SciBlogs

Explaining the blatantly obvious Marcus Wilson Apr 04

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I've had a few difficulties in some discussions with students recently. It comes down to this: "How do I explain something that is so blatantly obvious it doesn't need explanation?" 

The problem really is that a particular concept can be obvious to me, but not obvious to a student. The danger is then that, in a lecture, I just assume that a student is implicitly happy with such a concept and I plough on forward without any hint of explanation. The consequence is a bemused student who just doesn't get what I'm talking about. 

It is really, really hard for a lecturer on two counts. First, you have to recognize the fact that something might not be so obvious to a student. That's pretty tough when it's second nature to you. Secondly, you have to find a way of explaining the (to you) blatantly obvious. 

Here's an example. I was asked by a student why velocity was equal to rate of change of position. He didn't get it. My initial response was "But that's just the definition of velocity – it IS the rate of change of position – what's there to get?". But that didn't cut it for the student. I had to dig deeper to see what the stumbling block was. It turns out that he had a vague understanding of velocity from his everyday experience, but not one he could put down in precise, physical terms. He was also (as many students are) uncomfortable with using vectors. Therefore, he couldn't see how to match a rate-of-change of position, described in terms of vector calculus, with his everyday concept of what velocity was. When I said "They're the same thing by definition" – that didn't help one bit. Why are they the same? 

Often, when someone is not grasping the blatantly obvious, there's some underlying block in their thinking. In teaching and learning literature, we talk about threshold concepts – ones that are really difficult to get, but once grasped, transform the way that someone thinks. Once someone's crossed that threshold, it might well be blatantly obvious. But beforehand, it certainly isn't. Teaching a threshold concept is very, very hard indeed, especially if you yourself crossed that threshold many years ago. Often these things are best taught by those who have only just 'got it' – i.e. students teaching students, or peer-instruction. 

 

Apparent forces Marcus Wilson Apr 01

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A couple of weeks ago I had the misfortune to be on a bus which had an accident. I wasn't hurt, because I was safely seated, which is more than I can say for one unfortunate passenger who was still on his way to his seat at the time. It wasn't a high-speed event – I'd guess we were doing about 10 km/h. We had just pulled away from a bus stop, when a car that had been parked a few metres in front of the bus decided to pull out into the road right in front of us. The driver hits the breaks hard, and, as a result, the fellow passenger ends up in a heap on the floor at the front of the bus. 

While the cause of the crash I would say rests firmly with the driver of the car that pulled out, that's little comfort to the poor guy with blood dripping from a wound on his head, down the back of his shirt, which is probably now dyed a nice shade of maroon. Standing on buses is pretty dangerous, even at low speed. I do think the driver should have waited till everyone was seated before pulling away. 

So, from a physics perspective, what happened? One can explain this in two ways. There's the 'inertial' approach, as explained by the witness on the side of the road: The bus stopped, but the guy standing, who has inertia, carried on. Then there's my viewpoint, from inside the bus. Everything experiences a sudden acceleration forward. This causes the passenger to lose his balance, and down he goes. 

This forward acceleration, from the perspective of the person on the bus, is called an apparent force. It arises because the frame-of-reference, the bus, isn't an inertial frame. That is, it's accelerating (or, in this case, decelerating). It's called 'apparent' because the person on the side of the road wouldn't see it in this way; it only becomes apparent if the observer is in the accelerating frame of reference. It might be termed an 'apparent' force, but for the person on the bus it's a very real push forwards, one that splatted him on the floor and would have given the bus cleaners a more interesting job that usual.  It's the same kind of thing as centrifugal force (yes, the 'f' word), which one experiences when going round corners. To the person in the object that is doing the moving, the force is a very real thing (ask the racing car driver). But to everyone else, it doesn't actually exist. 

Apparent forces are pretty hard to teach (I've just been doing it), but I think the key is really to emphasize that they are there only to the observer who is in the accelerating frame. 

What happened to the passenger? Against the advice of everyone around him, including me, he refused to be taken to a medical centre, which was only a few hundred metres from the place of the incident, and insisted on carrying on the journey to his destination. Possibly if he'd been able to see the back of his head he might have thought differently. One shudders to think of the consequences at 50 km/h. Seat belts in buses? Yes please. 

