November 23, 2017

Galileo And The Way Things Really Move

 

I had never been a fun of non-fictional books but as the years went by I found myself picking up more books that fall under this category and finding them an enjoyable read. Most of these books were read on recommendation and one such great read was “The Ten Most Beautiful Experiments” by George Johnson, describing experiments that discovered what we may now consider basic science. Some of the experiments described were new to me, all the experiments were indeed beautiful and I couldn’t help but acknowledge the intricate and delicate designs of these experiments. So here is my take on one such experiment Galileo Galilei as described by George Johnson in the chapter “The way things really move“.

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THE MAN

The first born in a family of 6 and another great scientist who acknowledged the co-existing truth in both scientific literature and biblical scripture, Galileo is sometimes referred to as ‘The father of modern science’. Before his death in 1642 his contributions to science passed him off as a physicist, astronomer, mathematician and philosopher. Some of his notable contributions include discovering the four largest satellites of Jupiter, building an early stage thermometer, improving the design of telescopes and the observation of sunspots (presumably using his improved telescope designs). In addition to his great scientific achievements, he was also an accomplished musician, a talent that will later prove useful. However long before he started studying stars and getting into trouble for promoting the idea of a heliocentrism, he was studying the movement of objects. This is where his contribution to ‘Beautiful experiments’ is drawn from.

 

THE PROBLEM

Aristotle had previously proposed that an object falls in relation to its weight, that is to say, the heavier an object, the faster it falls. As sensible as this sounds anyone who paid attention in science class remembers that this is wrong even if the details are a bit fuzzy. For example, if you drop a 100 pound cannon ball and a 1 pound musket ball, even though the cannon ball weighs a 100 times as much as the musket ball, it does not fall a 100 times as fast. Actually, the timing between the two objects hitting the ground is pretty close and Galileo made note of this, arguing that factors such as wind resistance need to be considered.

We all appreciate that any object will increase in speed as it falls but this also raises a bunch of questions; Do objects of different weights equally increase in speed as they fall? Does the speed increase all at once at the beginning or steadily until the object lands? How about a huge burst half way down?. Although these are all genuine questions that drove Galileo, the real question is how can this be tested?.

Really now? lets go back a few centuries and try it again.

However take away all the fancy tech we have today and ask the real question; How do you measure the speed of a falling object if you found yourself in the year 1604 with no time lapse videos, stopwatches, Wikipedia or whatever modern technology was involved in your idea? Galileo set about to answer these questions armed with nothing more than a bronze ball, a fancy plank, ”apparently” a water clock (like an hour glass filled with water) and his musical skills (this makes up the beautiful part).

 

THE SOLUTION AND BEAUTY

The experiment in question here is discussed in one of his written pieces, ‘Discourse concerning two new sciences’. Galileo describes propping a 20ft long, 10in wide board at an angle and creating a smooth groove inside. A smooth bronze ball was then placed at the top of the groove and the time required to roll down from one end to the next was noted. After this the time required to roll various lengths of the board (quater, half, two-thirds and so on) was also noted.

Now the speed an object travels is calculated as the ‘distance’ covered divided by the ‘time’ it took to cover this ‘distance’. So here we know the ‘distance’ which is length of the board the bronze ball would have traveled, but how did he calculate the time? According to Galileo, this was done using a water clock (apparently). In this experiment, it was not important to measure time in terms of seconds and minutes. The most important thing was that the measure of time had to be constant (for example a beat or rhythm will work just fine). So for arguments sake lets just assume every drop of water from his water clock is the same as half a second. What he then did was scratch a tick on the board to show how far the ball had travelled with every drop of water (apparently). He then recorded the distance travelled by the time the ball reached each tick and recorded numbers that look just like this;

With his little set-up, he showed two things:
  •  Firstly, the distance between ticks made on the board increased as the ball rolled down. So the distance between ticks 2 and 3 will be greater than the distance between ticks 1 and 2. Surely we will expect this because we know the ball gains speed as it rolls down.
  • Secondly there was a rule which could predict how much this distance increased between every pair of ticks. So once you know the distance travelled between ticks 1 and 2, you will be able to predict the distance that will be travelled between ticks 2 and 3. This rule did not change even when the angle of the propped up board was increased or decreased, so you will expect it to also be true if the ball fell straight down rather than roll.Basically he explained how gravity increases the speed of a falling object.

So what was the rule that predicted how an object gained speed when falling? Its known as the times-squared law. Rather than explain, you can have a look at his original results with some added notes;

As ingenious as his measurements with the water clock may be, many scientist that studied his work after his death believed him to be fibbing (hence my constant use of the word ‘apparently’). Technically such an experiment using a water clock works, but it can have so many errors that it only really works with hindsight when you know what you are doing and looking for. So how did Galileo really measure times as small as half a second? Well if you remember, all he needed to do was find a way to divide time into equal portions, something that will come naturally to any good musician. Yes, Galileo’s talent on the lute will have been the secret to his accurate time measurements. Even non-musicians can notice when the timing of a beat is off. It’s like we all have this intrinsic clock which helps us to appreciate or criticise an orchestra, do the two-step or dance on time to a salsa beat.

 

THE LEGACY

One such scientist named Stillman Drake repeated Galileo’s experiments using the song ‘Onward Christian soldiers’ to establish a rhythm at two-beats a second and mark off his own measurements. Amazingly after a few tries it produced results similar to Galileo’s, proving that  this was a viable way to conduct the experiment without a stopwatch or water clock.

So if this was the f this was the initial method used to discover the times-squared law, why did Galileo not just say so? Well understandably, even now it will be considered silly to say to the world’s leading scientists that “I tested this law by singing a song while a ball was rolling down a plane and it proved quite exact”. Nonetheless, thanks to Galileo, the world of abstract mathematics was related to real life physical properties of motion. Thanks to Galileo we now know that all other things been equal, the speed at which an object falls is independent of its weight.

For all his efforts he has a few moons named after him, became a household name and even has the European global navigation satellite system named after him. Not bad for a man who spent the last years of his life under house arrest.