for various states of consciousness. What they found was very interesting. When in deep sleep, a pulse from the TMS machine generates a single slow wave of activity, which has the same form as the naturally occuring slow waves that are a hallmark of deep sleep.

Now, these slow waves are important - they have been linked with memory consolidation. The more slow waves you have when sleeping, the better you are committing things into memory. And artificially-generated slow waves do the job too. 

In other words, the TMS can be viewed as generating artificially enhanced sleep and therefore artificially improved memory. 

But wait, there’s more (as they say). When someone is awake, a TMS pulse doesn’t do anything. But for someone teetering on the edge of sleep, but still not quite in it, a pulse from the machine can be enough to send them over the edge. So here we have a way of pushing someone into sleep more quickly than they’d otherwise get there. A cure for insomnia? Perhaps not – I mean, TMS machines are hardly unobtrusive, but interesting nonetheless. The remaining question is, do we get one for us or the baby?

 

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Big and small Marcus Wilson May 02

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 Here’s a great interactive website by Cary Huang to give you an idea of how big and small things are. Thanks to Greta Dromgool for pointing me towards it.

It covers a whopping 60 orders of magntiude in length – from ten to the power of minus thirty five (the Planck Length) through to 10 to the power of twenty six metres – the size of the universe. Admittedly, there’s a great lot of nothing in the ten orders of magnitude between the neutrino ‘size’ and the Planck length, so one might more reasonably say there’s only 50 orders of magnitude covered.

This shows a couple of interesting (but not necessary greatly meaningful) points.

1. That we ‘live’ in the middle of this range, at about ten to the power zero metres.  (10^0 = 1). Things we experience are broadly on the metre scale. We see things that are millimetres in size, and experience kilometre distances as we travel, which is a range of merely six orders of magnitude, right in the middle of what exists. 

2. That most of what we have in the universe is physics. Yay!   Anything you ‘see’ about ten to the power six metres or larger can broadly be called astronomy / astrophysics. And anything you ‘see’ about ten to the minus ten metres or smaller is also physics. Physics covers the extremes. But it also features in the middle ground – don’t get the idea that this is exclusively the realm of chemistry and biology. 

So, enjoy. Don’t confine yourself just to scrolling, you can click on each object (and there are a lot) for further information.  I warn you, though,  the music gets a bit bugging after a while.

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A bigger splash Marcus Wilson Apr 26

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The crawling baby is now undertaking a series of physics experiments. His favourite is the investigation of vibrational modes on biscuit tins and their coupling to longitudinal waves in the atmosphere. But he’s also repeating Galileo’s (supposed) famous experiment in studying the free-fall acceleration of various objects. In this case the elevated position  is not the Leaning Tower of Pisa, but the spare bed, and the objects take the form of anything he can lay his hands on, including himself. But the one I’ll comment on today concerns energy transfer from rapidly moving objects to fluid. 

His method takes the form of sitting in the bath and whacking the surface in such a manner as to create the largest splash of water. What he needs to work out is the relationship between the area of the object hitting the water (his hand), the speed at which he strikes the surface, and the height to which the splash goes.

Fluid dynamics is governed by a collection of dimensionless numbers that relate various quantities. The most commonly used is probably the Reynolds number, which is the ratio of the intertial force to the viscous force on an object. A high Reynolds number shows that intertial effects are prevelant; a low Reynolds number shows that viscous effects dominate.  In baby’s case, he probably needs to look at the Froude number. This tells us that gravitational-velocity effects depend on the dimensionless term v/sqrt(gL), where v is the velocity of an object, g the acceleration due to gravity (9.8 m/s2) and L is a characteristic length. The pattern of flow obtained, for example the height h of the splash in terms of the length scale L,  is likely to be a function of the Froude number. So, if we want the height of the splash, we can say that h/L = f(v/sqrt(gL)) which tells us h  = L f( v /sqrt(gL) ) where f is some function to be determined. We’d expect it to be an increasing function – if we increase v we’d expect  h to increase – and if we did the experiment on the moon where g was lower we’d expect h to increase too. 