 

 

 

 

Don’t moan about it if you haven’t actually taught it. Marcus Wilson Mar 24

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At a recent staff meeting here, the topic of students' writing ability came up (yet again)! Why are our engineering students and physics students just so bad at writing in whole sentences, using correction punctuation and using consistent tenses? Why can't they string four relevant sentences together to make a paragraph that actually makes a point? In short, why can't they make themselves clearly understood in written form?

We have lots of stories of despair, and much of it is directed at 'the secondary school system', or lecturers in other departments not doing their job properly, or the rise of txt spk. 

But there's a very obvious point that we have to pay attention to: Have we actually taught the students how to write? Have we shown them how to put sentences together that make a coherent argument? It's very easy to say "not my job – mine's to teach thermodynamics, or materials science, or differential equations, or whatever". But if the assignments a lecturer sets demand that the students have good writing ability, isn't it the responsibility of the lecturer to ensure that the students have been taught how to write? 

I'm not saying every paper that a student does has to contain writing skills in it, but if we want to have students exit their degrees with the ability to communicate about their area clearly in written English, then we must make sure that somewhere they have opportunity to develop those skills. In short, don't complain about students' lack of ability in things that no-one has actually taught them. 

 

 

The advantage of a transponder Marcus Wilson Mar 17

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So, as I said, it appears that it's awfully hard to hide a commercial airliner from military radar.

But let's backtrack a bit. Why do aircraft carry transponders? (What is a transponder?) There are a couple of reasons here. First, we need to look at a big problem with radar. It has limited range. We can see this quite simply by considering what happens to the energy contained in a radar pulse sent out by an antenna. The pulse spreads out as it travels, and so the intensity of the pulse diminishes. It follows an inverse square law, which is very common in physics. If you are in a plane and you double your distance away from the antenna, the electric field strength you receive is quartered. This pulse is then reflected back toward the antenna. Again, the reflection spreads out, and it follows an inverse square law. By the time it gets back to the antenna, it has undergone two inverse square spreadings.  That makes an inverse fourth power law. In other words, if you double your distance from the antenna,  the radar station will receive only 1 over 2 to the power of 4, or 1/16th of the power. That rather limits the range of radar. 

Yes, there are other things to consider, such as absorption in the atmosphere, and radar ducts (paths of high transmission) due to interesting meteorological conditions, but, basically, if you rely on reflections of the radio waves to detect an object your ability to detect goes down rapidly as the object gets further away. 

That's where the transponder comes in. When the transponder on the plane detects a radio pulse coming in, it calls back. The power it transmits back with is much greater than the strength of the reflected pulse. Thus there'll be sufficient power to get back to the ground station, and the plane is detected. There's only one inverse square law that matters, and that helps considerably with range. 

Secondly, the transponder rather helpfully transmits an identifier that tells the ground station what it is. Rather than simply a blip on a radar screen, it's a labelled blip. 

Until the transponder is turned off, of course. 

A fun experiment to try at your desk Marcus Wilson Mar 13

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I received the latest PhysicsWorld magazine from the Institute of Physics yesterday. A quick flick through it reveals a fantastic demonstration you can do with kids (or grown-up kids) to show how strong friction can be. Take two telephone directories, and interleave the pages (so every page of book A has a page from book B above and below it, and vice versa). Admittedly this takes some dedication, but that's what graduate students are for. Then try to pull the directories apart. In fact, the photo in the magazine shows two such interleaved directories being used in the centre of a tug-of-war. I have got to try with my students. 

In fact, you don't need the patience to turn page-by-page through two phonebooks to do this. I've spent a couple of minutes interleaving my copy of the 84-page University of Waikato Science and Engineering Graduate Handbook with the slightly larger University of Waikato Science and Engineering Undergraduate Handbook.  (Some might say the two make a lot more sense arranged in this manner….) It didn't take too long to do. I can't pull them apart.

It's simply down to the large surface area that the interleaved books have. They are A5 in size (approx 21 cm x 15 cm), with 86 (84 pages plus inside covers) surfaces. That gives, very approximately 27000 cm2 area of contact, around two or three metres squared of contact. That's pretty sizeable. A pair of telephone directories could come in at about 30 metres squared or so!  Lots of surface are gives lots of frictional force. 

What makes something show on radar? Marcus Wilson Mar 11

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One of the questions on everyone's lips at the moment is "How does a large passenger jet simply disappear from radar without trace?"  It is clearly very distressing for anyone with friends or relatives on board – not knowing what has happened. As I write this, there still seems to be a complete lack of clear evidence pointing one way or another. I'm not an aviation expert so I really can't add anything of value here. But I can turn the question around to one of more physics relevance, which is "What allows a plane to be detected with radar in the first place?"

