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March 2017 Archives

A couple of days ago I arrived 'home' to discover our local ant colony at work. There's a nest located somewhere in the bushes at the front of our temporary home, and the occupants have become rather adept at raiding our kitchen. Anything left on the kitchen bench is fair game for the taking. Ants are amazingly strong for their size - any little bit of food like a small oat flake gets picked up and transported back to the nest.

Now, in this case the ants were after the grated cheese. Some sizeable flakes had been left on the bench and these were going to be a feast for an ant colony. By sizeable I mean something you get from a coarse grater - perhaps 3 mm wide and maybe 2 cm long. Now, to get them off the kitchen bench and to the nest, they had to take them across the bench, up the splashback by the sink, across the windowsill, out of the window and then down the wall outside. Getting them across the bench was no problem for a few tough ants - all heave together - and away goes this piece of cheese. Quite amazing to watch them move it so quickly.

But the next bit was tricky. They had to manoeuvre the cheese off the bench and up the wall. They did it by putting one end of the cheese against the wall - then a group of ants on this end slowly lifted it up - while a group on the other end pushed. At least, that's what it looked like they were doing. It seemed to be a touch random, but, on average, that's what was happening. Once the cheese had a bit of an angle to it, it got easier, since it was able to rest there, supported on one end by the friction of the wall, and the other end by the bench. Very soon it was on its way up the wall.

Watching them at work reminded me of the 'ladder on the wall' problem. This is a problem in statics that's often wheeled out to bring the over-enthusiastic "I can solve everything with equations" student back down to the earth with a thud. "A ladder of length 4 m (or whatever) and mass 10 kg (or choose your own) rests at an angle of 80 degrees against a vertical wall with coefficient of static friction 0.8.  The bottom end is resting on the flat ground with coefficient of static friciton of 0.6. (a) Draw a free-body diagram showing the forces acting on the ladder. (b) Evaluate these forces."

The point here is that this problem, as phrased, does not have a unique solution. I'll let you have a go at drawing out the freebody diagram. There's the weight of the ladder (which we know), and we can assume that acts downwards at the centre of mass. That bit is easy. At each of the two ends we have a normal force from the surface and a friction force. That's five forces in total. We know the weight, so it leaves us four to find.  But we can only find three independent equations - we know in equilibrium that (1) the horizontal component of force must be zero, (2) the vertical component of force is zero and (3) moments about the centre of mass are zero. Four unknowns, three equations. We can try to take moments about some other point, such as the ends of the ladder. But that doesn't yield any more information. In equilibrium, the coefficients of friction don't help us find new equations (just inequalities). We are stuck. This is called a 'statically indeterminant problem'.

Now, there are ways of proceeding (the enthusiastic student can read this, for example), but we need to know some more information about the elastic properties of the ladder, the wall and the ground. But my point is that there are some seemingly simple physics problems that just can't be tackled by a naive throw-the-equations-at-it approach. We do need some more careful thinking.

I reckon the ants were not too interested in the finer points of statics when they were manouevring this piece of cheese. In the same way, one doesn't need to solve statically-indeterminant problems in order to safely use a ladder. But, for a physicist, it begs the question "What is the coefficient of friction between a piece of cheese and a tiled wall when the surface is lubricated with ants? And then, "Is there a good way of modelling this?"

 

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,,,I have the following question. Why is it that electronic engineers like to find themeselves the most labyrinthine building on campus and place their reception area somewhere that no-one is likely to find? I can only assume it is because they don't want their own private world disturbed. Best leave them be.

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Sundials are fun. As someone who visited a lot of stately homes  as a child (usually under duress), I found sundials in the gardens a welcome distraction from the monotony of trudging round a place with no other redeeming features that adults somehow seemed to find attractive. Not all adults did, I'm sure, but certainly my parents did. 

First, there's always the question of whether the sun will be out. And if it isn't out now, will it be out soon? How long do I wait for the clouds to clear? Then there is the dechiphering of the roman numerals on the dial, and the question of whether to adjust an hour for British Summer Time. Then comes the excitement of whether the sundiial is actually telling the correct time. The answer was usually 'no'. Even when a sundial is correctly calibrated for its longitude, there is also the thorny issue of the Equation of Time. It can still be out by as much as 16 minutes, depending on time of year.

