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January 2013 Archives

For reasons best known to their small chicken-brains, Harriet and Henrietta have decided to abandon the coup and roost in a tree. Maybe this is because it is rather hot in the coup at night, or possibly because a neighbour's cat enjoys sitting outside the coup at six in the morning. (One day that cat is going to push his luck too far and find out what sixteen chicken-claws and two beaks feel like.)  Whatever the reason, they feel that a tree is the better place.

They manage to hop and waddle up their separate trees without too much problem and sit out on branches as thin as they dare go about three metres off the ground, presumably happy that they are safe up there for the night. Getting down again in the morning is more interesting. Henrietta usually chooses the same route down as up, through the low branches. But Harriet, suffering delusions of  aeronautical ability, takes a more direct approach. And believe me you don't want to be in her flight path when she launches.

Her flight-time is beyond the ability to time with a stop-watch, but I'd say this morning it was about one second. Given that she has dropped, I reckon, about three metres, she can't be generating much lift. A quick estimate can be made at this point.

First, recall that motion can be separated out into the vertical component and horizontal component. Under constant force (in this case gravity plus lift), the components don't affect each other. That means we can use simple kinematics to work out her acceleration. For an object accelerating from rest, the distance it travels in a time 't' is given by half times 'a' times 't' squared, where 'a' is the acceleration.  If distance is about three metres, time about one second, then we obtain an acceleration of about 6 metres per second squared. 

That's made up of gravity (10 metres per second squared) minus the contribution due to lift. This means the lift she's generating with her barely coordinated flapping equates to about 4 metres per second squared. In other words, she's managing to lift only about half her weight. Little wonder she has to climb the tree to get up it.




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With the start of semester less than four weeks away now, I've been writing my exam papers, test papers, assignments etc for the A-semester papers that I teach. If I don't get them done before the semester starts, it will be a real rush job to do them later on. Since the key to good teaching is in setting appropriate assessment items, they need to be done with careful thought.

Last year I trialled a couple of tests that students could talk in. I felt they were successful - they did their job in being a learning exercise in addition to being a test, and the majority of the students agreed with me, judging from the comments on the appraisal forms. This year I'm going to take it a step further, and have the students mark their own tests as well, straight afterwards. This brings in another successful strategy, which is immediate feedback to the students. Rather than them getting a mark sometime afterwards, they get to review their work straight away and identify where they did well and where they need improvement. I will, of course, read through their scripts and look at how they marked themselves - a student giving themselves ten out of ten for an empty script isn't going to wash. In fact, it may help identify those students who think they are performing better than they are, and who would normally be in for  a shock when they get their final exam marks back at the end of semester.

The goal is to get a single assessment exercise (called a 'test' - but a better name is probably just 'assessment') that combines summative assessment, formative assessment, assessment for learning, and immediate feedback. Can they all work together? I'll find out soon enough.

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Sam has now uploaded the videos I talked about last week onto physicslounge so you can view them for yourself. They take some time to go through (it is a three hour paper after all) but if your internet connection is up to it they are there in glorious high definition.

Before you go through them, grab yourself a copy of the exam paper from the NZQA website

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We've had a bumper crop of plums from our two plum trees. Way more than we can eat our way through in the short plum season. It appears that we aren't the only ones - the last couple of weeks have seen bucket loads of free plums turn up in the tea-room here. (And yet they are several dollars a kilo at the supermarket.) So, yesterday, Karen had a go making plum sauce, to add to the plum jam and frozen plums we already possess. As far as I can work out, the difference between plum sauce and plum jam is merely that plum sauce is more saucey. The mechanism appears to be the same - everything gets cooked up in a large pot and the hot sauce gets added to sterilized preserving jars. The lids go on and should seal shut as the temperature inside the jar drops and the small amount of air inside loses pressure.

A lid that's popped downwards is a good sign that there is a decent seal between the lid and the jar. If there weren't, then air could get in and equalize the pressure between inside and outside, and up would pop the lid. Conversely, if there were, for some reason, some multiplying nasties in the contents, producing carbon-dioxide, the pressure would build up inside and the lid will buldge upwards. That's a sure sign that what's inside isn't edible. The trick is to spot it before it explodes at the back of the pantry and splatters jam and glass everywhere.

That's why there's a warning on shop-bought jam - if the 'button' isn't down, don't eat the contents.

However, all this only works if the jar is up to scratch. I came home from work yesterday to discover that parts of the kitchen had been painted in plum sauce. This wasn't the work of the baby - it was down to a jar that had failed. When the sauce went in, the lid went on, and, sure enough, the lid popped downwards. But it wasn't the only thing that 'popped.'  The jar did as well, leaving it with no bottom.