A series of experiments should tell us whether such a relationship indeed holds for whacking the surface of the water with a hand of length L, at a speed v, and the form of the function f. We shall collect the data over the next couple of weeks and hope to have a paper  published soon. 

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Turning moments Marcus Wilson Apr 16

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 The last couple of weeks has seen a few changes in the house as Benji has finally mastered crawling. Being a rather LARGE baby, he’s been the last of his coffee-group babies to become mobile, but now he’s got it worked out he’s away at high speed. No peaceful sunbathing for the chickens or the neighbour’s cat now. 

So, one thing we’ve had to do is to work out what he can get into, up, along, through, etc, that we’d rather him not. The freestanding coat stand, for example, we’ve now bracketed to the wall. Our bookcases are secured anyway from an earthquake point of view, there are some bits of furniture that aren’t. I mean, you can’t practically bracket down a chair, can you? With a couple of pieces, I’ve had a quick go at working out whether he could, in principle, pull them over. 

To pull over something on four legs, you need to shift its centre of mass so that it crosses the line between the two legs that are touching the floor  - then gravity will ensure that it falls over. That generally means pulling it towards you. (Pushing just pushes it into the wall). What is of importance is the turning moment you apply to the object about the two nearest legs, compared with the turning moment that is generated by gravity. If you win, then over comes the object. The turning moment about the point is the product of the force applied, multiplied by the perpendicular distance between the force and the point.  Basically, then, the greater the force applied, the larger the turning moment, and the greater distance between where the force is applied and the contact point between the legs and the ground, the greater the turning moment. Thus an adult will be able to tip over a piece of furniture much more effectively by pulling at the top, rather than pulling a quarter of the way up. (This acts in our favour when considering Bubble’s abilities.)

Assuming aforementioned child doesn’t CLIMB the object (and he’s not doing that yet), it’s a simple estimate as to how far up he can pull from. But how hard can he pull? 

 It’s tough to pull more with a force more than your own weight, unless you have your feet clamped to the floor. The reason is that at some point the friction between one’s feet and the floor is insufficient to keep your feet in one place. Try pushing a heavy box along a polished floor while wearing socks. The box might stay put, and it’s your feet that do the sliding. 

So that gives us an estimate of how much force he could reasonable pull with. Therefore we can work out the turning moment, and compare it with that generated by gravity the other way. That’s fairly easy too – estimate the weight of the object and where the centre of mass is in relation to the legs and do the multiplication. A heavy object, with legs wide apart – a light one with only a small footprint on the ground, like our CD rack, will go over rather more easily.

So, at present, I’d be surprised if he’s able to tip anything that has to the potential to cause real damage. But that will change.

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Watch the students Marcus Wilson Apr 10

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This week I sat in on a lecture given by a junior colleague of mine. Partly this was so I could offer him some guidance, but partly so I could see how someone else approaches the the teaching of physics and engineering material. It was enlightening experience for me. One thing I did was to watch the students. There were a lot of different things going on, suggesting that while the lecturer was talking students were engaged in range of tasks – such as detailed concentration, helping others to understand what was being said, checking emails, discussing their recently returned test scripts, or plain daydreaming.

 My assumption is that this probably is a fairly standard range of activities for students in a lecture. Which, most likely, would include my lectures. How would I know what’s going on with my students? One immediate way that springs to mind is to get a colleague to come in and watch the students, rather than me. Another is to get a camera on them. In many of our lecture theatres we have cameras that are often used to capture the ‘lecture’ so students can review it afterwards, and sometimes used so that the teacher can review how they performed. But better might be to turn the camera around and film the students (with their permission, obviously).

Although, having said that, what would a ‘good’ range of reactions from students look like? Talking to one’s neighbour isn’t necessarily a bad reflection on what the teacher is doing. And avid concentration might be a sign of lack of clarity from the teacher. One thing that is clear is that knowing when you’re teaching something well and when you are not is pretty difficult at the time. I can think of times when I thought I’d had the students attention throughout, presented something clearly just as I would have liked, and then found when the students were assessed on it that they hadn’t got it at all. Equally, there are other times that I’ve felt I’ve given a really bad lecture but the students have grasped the material in it. Tricky stuff.

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