I am still stuck on inclined planes. In order to find the force that keeps the object on the surface of the plane, that is, the normal force, I am supposed to do a calculation based on the sine of the angle of the plane's inclination. Diagrams of this process are provided in all my physics texts which deal with inclined planes. However, I was mystified by these diagrams (as I said in my last posting). The closest I got to something that made sense was at The Physics Classroom on their Inclined Planes section where the vector triangles were drawn out. But why would you multiply by the sine of the inclined plane, when the triangle side you wanted wasn't even on the diagram?

You know by now that if something doesn't make sense to me, I will go at it until I either solve it or go crazy. This time, I sensed that a geometric proof lay behind this drawing, with a lot of assumptions about equal (and opposite, according to Newton) quantities and parallel lines. I lugged out my geometry and added another triangle superimposed on the original ones, made out of the vector lines that described the "normal force" and its perpendicular "parallel force." Then I cranked out a proof that showed me that the same angle of inclination reappears in that superimposed triangle where its sine will actually deliver the proper measurement for "normal force." It is just about impossible to demonstrate geometrical proofs in a written Webjournal like this one, so you'll have to take my word for it. Now I'm satisfied that this works, and I can go on to do as many vector and inclined plane problems as I can find.

I am still fascinated, and somewhat dubious, of the evident fact that abstract diagrams which express quantities in length of lines can say anything about the real behavior of mass in gravity, moving down an inclined plane or anywhere else. It all goes back to old Pythagoras, one of my favorite philosophers and scientists of all time. He was one of the first in the West to prove that the natural world can be described with mathematics. Every time I do vectors and geometry, I owe something to Pythagoras, his predecessors in the ancient Middle East, and his successors in the Mediterranean. The idea that the world has a mathematical order, in which things can be discovered by doing abstract calculations, is still a new concept to me, even if it is more than three thousand years old.

The Day the Music Died

Today, Sunday February 27, is the last day that my local public radio station will play classical music. It has been switched to an all-talk, all-news format. I am devastated by the change, a sell-out which was done purely for monetary gain. It is a betrayal of all that I expect from public radio. Because of this, I have decided never to give any money to that station again.

I will instead spend my money on gadgets and services which will allow me to connect to Internet radio, or download music files to a portable player, but it won't be the same. There is still one classical music radio station left in my area, but it chops classical music up into little bits to fit a pop music format with noisy, obnoxious ads. Now that classical music and commentary is gone from this radio station, I feel as though I have lost a dear friend or even a family, because their broadcasting was more than classical music. It was music-loving announcers with quiet, comforting voices, telling us interesting facts about music as well as weather reports and a few comments here and there. It is one less quiet haven in a world which is too often, for me, a place of screaming sonic assault.

Posted at 3:30 am | link