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September 2015 Archives

A colleague remarked to me yesterday, as we were trudging up the two flights of stairs from the tea-room to the third floor, "I'm sure they turn up the force of gravity in this building each year." I feel like that too, sometimes. However, I suspect it has more to do with the aging process that any changes in physical constants. 

But...what if...? What would life be like if gravity were say, double what it is now. How different would life be? There are many ways of tackling that question. So I'll phrase it in this way. Imagine that there's another universe in which a similar-sized and atmosphered Earth exists, but where the force of gravity is double what it is in this universe. What might life look like on that Earth?

First, I need to say that the 'Earth' itself would be different in many ways. The atomosphere could be very different, the structure of the earth very different, the shape and size of mountains very different, etcetera etcetera. But let's narrow it down, and suppose the Earth itself is the same, It's just the force of gravity that's different. What would people look like? (Again, assuming this new Earth evolves people). Well, we'd need stockier legs. Why? If we double our weight, we'd need more surface area in our leg bones to support it. We'd start looking more like elephants. 

But, that's just one option. An alternative is that double-gravity-Earth-humans could look exactly like our-Earth-humans, but with all our dimensions halved. (Yes, with a bucketful of assumptions.) How does that work? The stress in our shin bones would be given by the weight supported by the bone, divided by the area squared. Now, our weight would scale as the force of gravity times our volume; the latter scales with our dimension (e.g. height) cubed. But the surface area squares as our dimension squared. So the stress in our shin bone would scale with gravity times dimension cubed divided by dimension squared, which is gravity times dimension. If gravity doubles, and our dimension halves, we our back to the same stress. So, our sister-beings could look exactly as we do, but just be half our height (and half our width). Rather like hobbits, minus the furry slippers. 

However, that's not the same thing as saying that life for them would be the same, just on half the scale.  Let's consider the double-gravity-Earth-Olympics. Would they be able to do the same sports that we do, just at a different scale? At first glance, it might seem yes. Take running. Half the size, and (roughly speaking) you'd expect them to run slower than us - they cover less ground with every leg swing. (Although they'd also be able to swing their legs quicker.)  So they'd still be able to have running races, but for them the 100 m would seem like a longer distance than it would for us. To compensate for this, they'd make their track a bit shorter.

But what about the pole-vault? This event is a great example of physics. The faster you run with the pole, the more it bends when its planted in the... what is it called?....and the more spring force upwards it gives you. Basically, it comes down to kinetic energy of the athlete being converted to gravitational potential energy, via elastic potential energy in the bent pole. How would this work in the double-gravity-Earth-Olympics?

Let's just estimate the height one can pole-vault by a simple equating of kinetic energy to potential energy. That gives us mv2/2 = mgh, or h = v2/2g, where m is the athelete's mass (note how it cancels in the expression for h), v is his or her velocity on the run,  g the acceleration due to gravity, and h is the height they vault  to.  If we double g, h will halve, so long as v stays the same. But  our diminuitive sister-humans will be running slower than us. So v doesn't stay the same, it's lower. With g doubling, that means h, the height of the vault,  is more than halved. So, measured in terms of how many times their height they can vault, it will be less that us. The pole-vault event isn't then just a halved copy of ours - it would look different. 

One can take this line of thinking a whole-lot further still. In a double-gravity-Earth-Rugby-World-Cup, Namibia would be hot favourites, for example. But I'll leave it there.

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I read the 'Rental Nightmare' article on stuff.co.nz last night. Some of the stories are horrific indeed, and I'm reasonably confident that the writer has deliberately sought out the worst situations rather than the most common situations. But one cannot deny that a great deal of housing in New Zealand is sub-standard. In housing-deficient Auckland, in particular, families are forced into cold, damp homes because there is nowhere else they can afford. 

I've been in NZ eleven years now, and I have still to wrap my head around why this is. It seems that up to the 1970's, houses were designed with three underlying assumptions: 1. New Zealand has a warm climate, 2. New Zealand has a dry climate, 3. Everyone needs a large, detached house. While the first is arguably true for parts of the country for parts of the year, the second is true almost nowhere and unfortunately the consequences of the third are coming home to roost as Auckland has to struggle with the concept of high-denisty housing inside the city or yet more expansion on its already sprawling fringes. 

So New Zealand is left with uninsulated, poorly ventilated, high-surface area housing, in which we put our most vulnerable families. 

Back to the article. As I said, I expect sensationalization in an article like this. But I do take issue with the comment from Andrew King, whom the article says is representing the Property Investor's Federation. The article reports him as saying (note that this is the words of the reporter, not Andrew King's direct words):

He says tenants often do things that encourage mould, such as not heating homes and drying clothes on clothes racks.

Not heating your home isn't clever. But there's only so much money you can fork out on power bills, and when the house isn't insulated the benefit you get per dollar spent on heating isn't high. So it's not at all surprising that some houses are left unheated. Money is better spent elsewhere. 

