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April 2013 Archives

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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 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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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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 Happy Easter everyone. Sorry for lack of blog activity - lots of marking has been building up that I've needed to get through. 

Yesterday we experienced the vacuum-packing ability of a clip-container in a microwave. In this case, it was being used to cook some vegetables for Benjamin's dinner. The veges were placed in the microwave, the lid put on, and then zapped for a few seconds. The problem was then taking the lid off, since it had sealed tightly shut. 

I've had a comment on my blog about this before, from someone who's experienced it. I think what's happening is that, as the contents heat up the air inside expands. It is able to push it's way out through the seal. The mass of air on the inside is then rather less than what it was to start with. Once the heating has stopped, however, the temperature reduces and the air contracts. However, this time the seal doesn't let air back in - instead the lid is sealed and the air inside reduces pressure. Consequently we are left with lower pressure on the inside than the outside.

Just how big a pressure difference do we have? Suppose the air inside is heated to 100 C, as opposed to the 20 C that it is on the outside. At constant pressure, volume scales as absolute temperature, so we have a volume increase of about (100 + 273) / (20 + 273) =  1.27 times. That is, about 30% of the air is pushed out in the heating process. This air doesn't get back in during the cooling. Therefore, once cool, the container has 30% less pressure inside (pressure being proportional to volume at constant temperature).

What does this equate to in everyday terms? Air pressure is about 100 kPa, meaning a force of 100 thousand newtons over an area of 1 metre squared. 30% of this would be 30 000 newtons over a metre squared. Since a kilogram weighs about 10 Newtons, that's about the equivalent of 3000 kg spread over a metre squared. 

Now, the little container wasn't a metre squared in area. It's about 10 cm times 6 cm (approximately) , which is 60 cm2 or 0.006 or a metre squared. Multiply that by 3000 kg per metre squared, gives us 18 kilograms. That is to say, the force due to the air pressure is equivalent to sticking about 18 kg of mass on top. Little wonder it was tough opening. 

This calculation has a few assumptions in it, not least that the air had cooled back to room temperature (it hadn't). The reality I think is that it would be rather less force. I managed in the end to get a flat knife under the seal and let some air in - that got the lid off. 

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