My weblog ELECTRON BLUE, which concentrated on science and mathematics, ran from 2004-2008. It is no longer being updated. My current blog, which is more art-related, is here.

Mon, 27 Dec, 2004

Falling Objects in Nashville

I did not forget my physics and mathematics while I was away on my vacation. I took a couple of my introductory physics books with me and when I had extra moments, read some sections and took notes. My hosts in Nashville have the schedules of normal human beings, who go to bed around 9 or 10 at night. My life is nocturnal and inhuman, so this left me with many hours on my own to do what I wished, as long as I was quiet about it. So I set up my physics study in their den.

In the four years I have been studying mathematics and physics, I have not yet gone beyond the most basic classical mechanics. I feel I must apologize for this regrettable lack of speed and brilliance. I am doing physics study that I should have done in junior high school. But by junior high I was already so behind in math skills and ability that my life path was locked into art and humanities. It would take almost forty years until I resolved to acquire what I never had. I am using texts designed for middle and high school children, even including one which uses cartoons to instruct the reader: THE CARTOON GUIDE TO PHYSICS by Larry Gonick and Art Huffman. This cartoon book was actually recommended by one of my Friendly Scientists, and despite its childish format, it uses real math, without which there is no real physics.

My original resolution, inspired by my Fermilab epiphany, was to learn physics all the way to the advanced level practiced by the scientists I am in awe of. Given my very, very slow pace, it may take decades before I get to quantum mechanics, let alone string theory. It is frustrating for me to watch the science guys throw around all these formidable concepts about which I have no clue, but which seem to connect with the fundamental structure of the universe. It is entirely possible that no one except these elite professionals actually works with string theory, that there are no honest, non-pseudo-scientific individuals who learn it simply for their own curiosity.

But back to Nashville. It snowed in Nashville, when I wanly hoped that being in the "South" would bring me warmer un-winterly weather. So there was plenty of time for me to stay indoors and work on my physics. I use another, non-cartoon book called BASIC PHYSICS, A Self-Teaching Guide by Karl F. Kuhn. This is a workbook with very easy mini-problems and it is usually quite clear. But when it came to the question of air resistance and the acceleration of gravity on falling objects, I was in the winter clouds. Kuhn's book explains:

"As downward speed increases, so does air resistance. Thus, there comes a time when air resistance equals the weight of the object. At this speed, the object no longer accelerates, but instead it continues at the same speed.….The final speed attained is called the object's terminal speed. … When an object finally reaches terminal speed, the air resistance is equal to (its) weight. At slightly less than terminal speed, air resistance may be considerable, but it is less than the (object's) weight. The net force on the object is its weight minus air resistance. Since air resistance is less than the object's weight, the acceleration must be less than the acceleration of gravity."

This kept me pondering for hours. The first thing that puzzled me was how weight was different from acceleration. If "weight," as the book explains, is an object's mass times the force of gravity, a quantity measured in "newtons," then what is its weight as it is falling? I finally figured out that the object's weight remained the same, as long as it was near the earth's surface. But the acceleration, due to air resistance, would not be the full acceleration of gravity at any point in that virtual object's fall. This would be more apparent if you dropped a ball of sponge foam rather than a ball of stone. I suspect that a stone ball's terminal velocity (in the atmosphere) would be much closer to the full acceleration of gravity than a ball of sponge foam, which would rather quickly attain a rather low terminal velocity and would sail on air currents before settling to earth. Thus the folks in Galileo's time, and for many years afterwards, assumed that heavier objects fall faster than lighter ones.

No actual objects were dropped that night in my hosts' house, though I thought about it. I didn't want to wake them up. The cranking of gears in my head, though, was loud enough that I kept my door shut. Here I was faced with an equation where all the quantities were changing at every moment. It was Newton's second law, F = ma, but in the atmosphere the acceleration would decrease as the resistance increased. Gravity pulls on the object, making it go faster and faster, but air pushes on it more as it goes faster, making it go slower until it reaches terminal speed. But if it's heavy enough, and close enough to the earth, it won't attain terminal speed before it smashes into something on the ground. Or more specifically, the terminal velocity of ideas as the perplexed physics aspirant sinks into the pillows of the sofa in my friends' den. (thud)

Posted at 3:42 am | link

Why the Title?
About the Author
What this blog is about: the first post
Pyracantha Main Page

RSS Version


November 2014 (4)
October 2014 (16)
September 2008 (5)
August 2008 (5)
July 2008 (7)
June 2008 (4)
May 2008 (6)
April 2008 (5)
March 2008 (8)
February 2008 (9)
January 2008 (8)
December 2007 (9)
November 2007 (9)
October 2007 (1)
September 2007 (7)
August 2007 (6)
July 2007 (10)
June 2007 (7)
May 2007 (10)
April 2007 (7)
March 2007 (11)
February 2007 (10)
January 2007 (6)
December 2006 (9)
November 2006 (9)
October 2006 (8)
September 2006 (8)
August 2006 (10)
July 2006 (9)
June 2006 (10)
May 2006 (10)
April 2006 (8)
March 2006 (12)
February 2006 (10)
January 2006 (11)
December 2005 (11)
November 2005 (9)
October 2005 (10)
September 2005 (10)
August 2005 (12)
July 2005 (9)
June 2005 (10)
May 2005 (8)
April 2005 (7)
March 2005 (8)
February 2005 (9)
January 2005 (7)
December 2004 (7)
November 2004 (7)
October 2004 (8)
September 2004 (5)
August 2004 (9)
July 2004 (9)
June 2004 (8)
May 2004 (6)
April 2004 (13)
March 2004 (12)
February 2004 (13)


Cosmic Variance
Life as a Physicist
Cocktail Party Physics
Bad Astronomy
Jennifer Saylor
Thus Spake Zuska

Listed on Blogwise