There are a couple of reasons I can think of why this might have happened. First, it could simply be down to rapid thermal expansion of the glass. When the hot sauce goes in, the inside of the glass jar gets hot much more quickly than the outside, and so there is stress built up as a result of different amounts of thermal expansion on the inside and outside. This is what happens pouring boiling water into a cold glass.

Or, perhaps the bottom of the jar acted as a popping lid. If there were some air trapped at the bottom, it would reduce its pressure as it cooled, and create a force on the bottom of the jar. If that force were great enough, it could break the glass. An implosion, rather than an explosion.

Now, neither should have happened because the jar concerned was a proper preserving jar, designed for the purpose of having hot stuff poured into it and being sealed. But, for some reason, it did. I was tempted to bring in the jar to work today and get one of our materials engineers to examine it to determine the mechanism of failure. It would have been interesting, but I thought they had better things to do with their time, so we may never know exactly what happened here. But the good news is that there are still several intact jars of sauce, so we will be well supplied for the coming months.




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Over Christmas, we were staying with my wife's sister and her family in Dunedin. Early one morning (sometime before I got up, anyway - that is my definition of early) a loud 'bang' came from the direction of the kitchen, followed by the sound of eight paws beating a hasty retreat. There are two young cats in that house, and my  first thought was 'pesky felines - I wonder what they've done now'. And I went back to sleep.

As it turned out, the cats were entirely innocent. The culprit was the coffee pot (now ex-coffee pot). It was a stove-top machine - one where water goes in the bottom half, the coffee is placed in a holder and inserted on top of the water, and the top half of the pot (which will contain the finished product) is screwed on. Whether there was too much coffee in it, or it was packed in too tightly, or some other problem, we don't know, but clearly the steam made in the bottom wasn't finding its way to the top. Instead, as the water boiled, the pressure inside the bottom half just kept increasing, until there was a mechanical failure and the top half departed from the bottom half in a hurry.

The bang I heard was the top half hitting the underside of the range hood at high speed. The dent in the latter was sizable. There was also a trail of coffee up the wall above the stove, and onto the ceiling, where coffee grinds were pasted in place. And splatterings of coffee were in every cup, box, drawer, container and cupboard that had the misfortune to be in the kitchen at the time.

It was rather fortunate that no-one was near it at the time. Beware the ideal gas law: Pressure times volume is proportional to temperature. In this case, with a constant volume, high temperature implies high pressure, and there is only so much pressure a coffee-pot can take.



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On Tuesday my physics skills were put under the spotlight. Back in November, I think, I was discussing with Sam Hight from the Physics Lounge  ( ways that we could, together help high-school students in their physics. One of the things we came up with is that I had a go at doing the 2012 Scholarship Physics Paper, live. In other words, I'd get filmed attempting the paper - under pseudo-exam conditions - specificially, I wouldn't have seen the questions before -I'd be going straight into it.

The idea here was to give the students a realistic view of problem solving and how an experienced physicist (if I may be so bold as to call myself that) reasons and decides what's important and what isn't. Too often when model answers are presented to a problem one is left wondering: "That's all very well, but HOW do I know I should approach the problem that way?", or "HOW do I know that such-and-such bit of physics is what is relevant and will get me to the end point before I start?" With hindsight and enough time, most answers to exam questions can be condensed down into something really neat and snappy (the model answers!), but the reality is that hindsight doesn't occur until a couple of days AFTER the exam when it isn't much use.

So Sam filmed me going through the paper. We had a few teething problems with the camera equipment, which meant we only got through four of the six questions, but hopefully we'll get the other two filmed soon. (Of course, I've seen the questions for these other two so it won't be quite as authentic.) Sam will work on the videos and hopefully they'll appear on Physics Lounge before too long. I hope they are useful. If students hadn't worked it out already, these questions are tough, and they take a bit of thinking about.

So, if you dare, turn with me to question 5, part (b) on the paper.  I wonder sometimes just how the examiners dream up some of these questions. In this question, twelve electrical cells (commonly called batteries), each of 1 volt  are connected in a loop. That's it - no other electrical components. This question should have carried a warning "Don't try this at home!" So, if a voltmeter is placed across three of these cells, what voltage does it read?

Well, you will see the embarrassing shambles I made of it on the movie, when it gets posted. But I got there in the end, and Sam and I had a good discussion on it that's captured on the movie. In fact, the more I think about it, the more blindingly obvious it is. It really is just such a simple argument. By symmetry (a powerful tool in physics), each cell must have the same potential difference across it. Call it V.  If we move one terminal of the voltmeter all the way around the loop, adding one cell at a time, the potential must increase by V each step, so a total of 12 times V. However, after going around in a loop, we get back to where we start, so the potential cannot have changed. So 12 times V must be zero, and V must be zero.