But drying clothes on clothes racks? Where do you expect people to dry them? Outside on a washing line? Try doing that in Hamilton yesterday, or, I suspect having seen the forecase, for the next week. What about in a dryer? First, that assumes the tenants can afford to run a dryer, and that, secondly, the dryer is properly vented to the outside of the house. Putting a hole in the wall for a permanent vent is the landlord's job. How many of them make that a reality? Venting the air into a room puts the same amount of moisture into the room that drying on a rack would do - but in a much shorter space of time. 

So what's the problem with drying clothes? Imagine a load of washing that leaves your machine after a wash and spin. How much water does it contain. A large load might contain around three kilograms of water. (That's my estimate based on the weight of the laundry basket when laden with wet clothes compared with when the clothes are dry.) All that water needs to evaporate. How much air is needed to do that?

Let's assume you are drying at 18 Celsius (in a student flat in Dunedin in winter, yeah, right). How much water can the air in a room hold? Consulting a psychrometric chart, you can see that at a relative humidity of 100% (the air holding as much water as it can) air can hold about 13 grams of water per kilogram of dry air. Roughly speaking a kilogram of dry air is about a metre cubed (1000 litres) in volume, so that's about 13 grams of water in a thousand litres of air. So to soak up say three kilograms of water, you need about 250 thousand litres of dry air. The ambient air almost certainly isn't dry - if it's a relative humidity of 70% outside, the air is already containing 70% of all the water it can hold. So that boosts the requirment to around 800 thousand litres of air needed. Call it a round million litres of air to dry your load of washing.

Now, a small room (3 m x 3 m x 2 m) would be about 20 metres cubed, or contain about 20 thousand litres. You need therefore about 50 rooms-worth or air to provide enough capacity to suck the water out. If you dry your clothes in that room (and they will dry eventually) it helps considerably if the room is well ventilated. That allows the damp air inside to exchange with the slightly less damp (this is Hamilton) air outside. 

So where does condensation come from? Let's suppose you hang out your clothes on a rack on an 18-degree cloudy afternoon, with 70% relative humidity. Your house is uninsulated (and unheated), so it's also 18 degrees inside your laundry-room. You won't get condensation. The psychrometric chart will tell you that the dew point is about 15 C - that's the temperature below which air of this humidity will start dropping its water content. Your walls are at 18C so it's not a problem. But as you head through the night, the temperature outside drops. The clouds clear, and you go down to 5 Celsius, say. Your house is uninsulated, and your interior walls find themselves at 5 Celsius, with a room full of moisture laden air. The walls are well-below dew point, and now the water condenses onto them. 

The problem then? The house is uninsulated and poorly ventilated. Fix the fundamental problem (a bad house), the walls stay above dew-point, and then there is no reason why you shouldn't dry your clothes inside when it's a damp day. 

 

 

 

 

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I had a conversation with a class this morning regarding the labelling of axes on graphs.In particular, how we should indicate the units. Most quantities we deal with in physics carry units. A speed might be 35 km/h, a distance might be 16.8 mm, a pressure could be 28 kPa. Saying that a speed is 35 is wrong and meaningless. 35 km/h is rather different to 35 m/s or 35 inches/day. 

If we are plotting two quantities, for example to find a relationship between them, we need to indicate what units the axes are in. A typical way to do that would be to include the unit in brackets after the label. So if we are plotting a distance, we might label our axis 'distance (m)', with the '(m)' indicating that the numbers on the plot are in metres. But let's say we are dealing with small distances, such as the spacing between atoms in a crystal. Then nanometres (one billionth of a metre) would be more appropriate as units. So we could label our axis as 'distance (nm)', indicating the numbers on the plot are in nanometres. 

That's the easy, pragmatic approach an engineer might take. For the physicist, however, it is not rigorous enough. So the physicist takes the same plot, crosses out 'distance (nm)' and instead writes '109 distance / m'. 

How do we decipher that? (One of my students this morning suggested this was like a secret code physicists use to make sure their work is unreadable to anyone outside their area.) To a physicist or mathematician it's perfectly logical. Let's suppose we want to indicate on the plot a distance of 5.6 nanometres (that is, 5.6 x 10-9 metres). Then '109 distance / m' is just:

109 distance /m = 109 (5.6 x 10-9 m) / m = 109 x 10-9 x 5.6 x m/m = 5.6

We are left with our '5.6' to show on the plot. Note how the 109 at the front cancels the 'nano' within the nanometre, and the '/m' cancels the 'metre' within the 'nanometre'. It's easy and logical once you've got it, but if you haven't, it looks a unweildy and pointless mess. 

Really, it comes down to a physicist recognizing a unit for what it actually is  - something that the quantity is multiplied by - rather than a tag-on descriptor. I'm currently revising my presentation on preparing for the NZQA Scholarship Physics exam, which I'm giving again on Saturday (19th Sept). There's a deeply annoying question from last year's exam which says

By considering energy conservation, show that at the lowest point of the jump, mgh = 1/2 k(23-L)2, where h is the change in height of Emma's centre of mass. 

