Elementary chemistry

I named 50 out of 118. That’s not as bad as it sounds, once it’s fairly evaluated. First, there’s extra credit for naming Francium. Then, we all know that nothing over 100 really counts. We never talked about the transition metals in class, and a bunch of the other so-called elements are just stoopid (Lanthanides? yeah, right…). I should also get extra credit for posting about it here. So with the curve, 50 is a solid ‘B’.

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Galileo

I assigned this the other day:

Galileo drops from the top of a tower a rock weighing 15 pounds. The speed s of a falling object is given by the formula s=\sqrt{2gh}, where h is the distance in feet the object has fallen. g is the acceleration due to gravity, about 32 feet per second per second. At the base of the tower the rock hits Aristotle at a speed of 80 feet per second. Estimate the height of the tower.

This gives the students a word problem involving square roots, practice applying a general formula to a particular case, and a lesson in physics and history. Someone will try to use 15 somewhere, and so allow me to say Aristotle made the same mistake. Galileo gets the credit for finding that the weight of the object has nothing to do with its speed. Finally it lets me point out that although Galileo was right, he was kind of a jerk.

The details are more complicated. Aristotle of course was no dummy. To the extent I understand it, he was considering a different set of questions. He may have understood motion as an interaction between the falling body and the medium through which it falls, and overestimated the density of air. “A heavier body falls faster than a lighter one of the same shape in a dense medium like water, and this led Aristotle to speculate that the rate of falling is proportional to the mass and inversely proportional to the density of the medium. From his experience with objects falling in water, he concluded that water is approximately ten times denser than air,” says the Wikipedia article on Aristotelian physics. For anything involving Galileo I would want to verify the sources. The Order of Nature in Aristotle’s Physics, by Helen S. Lang, looks like a place to start.

Some people say that it was really Giambattista Benedetti who found out heavier and lighter balls fall at the same rate. I suspect that science then was like science now. Lots of people knew how things worked in practice. Children had been successfully throwing and catching balls for some time. Men heard about Galileo and thought, “Yeah, no kidding. How much did it cost to figure that out?”

Coincidently, Doc Rampage has the top search result for Aristotlean physics.

Helping with homework

“It often happens that two schoolboys can solve difficulties in their work for one another better than the master can. When you took the problem to a master, as we all remember, he was very likely to explain what you understood already, to add a great deal of information which you didn’t want, and say nothing at all about the thing that was puzzling you. I have watched this from both sides of the net; for when, as a teacher myself, I have tried to answer questions brought me by pupils, I have sometimes, after a minute, seen that expression settle down on their faces which assured me that they were suffering exactly the same frustration which I had suffered from my own teachers. The fellow-pupil can help more than the master because he knows less. The difficulty we want him to explain is one he has recently met. The expert met it so long ago that he has forgotten. He sees the whole subject, by now, in such a different light that he cannot conceive what is really troubling the pupil; he sees a dozen other difficulties which ought to be troubling him but aren’t.” — C.S. Lewis, in the introduction to his Reflections on the Psalms