Radar, in concept at least, is pretty simple physics. It's name comes from an acronym "RAdio Detection AND Ranging". However, it has out-grown its acronym, since it now does more than simply detect and 'range' (tell the distance to), and 'radar' is now a word in itself and not spelled in uppercase.  The basic idea is that a radio wave will reflect off a metal object (a plane, ship, your car…) and some of that wave will return to where it came from. To be pedantic, while we often think about the radio transmitter and detector being in the same place, this doesn't need to be the case. In fact the first radar systems had detectors physically separate from the receivers. Anyway, we know the speed at which radio waves travel (pretty well the speed of light in air) and therefore by timing the delay between transmitting and receiving we know how far the object is away. By also knowing the direction the reflections come from, we can therefore work out a position. 

It gets a bit more difficult in practice, since radio waves don't necessarily travel in straight lines, but can be bent due to atmospheric conditions. And radar can tell us more than just position. For example, we can exploit the doppler effect to measure the how fast an object is travelling. Waves reflecting from a moving object return with a different wavelength – measure the wavelength shift and you measure how quickly the object is moving towards or away from you. 

So why does a metal object reflect radio waves? That's down to its high electrical conductivity ensuring that there must be no electric field at the surface.  The waves simply can't get into the material and are completely reflected. I won't bore you with the analysis of Maxwell's equations to show this – unless you happen to be in my third year electromagnetic waves class in which case I'll bore you with it – whoops, make that excite you with it – in a week's time.  Metal makes a pretty good shield for radio. 

Just what fraction of the power of the incident wave that gets reflected back towards the transmitter can be tricky to calculate. It's encapsulated in a term known as the 'radar cross section' (RCS). The definition of RCS is a little tricky to wrap one's head around, but I'll give you it: The radar cross section of an object, in a given direction and a particular frequency, is the cross sectional area of a perfectly-reflecting sphere that would give the same power return as the object gives in that direction. In other words, imagine a large, metal sphere, that reflects the same amount of power that our plane does. Take the cross-sectional area of it (pi times the radius squared) and that's the RCS. A large RCS means a large amount of power returned.

To some extent the RCS simply depends on how big an object is, but just as important is the shape of an object.  Geometry with right-angles in it will cause large reflections back in the direction of the transmitter (think of a snooker table – if a ball bounces off two cushions it's direction of travel is reversed – it doesn't matter about the angle of incidence). Long edges also give large returns – they can act rather like antennas and re-radiate the incoming radiation. Unless you specifically set out to design an aircraft with a low RCS the chances are that what you'll end up with is something which has a pretty substantial RCS. The tail is at right-angles to the fuselage, it has long straight wings, and is made from highly reflective metal. 

And that means that a Boeing 777 isn't likely to vanish off a radar screen while it remains in one piece. 

 

 

In cyberspace no one can hear you scream Marcus Wilson Mar 04

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So, you spend six days working frantically on a large project proposal in order to meet the ludicrous deadline (see previous post), and just as you think that the it's under control and the goal is in sight, someone walks onto the pitch, picks up the goal posts and deposits them in the vicinity of the dug-out. 

43 hours and 13 minutes before the deadline (the email has a time-stamp on it), we're told that (a) we have another week to get things in order and (b) the template we are using to write the proposal has changed. So I've been jumping up and down frantically on the wrong side of the pitch a week early. Mixing metaphors,  while I don't wish to bite a hand that might feed me, I'm still going to scream at it. Fortunate then that in cyberspace no one can hear you scream. 

 

Sorry I’ve blogged-off Marcus Wilson Mar 04

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Hello everyone. Are you still there? It's not much fun reading a blog that doesn't update for several days, is it? My excuse is two-fold.

1. That the University of Waikato Semester A has just started. Actually, that isn't a real excuse since I've known about it for a long time. It just acts to aggrevate the second reason.

2. A project call for some of the National Science Challenges has been released.

What are the National Science Challenges? Have a read on the MBIE website. The government is putting a lot of money into research focused on addressing ten, grand challenges. There was a bit of debate about these when they came out as being 'more of the same' for New Zealand (i.e. doing just what we've been doing anyway), but, whatever your view, they are here to stay a while. Now, a call for proposals has just been put out for some of these. The timescale isn't terribly long – I learned about it on Wednesday last week and I have till 5pm Wednesday this week (tomorrow!) to get something pulled together. With a team split over different institutions and numbering about eight researchers, this isn't an easy or quick job. But when someone dangles half a million dollars in front of you and asks you to jump up and down for a week (plus fit in some undergraduate lectures while you're at it)  it sometimes pays to do it.