In other words, there is no voltage over a short-circuited battery. Which is obvious - it's a short-circuit -by definition they are at the same voltage.  Obvious in hindsight, that is.







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This one has hit the blogs recently, but, since it's quite amusing - and perhaps a bit disturbing - it's worth a comment.

Kimmo Eriksson has recently published a paper on 'The Nonsense Math Effect'. The study was conceptually very simple. It used two hundred participants, all of whom had postgraduate degrees, with the participants spanning the various fields of academic study, including maths, science, medicine, humanities, education and more. Each participant was given two abstracts to read (the same two abstracts for each participants - though see the catch below). For those who don't know, an 'abstract' is a short summary of a piece of work - typically a couple of hundred words. The idea is that the reader can work out from the abstract whether it's worth his while to read the full work, or to attend the presentation at the upcoming conference, etc. Participants were asked to rate on a scale of 0-100 how good they thought the work was, based on what they read in the abstract. Now, the abstracts weren't in the fields of expertise of the large majority of the participants, meaning they were reading them without specialist knowledge.

But here's the crucial catch. Half of the abstracts were doctored by adding a sentence at the end which included a maths equation in it. The sentence was taken from a different paper and was therefore entirely irrelevant. The aim was to see whether this sentenced changed the readers' perceptions of the work.

And the results of the study? Those participants with a maths or science background weren't impressed by the added maths. The overall score of the doctored abstracts dropped slightly, although the drop wasn't statistically significant. However, those with backgrounds in humanities, social science and education were impressed by the addition of the nonsense maths, and rated the abstract more highly. (By the way, so did the medics, but that difference isn't statistically significant because of the low numbers of medics participating.)

So maths impresses those that are not mathematically literate. Is this phenomenon only seen with maths, or is it more widespread - i.e. one is impressed by what one doesn't understand? This might link to Dan Sperber's "Guru Effect" as evidenced in many of our politician's speeches, where sentences that are hard to understand sound impressive. 

Maybe I should start slipping some random social-science or education theory rubbish phrase into things I write so that the writing is viewed more favourably. This will elucidate the sentimental effect and related social discovering strategies.







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Well, I'm back in at work after a lovely Christmas break. Lots of sunshine (we dodged the bad weather by going southwards for Christmas and then back north for New Year), beaches, playing with baby, and hacking back the jungle that sprung in the back garden in our 10 days' absence.

Benjamin has now pretty-well mastered sitting upright, which makes playtime a bit easier. Sometimes he leans too far and falls over, usually as a result of over-reaching for something that's caught his eye. A couple of days ago, he toppled backwards after a sneeze. Though it would be fun to think that the recoil from the momentum of the sneeze is what sent him over backwards, I think it is more likely that it just took him by surprise and he lost his balance.

A quick estimate shows the situation. A sneeze, in physics terms, is a jet of air. We can think of it in terms of conservation of momentum. A jet engine on an aircraft sends a high speed stream of gas backwards, and at the same time the aircraft exhibits a forward force - the two are related - the force is equal to the rate at which momentum is transferred to the stream of gas. To work this out we need to think what mass is moved backwards every second, and what is its velocity; the product of these gives the momentum transfer every second.

If we consider the jet as a cylinder whose ends are of area A (real jets aren't cylindrical, but let's not worry about that for a quick estimate), then in one second a length v metres of gas is emitted, where v is the velocity in metres per second. So the volume is Av, and the mass is pAv, where p is the density of the gas (for air it is conveniently about 1 kg per metre cubed). Since this gas moves at a velocity v, then the momentum per second is given by pAv times v, that is p A v squared.

So what force does Benjamin's sneeze provide? We have p=1 kg/m3 for air. Let's assume an area of about 2 cm2 for his open mouth (2 centimetres squared = 0.0002 metres squared). The velocity of a sneeze is pretty fast - a bit of googling and I find around 100 miles an hour (160 km/h or 44 m/s). For round numbers let's say 40 m/s. That means the force a sneeze gives him is 1 kg/m3 times 0.0002 m2 times 40 m/s squared which is about 0.3 newtons.

What does 0.3 newtons mean? That the force that gravity would exert on 30 grammes. Since Benjamin's legs weigh considerably more than this, the sneeze recoil isn't anywhere close to being sufficient to lift his legs off the ground and send him toppling backwards from a stable sitting position. Just maybe he was at the point of tipping and the sneeze is what sent him 'over the edge', but that would be quite a coincidence. So, while it was fun to think a sneeze can catapult you backwards, it's not going to happen outside of Roadrunner cartoons and that ilk.




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