## Galileo and the Leaning Tower of Pisa

Galileo Galilei is reported (see addendum) to have dropped a ten-pound weight and a one-pound weight off the Leaning Tower of Pisa, and proved that both fall at the same speed. Of course, a more general principle was being demonstrated, the fact that objects of any weight fall at the same speed (with the same acceleration, actually). Does this experiment fit the bill? Does it, in fact, prove that objects of any weight fall with the same speed or acceleration?

At first thought, since Galileo (or anybody) could not measure speeds with perfect accuracy, he could never prove that these two weights fell with the same speed. But, the alternative hypothesis, predicted by Aristotle, was that the ten-pound weight would fall ten times faster than the one-pound weight. Galileo clearly shattered Aristotle's hypothesis. And the experiment was more or less proof of Galileo's hypothesis.

Aristotle was not a person to perform experiments. The folks back then believed that all knowledge could be deduced from basic principles. Well, Galileo also based his hypothesis on basic principles. Let me describe how I reason it out. Let's say that you have three identical one-pound weights, side by side. You drop all three, and they all fall at the same speed, being identical. Then you link two of them together with a spider web. Is this now a two-pound weight? When we drop the three weights, will the two linked by the spider web now fall twice as fast? I doubt it. If we link them with a string, will they fall twice as fast? With several strings, with glue? It seems to me that when we attach two weights with glue, that they are still two weights falling at the same speed that they did when they were separate, and that ten of them (a ten-pound weight, in other words) would still fall at the same speed. Galileo was bright enough to confirm this with experiments.

We all know that some objects (a feather, for example) fall much slower. The metal weights were dense enough that gravity overwhelmed air resistance. Galileo was performing an experiment about gravity. Air resistance was merely a small complication which could be ignored. In the absence of air (in a vacuum), the feather falls at the same speed as a ten-pound weight. Astronauts on the moon performed this experiment, and the feather fell at the same rate as a metal weight. Actually, that experiment has been performed thousands of times, by students, in partial vacuums here on earth.

Some people criticize the formulas and laws of physics, for applying only to idealized conditions. In physics, you hear the phrases, "ignoring air resistance," or "ignoring friction," or "ignoring outside forces," etc. Well, a formula or physical law which takes into account all possible forces, is often so complicated that it becomes useless. Instead, you start with the simple law, like Galileo's hypothesis above, and then make small corrections for the outside forces, if you have to. Then, you get a much more basic understanding of the principles involved.