Sundials at these houses usually came in two forms. There's the 'traditional' pedestal-style sundial, with a metal dial and a triangular piece of metal (the 'gnomon') sticking up by which to cast the shadow, and there's the wall-mounted sundial. Here's the wall sundial at UWA. It's marked out in terms of 'hours till sunset', making it pretty useless in terms of telling the time, but a bit more exciting than normal. It's complemented by a beautiful swan weather vane which, given the usual predictability of the winds, also doubles as a time-piece in summer.

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Now, here's an interesting question about wall-mounted sundials. Besides from having to be mounted on south or north facing walls depending on hemisphere, an obvious disadvantage would appear to be that  they will only be in sunlight for a maximum of 12 hours a day, even in summer. But that is not actually true. It may seem odd, but it is possible for a wall-facing sundial to have more than twelve hours of sunlight per day. That comes down to the inclination of the earth's orbit to the equator.

I remember this point being inflicted on us with delight from our lecturer in our first year at university. We had a computing project to do (in FORTRAN77 - remember that?) and the task that our sundial-fanatic of a lecturer got us to do was to plot out the markings for a wall-mounted sundial given its latitude (that way everyone got a different task so we couldn't copy each other's results). Fortunately he did provide us a nice formula for the angles of the various markings, but programming it was still a bit of a mission. I was very relieved to come out of it with a good result.

What I did learn, in addition to some FORTRAN and trigonometry, is that there is more to the sundial than meets the eye.

 

 

 

 

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A couple of hours ago I gave a talk to the 'education group' in the Faculty of Engineering and Mathematical Sciences at the University of Western Australia. Broadly speaking, the audience was a group of physicists and engineers who are interested in education.

I recycled a talk that I'd given a couple of years ago on the role of mathematics in physics - specifically comparing and contrasting how practising physicists and students think about how maths works within physics.

My conclusion from the research I've done (based on interviewing students and physicists (you can read it in the Waikato Journal of Education here) was that many students find the statement 'Physics is a science' difficult.  They would rather prefer to re-write it as 'Physics is applied mathematics'. 

Now, by science here, I mean a body of knowledge based on a systematic, empirical observation of the world. A body of knowledge that is able to generate testable predictions and then accept or reject or refine hypotheses in light of the results of experiments.

I (too naively) assumed that my audience wouldn't need convincing that physics is a science. Actually, there was some debate on this. One person in particular, a physicist in fact, presented the view that physics is not a science. Biology and Chemistry fit my description of science - being based on experiment - but physics, in its actual outworking, does not. His argument was that the greatest advances in physics have been theoretical and not based on experiment. Quantum mechanics and general relativity are highly theoretical - drawing intensely from mathematics - and any experimental validatiton of them came long after the theory was accepted (and, in the case of Eddington's eclipse data, quite possibly fudged). One might put the Higgs Boson into the same category - I suspect that most physicists never doubted that the Higgs Boson would eventually be discovered. That is to say the physics was not based on experiment - the experiments were merely confirming what physics 'knew' already. Who is the most famous physicist?  Albert Eintein - who never did an experiment in his life. But clearly he was a physicist, not a mathematician.

BUT, his was not the only view. For example, Einstein, the theoretical physicist, obtained his Nobel Prize for his explanation of the photoelectric effect. This was an observed phenomenon that had puzzled physicists - results just didn't fit with the understanding of the time. And what about the ultraviolet catastrophe?  So theoretical approaches were not made in the absence of experiment - there were some uncomfortable phenomena around that were prompting thinking.

So, back to my point. "Physics is a science" being uncomfortable for students of physics. It is clearly not just students that find this uncomfortable.  Is that a reason why, perhaps, the University of Western Australia has now moved 'physics' out of the Faculty of Science and put it in with engineering (which Waikato did many years ago)?

And, if physicists can't agree on what physics is, what hope is there convincing students that they should study it? Maybe I should just surrender and become an engineer.

 

 

 

 

 

 

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I came across the following on the BBC website  "Australia's summer broke 205 records..." It draws from the recent Climate Council report. The BBC article doesn't list them all 205 of them, but does pull out the most impressive - the hottest summer on record for Sydney, Brisbane and Canberra,  and the wettest on record for Perth - a whopping 193 mm.

