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Mostly Mozart


Posted April 8, 2001

You're listening to Kootenay Co-op Radio. CJLY Nelson, 93.5 fm. This program is Mostly Bluegrass. I'm your host, Tom Clegg. Tune in every week at this time to hear all manner of bluegrass, from bass solos to ballads. If you don't like bluegrass music, you should listen anyway, because during intermission, I will be reading to you from my unrivalled collection of obscure facts about science.

Mostly Bluegrass is sponsored by Comfort and Joy, a unique children's store.

Eureka! I've got it! Eureka is Greek for "I've got it." That's what Archimedes said as he became the first recorded streaker in the western world, 2200 years ago in Syracuse. The one in Greece, not the one in New York.

Archimedes was about to take his monthly bath when he unexpectedly solved the riddle he was working on. He was looking for a way to determine whether a gold coin was really pure gold, or whether it was an alloy of silver. As he stepped into his bath, and the water level rose, as it always does, he realized that he could measure the volume of the coin simply by dunking it in a cup full of water, and measuring the water that spilled over the top. The volume of water spilled would be exactly equal to the volume occupied by the coin. He could repeat this experiment with an equally heavy piece of solid gold, and compare the results. If the suspect coin displaced more water than the real gold piece, then it was less dense than gold, and it was therefore... not gold.

The idea that a one litre ball displaces one litre of water may not seem like an especially insightful contribution to modern science, and that's probably why it's not called the Archimedes Principle.

There is something else called the Archimedes Principle, though, and that happens to be what Shannon called to ask me about last week. How come some things float and some things don't?

Well, the simplistic answer would be that some things are lighter than water and some things are heavier. Wood floats because it's lighter, and stone sinks because it's heavier. But steel is heavier than water, and they make ships out of steel. And they float. And if you think you've got it all figured out, and they only float because they're full of air, then tell me this: how can I make a steel box full of water float across the ocean?

If you stick around for the rest of the show, I'll tell you how to do that, and what the Archimedes Principle really is.

And before the music starts, I just want to make sure that you're not confusing Archimedes with Achilles. Achilles was the one with the Achilles heel. As a child he was dipped into the River Styx, which was supposed to make him immortal, and his skin was supposed to become spear- and arrow-resistant. When he was dipped, of course, someone had to hold onto him by his ankles, so his ankles didn't make contact with the magic water, and they weren't protected. So the only way to kill the guy was to go for his ankles. So that's what the Romans did. Or something like that.

So your achilles heel is the weak spot in your armour; and your achilles tendon is the huge tendon on the back of your leg that inserts into the back of your heel. But anatomy makes me queasy, so I won't tell you why achilles tendonitis is commonly caused by over-pronation, or anything like that.

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I hope you are enjoying my new musical theme. Please feel free to call me at 352-3706 if you have any comments about the show, or if you have a topic you'd like me to address on a future episode.


You're listening to Mostly Mozart on Kootenay Co-op Radio, CJLY 93.5 fm in Nelson. My name is Tom Clegg and this show is once again called Mostly Mozart.

Mostly Mozart is sponsored by Comfort and Joy, a unique children's store.

The Archimedes principle explains floatation using the same idea of rising water levels that I mentioned earlier. The logic goes something like this.

When you get into a bathtub, the water level rises. When you get out, it goes back down to its initial level. Obviously, gravity is at work here. When you get out of the tub, gravity pulls the water down. That means that while you're in the tub, you are effectively pushing the water upwards, against the force of gravity.

But where does that force come from? It doesn't feel like you're pushing water upwards when you're sitting in the tub; in fact, it can be quite relaxing, if the water is warm enough. It doesn't take much of a leap to conclude that the force comes from your own weight. Gravity pushes you downwards into the water, and the further down it pushes you, the further up you push the water.

We've already covered the idea that the volume of water displaced is equal to the volume of the object that is displacing it. So if your leg occupies 20 litres of space, and you put your leg in the tub, you will lift 20 litres of water in the process. The force required to lift 20 litres of water is, by definition, the weight of 20 litres of water. So in order to submerge your leg, you have to apply a force equal to the weight of 20 litres of water. In other words, when your leg is underwater, it feels an upward force equal to the weight of 20 litres of water. Whether your leg floats depends on whether that upward force exceeds the downward force of gravity.

The Archimedes Principle is simply that: the upward force felt by a submerged object is equal to the weight of the displaced water. If the upward force is greater than the object's weight, then the object floats. If it's less, the object sinks.

Consider how ice floats. As I mentioned on my last show about water, ice is slightly lighter than water because it expands just before it freezes. Let's say a 1.1 litre block of ice weighs the same as 1 litre of water. If the ice is totally submerged, it displaces 1.1 litres of water. This is a greater force than the gravity acting on the ice, so the net force is upwards. The ice will rise to the surface, and when it's just poking its head above water, the downward force will be equal to the upward force. And you'll see the tip of the iceberg.

So the trick to floating is to find how many litres of water you need to equal your own weight, then simply make sure that you take up more space than that much water. This is how boats work. A fifty pound boat filled with air takes up way more space than fifty pounds of water... so it floats.

And while we're on the topic of icebergs: there are two kinds of ships. Ones that can sink, and ones that can't. The Titanic was the first kind. Your canoe is the second kind. The difference is in how they ensure that they occupy more volume than their own weight in water.

The Titanic did it simply by having lots of air inside. The trouble with this is that when the hull breaks, water gets in, and fills up all the space where the air used to be. Now it's just steel against water, and steel is heavier, so the ship sinks.

Small boats like canoes tend to use a different approach. They can float even if they're filled with water, either because they're made of wood or some other material that's lighter than water even when soaked; or they might be made mainly of heavy material but also have big chunks of styrofoam, or sealed air pockets, or something like that, so that the average density is less than the density of water.

So, how does water float on water? Well, that's just a word game. Salt water is heaver than fresh water. So if the steel is thin, and you maximize your ratio of volume to surface area by making a spherical box, then it's quite easy to make a steel box of water that floats. You can tie a string to it, and use it to test whether you're in salt water or fresh water.

Hey, I never said you would learn anything useful on this show...