Skip to main content

The interesting history of stretchy and swingy

Now that's what I call a pendulum
(chaotic pendulum from Dice World)
Not surprisingly, science writers tend to focus on the exciting stuff. Apart from anything else, we get a lot of the less shiny bits at school, and most of us probably don't want to hear any more. You don't get far doing a popular science book on pendulums, say. But this is a bit of a shame, because science writing isn't just about explaining concepts, it's also about context, and the difference between the 'facts' of school science and the fuzzy reality of science as it truly is. So let's take the plunge.

Two favorites of the physics world are springs and pendulums, both examples of objects that undergo regular motion. Galileo is supposed to have first considered pendulums while watching a lamp swinging on a chain at Pisa cathedral. Up to then, no one had thought about the significance of a pendulum’s swing, because their ideas of motion were based on the ancient Greek concept of objects trying to get to their “perfect” place, the center of the universe. This was used to explain why items fell to Earth. But it didn’t help with something that oscillated like a pendulum.

What Galileo noticed, timing the swinging lamp with his pulse (possibly bored in a sermon), was that the time a pendulum took to swing wasn’t linked to the distance the object on the end of the pendulum travelled. Whether it made a long stroke or a short stroke, the time it took was the same. It didn’t depend on the weight on the end of the pendulum either, just the length of the string. At least, that's what they tell you at school. In fact this only applies to relatively small swings and goes out of the window for bigger ones. Galileo had a lot of interest in pendulums and inclined planes as they gave a way to study falling under gravity in a controlled way - despite the legend, the chances are he never dropped balls off the leaning tower of Pisa.

Pendulums were a breakthrough technology in making accurate clocks, but clockmakers soon found there was a problem – metal pendulum arms changed in length with the room temperature, and this resulted in variation in the timing (the swing wasn't small enough). This was overcome by using materials that don’t vary much with temperature, or by using a complex pendulum called a gridiron that linked bars of different materials whose expansion countered each other.

Springs also provide a regular, oscillating motion, provided they aren’t pulled too far. Springs (and anything else elastic, like a bungee) have a limit called the elastic limit. Pull them further than this and they transform permanently. Instead of returning to their original length when released, past the elastic limit they deform. But when springs are kept within the limits, they work according to a simple ratio discovered by Robert Hooke, one of Newton’s contemporaries. Hooke discovered that the further you stretch a spring, the more force you get. Double the stretch, double the force. Technically it’s a negative force because it goes in the opposite direction to the stretch.

Robert Hooke was on the receiving end of a barbed comment from Isaac Newton. Newton said in a letter to Hooke, “If I have seen further it is by standing on ye shoulders of giants.” This sounds modest, suggesting that Newton built on the work of others, and it is often how the quote is used. However, Hooke had a deformed back that made him seem small in stature. No one could accuse Hooke of being a giant and it seems that Newton, whose certainly despised Hooke, was getting his revenge.

Comments

Popular posts from this blog

Why I hate opera

If I'm honest, the title of this post is an exaggeration to make a point. I don't really hate opera. There are a couple of operas - notably Monteverdi's Incoranazione di Poppea and Purcell's Dido & Aeneas - that I quite like. But what I do find truly sickening is the reverence with which opera is treated, as if it were some particularly great art form. Nowhere was this more obvious than in ITV's recent gut-wrenchingly awful series Pop Star to Opera Star , where the likes of Alan Tichmarsh treated the real opera singers as if they were fragile pieces on Antiques Roadshow, and the music as if it were a gift of the gods. In my opinion - and I know not everyone agrees - opera is: Mediocre music Melodramatic plots Amateurishly hammy acting A forced and unpleasant singing style Ridiculously over-supported by public funds I won't even bother to go into any detail on the plots and the acting - this is just self-evident. But the other aspects need some ex

Is 5x3 the same as 3x5?

The Internet has gone mildly bonkers over a child in America who was marked down in a test because when asked to work out 5x3 by repeated addition he/she used 5+5+5 instead of 3+3+3+3+3. Those who support the teacher say that 5x3 means 'five lots of 3' where the complainants say that 'times' is commutative (reversible) so the distinction is meaningless as 5x3 and 3x5 are indistinguishable. It's certainly true that not all mathematical operations are commutative. I think we are all comfortable that 5-3 is not the same as 3-5.  However. This not true of multiplication (of numbers). And so if there is to be any distinction, it has to be in the use of English to interpret the 'x' sign. Unfortunately, even here there is no logical way of coming up with a definitive answer. I suspect most primary school teachers would expands 'times' as 'lots of' as mentioned above. So we get 5 x 3 as '5 lots of 3'. Unfortunately that only wor

Which idiot came up with percentage-based gradient signs

Rant warning: the contents of this post could sound like something produced by UKIP. I wish to make it clear that I do not in any way support or endorse that political party. In fact it gives me the creeps. Once upon a time, the signs for a steep hill on British roads displayed the gradient in a simple, easy-to-understand form. If the hill went up, say, one yard for every three yards forward it said '1 in 3'. Then some bureaucrat came along and decided that it would be a good idea to state the slope as a percentage. So now the sign for (say) a 1 in 10 slope says 10% (I think). That 'I think' is because the percentage-based slope is so unnatural. There are two ways we conventionally measure slopes. Either on X/Y coordiates (as in 1 in 4) or using degrees - say at a 15° angle. We don't measure them in percentages. It's easy to visualize a 1 in 3 slope, or a 30 degree angle. Much less obvious what a 33.333 recurring percent slope is. And what's a 100% slope