Let's put 193 mm over 3 months into perspective. Hamilton, NZ, gets (according to metservice.com) 280 mm of rain on average over December to February. A Perth record-breaker would still be called a dry-ish summer back at home. But locally, Perth averages 40 mm over the three months. Also, of that 193 mm, the majority fell in just one day, soon after we arrived here - 112 mm fell on 9 February. That's a pretty wet day anywhere, but it wouldn't be threatning any records back at home.

What I love is the sudden jump in the Bureau of Meteorology's mean February rainfall data. When I wrote my post on 9th February, the mean February rainfall (averaged from 1993 onwards) was 8.5 mm.  It now stands at 13.5 mm.   When you have low values, averages can fluctuate considerably.

There's been another noticable weather failure for Perth this summer - one that is rather disappointing as a physicist. Take a look at the 3pm wind statistics chart, to be found here.  The wind is utterly predictable. At 3pm, it blows from the south west. This is the famous 'Fremantle Doctor'  (Fremantle lying southwest from Perth city centre) - a classic sea breeze produced by the rapid heating of the land generating rising air, pulling in the cooler air from the sea. The doctor brings relief from the otherwise soaring temperatures, and makes summer afternoons tolerable.

Except this year. We have experienced very little of the 'Doctor'. It's been rather disappointing, really. Where has he gone to?  And will he be back next year?

In a country 'defined by heat', as the climate council report states, climate change is a BIG issue.

 

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As part of our trip southwards last week, we visited one of the many caves scattered across the Margaret River region. The immediate impression on entering the 'Jewel Cave' is its vast size. It's hard to estimate just how big the main cavern is, but as a rough guess maybe 100 metres by 50 metres by 10 or so metres high - probably higher in places. The guide told us we had walked nearly a kilometre on the tour and climbed up and down 500 steps as part of it. There's a lot of volume to it. 

The cave was discovered only relatively recently, in the 1950's (from my memory of what the guide said). What drew people's attention to something special was the 'blow hole' on the surface. There is only one natural way into the cave, through a pot hole that's conveniently (for the cavers) wide enough to get a person down, but not much wider. The original explorers had to lower themselves tens of metres down the pothole and then through the cavern, before they touched the ground. We, on the other hand, entered through a man-made tunnel in the side.

This pot hole used to (until the new entrance was built) blow out air or suck in air as the atmospheric pressure changed. A sudden drop in atmospheric pressure outside, for example, would create a pressure differential between the inside and outside of the cave, and the cave would expel air. With a vast volume inside and a pretty tiny hole to come out of, a small shift in pressure can create an intense flow of air at the pothole. it was this extreme flow of air in and out that suggested there was something very big down there, and that this hole was possibly the only way in.

A surprise was also how dry the cave was. The Margaret River region is not a dry area of Australia by any means, but there wasn't a drop of water visible. In fact, the water level has dropped considerably over the last 30 years,without any obvious reason. The cave shows evidence of large changes in water level throughout its history, but why is unclear. There are some hypotheses, such as the lack of a large bushfire above the cave in the last 30 years leading to more leaf litter than might be normal, but the reality is that this is an open research question. There's a lot of science to do here.

Oh, and the biologists can get excited too because there have been thylacine remains found here (Where a human can squeeze, so could an unobservant thylacine).

There's a lot more to this cave than meets the eye.

 

 

 

 

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We put our trust in someone else's calculations and measurements all the time. It's just part of the modern world. Cross a bridge, drive a car, use anything electrical, and we implicity trust that the people who designed it, built it, installed it and tested it have done their job correctly. Occasionally things go wrong and disaster strikes, but, by and large, the things we make use of in our lives work properly. 

That said, do you fancy trusting the people who designed and installed the ladder up the Gloucester Tree, at Pemberton?

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This was originally built as a fire lookout, amongst the majestic Karri trees of south-west Western Australia. But now it's a tourist attraction. People come to climb it, or to watch people climb it (as we did).  I was happy to go up to about rung four, but that doesn't really count.

Now, there must be some trees in Waikato that could benefit from such an addition. And to do so would require a bit of physics and engineering calculation and implementation. I reckon it would be a fantastic project for a student  to tackle - pick the right material (please don't poison the tree or choose anything that won't cope with the weather), work out the loading profile, worst case scenarios (e.g. what happens when two large people cross - one going up and one going down), tackle the safety and ethical issues, and so on. And then, to get a grade A+, the student concerned has to be the first to climb to the top!

 

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