Why is that wrong? Yes, I do mean wrong, rather than just clumsy. L here is a length (the length of a bungy cord, as it happens). So what is 23-L?  The 23 is dimensionless - something dimensionless minus a length makes no sense (unless we go into geometric algebra where it is quite reasonable but I really don't think that the examiners are wanting that...) It should say '23 m', or '23 metres'. "Ah", you retort, "but here we are using S.I. units, so m is in kg, g in m/s2, h in metres, k in N/m and L in metres. When we understand the units, there is no issue. 23 - L is 23 minus the number of metres that L is". That would be true, if the question had said this. But it actually says that 'h' is the change in height of Emma's centre of mass - i.e. it implies that h is dimensioned, it isn't just the number of metres that the height changes by. A similar statement tells us that L also is a length, and is therefore a number times a unit. 

You might think that is over pedantic, but it does betray some sloppy thinking regarding the nature of quantities on behalf of the examiners. 

So what should it say?  "... mgh = 1/2 k (23 m - L)2 ..." would be the way to write this. 

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This isn't physics but I do feel strongly about it. John Key today is reported by the New Zealand Herald today as saying, with regard to the refugee crisis:

It's a global problem. I accept everyone needs to take their fair share of responsibility but actually as a government we have been doing quite a lot over recent years and I have every confidence we'll do more in the future.

Has Mr Key done his maths on what is New Zealand's fair share of responsibility? Because it's rather more than the yearly 750 quota that I've heard reported as being New Zealand's current contribution. Just how many refugees have fled or are fleeing Syria alone. My understanding is that it's the majority of the population. OK, so I'm not a demographer, but I think 10 million is not an unreasonable estimate. How big is New Zealand on a world scale. Population about 4 million out of about 7 billion worldwide. Roughly speaking 1 in every 2000 people lives in New Zealand. What does 1 in 2000 displaced Syrians look like?  That comes to about five thousand people. It's an order of magniitude increase in what New Zealand is currently doing. That is just the Syrian contribution. With estimates of about 60 million refugees worldwide, we might reasonably up NZ's fair share to about thirty thousand people. I know these numbers are very rough but there's no doubt in my mind that NZ's current idea of a reasonable refugee intake is at least an order of magnitude too low. 

 

 

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So, I'm now back from a lovely holiday in the UK, following a not-so-lovely period of being sick. Quite possibly I can also get back to blogging. Among the great many emails awaiting for me yesterday were a few about school physics and university physics. They were coming from different sources for different reasons, but there was a co-incidental unifying theme which went along the lines of 'how well does school physics prepare students for university physics?, and how well does university physics prepare students for a career in science?'. 

First, the school-to-university transition. Here's a quick little piece by Peter Coles in  Times Higher Education, drawing from an Institute of Physics report on the male-female balance in 'A'-level physics. A key point he makes is that efforts by universities to recruit more women into physics degrees is rather hampered by the fact that the number of women doing A-level physics (i.e. the 'pool' that can be drawn from) hasn't increased over the last ten years. One can't admit a student who hasn't done 'A'-level physics, and if few of these are women, then the university will inevitably have few women taking the physics degree. 

But, as Peter Coles points out, universities set their own entry requirements. Who says that incoming students need 'A'-level physics? Does 'A'-level mathematics in fact provide at least as good, or maybe even better preparation for studying physics at university than 'A'-level physics? The male-female balance in mathematics is much better than in physics. Many university lecturers very vocally point out that incoming students are very much under-prepared for the mathematical rigour of a physics degree, and would like entry requirements on mathematics ability as well as physics. Peter Coles says they should go 'the whole hog', and in fact axe the entry requirement on physics altogether, leaving just the mathematics one. 

An interesting proposal. But it's not one that sits happily with me, because physics is not mathematics. It is a science. Having done some research on this, I know that the simple statement "physics is a science" is problematic for many students, who are much happier with "physics is applied mathematics". The experimental side of physics - the observation, making and testing hypotheses with experiments (what Eugenia Etkina was talking about at the recent NZIP conference) is something that many students struggle with. I suspect that this is because it is not well taught. 

Which brings me to the other point. "How well does university physics prepare students for a career in science". I've had some correspondence with the authors of a study that I commented on some time back on 'virtual labs' - which found that computer-based lab experiments were just as good in terms of supporting theoretical concepts than actual lab-based experiments, amongst bioscience majors at least. However, what the computer-labs can't do is to support learning outcomes connected with doing actual experimental physics work, such as learning how to put an experiment together, how to control for different effects, how to assess where equipment is failing and track down systematic uncertainties, and so-forth. These are skills that many (but not all) graduates will need if they have a career in physics. My own experience is that these skills have been learnt outside of the university system, when I've actually had to use them in a real situation. I would say very little of the experimental work I did at university was actually particularly useful in preparing me for doing science. But is that just because my university experimental work wasn't well taught (see the Etkina talk again!)

There are a great many questions here and I don't pretend to have a great many answers to match, but I do think they are things that we need to think carefully about. 

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