So sorry for no blog entries. Things might get calmer at 5.01pm tomorrow.

Dem Cables Marcus Wilson Feb 21

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I've just been shifting around various bits of equipment and computers in our 2nd and 3rd year physics lab, to make way for an item that's shifting in there from a nearby lab. It's gone something like this…(rising in semitones, with apologies to the original performers) 

Da power socket is connected to da extension cord;

Da extension cord is connected to da monitor;

Da monitor is connected to da computer;

da computer is connected to da control box;

da control box is connected to da MRI machine;

da MRI machine is connected to da MRI-machine stand;  

da MRI-stand is connected to da floor*;  

Now why are there so many cables?

Dem cables, dem cables, dem power cables;

dem cables, dem cables, dem ethernet cables;

dem cables, dem cables, dem USB cables;

What a mess of knitting!  [Roll on wireless power transmission!]

 

*The MRI-stand is connected to the floor because we don't want the thing to move. The unit is calibrated for the position it's currently in; I'm not inclinded to move it in a hurry. The other things, however, might be more sensibly located. 

A load of rubbish Marcus Wilson Feb 19

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I've been reading through a student's report of his summer work placement. He  had a project on improving the performance of a heat exchanger used for getting rid of heat from a cryogenic cooler. The basic concept is that materials are being cooled to about 40 kelvin (that's 40 degrees above absolute zero, minus 233 degrees celsius, by removing heat from them. That heat needs to go somewhere, and the job of the heat exchanger is to dump it.

I was struck by the similarities of the problem of 'dumping waste heat' with that of 'dumping rubbish'.  What do we do with household rubbish – stuff we don't want that is generated by our day-to-day activities. Well, various things happen to it. 1. Some of it gets put in the pretty blue (in Waipa) recyling box and gets put out on a Thursday morning.  2. Some of it gets put into the equally pretty yellow pre-paid rubbish sacks and also goes out on a Thursday morning, and ends up in landfill :-( 3. Some of it accumulates in the garage, until such time that 1. or 2. applies (or it gets taken to the recycling centre / tip, which is the same as 1. or 2.) 

We do the same with waste heat. It is generated by just about everything that we do. Car engines generate waste heat, car brakes generate heat through friction, electrical appliances generate it, running up and down stairs creates it – basically it's an inescapable consequence of the second law of thermodynamics. Heat gets made, and usually we want to get rid of it. So, what do we do with it?

1. We can, if we're clever, recycle it. A sensibly-designed industrial plant will tap into the waste heat it makes to do useful things. Smart tumble dryers will use the waste heat in their exhaust to pre-heat the dry air being sucked into the machine, saving electricity. Heat engines can be put into effect where there is a consistent difference in temperature between two objects. 

2. We can dump it. That's what happens to most of it. We let it end up in cooling water, or the atmosphere, where we conveniently forget about it. However, unlike landfill, it's not usually a problem in itself (warm rivers near power stations might be, however). The amount we generate over the earth is pretty tiny compared to the amount that the sun gives us. The real issue is the amount of carbon dioxide and other greenhouse gases that have been generated in the process (plus, economically, the generation cost of the energy that is being wasted). 

3. We can store it and do something with it later. This isn't so easy, but can be done. We can exploit gels that have high latent heats, meaning that as they undergo a phase change they take in heat, and then as they undergo the reverse change they will give it out again. We can heat up objects with high heat capacity, keep them well insulated, and then release the heat later (e.g. night storage heaters). 

So does 'dumping' heat mean that we're treating energy in a similar manner to rubbish? Chuck it away and pretend it's not an issue. With the landfill problem, the first thing to address is not recyling, but simply not to consume so much stuff in the first place. If we did the same with heat, we'd have lower energy bills and lower greenhouse gas emissions. The two, and their problems, are perhaps not so wildly different. 

Here's a final thought then. My work emails (if I don't delete them) get stored somewhere in the world on a server belonging to a well-known and rather enormous company. How much power does it take to keep one of my emails on file? I don't know the answer to that one. If everyone in the world deleted their email and the data they really didn't need anymore, what difference does it make to the world's energy consumption? Anyone know?

 

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