Don Kanner (Lane Tech HS Physics
Teacher) Helicopter Whirligigs, General
Relativity, and
Forces
At our last meeting John Scavo was wondering how the number of
blades on a propeller related to airflow and
Richard
Goberville had propeller whirligigs for all of us to take and
experiment with.
Don had collected all of the
whirligigs from the other Lane Tech teachers at SMILE
and modified them in an attempt to answer John's question.
Here is the data
table:
Helicopter Whirligig Data |
||
Number of Blades | Mass / grams | Result |
4 blades | 11.3 | hovers |
2 blades | 11.3 | hits ceiling |
2 blades | 5.8 | hits ceiling |
2 blades | 4.0 | hits ceiling |
2 half-blades | 9.5 | halfway up |
1 blade (balanced) | 9.5 | hovers |
Having just used Karlene Joseph's and Dan Caldwell's paper plate and marble centripetal force demonstration in his classroom, Don showed us how to illustrate a celestial object being pulled into a black hole (sparing no expense -- ha!) using a marble whirling around inside a the top of a 1 liter plastic pop bottle held vertically with its mouth pointed toward the floor. When one stops rotating the bottle, the marble continues to whirl around the inside until it falls out the mouth. In Einstein's General Theory of Relativity, gravity corresponds to a distortion (intrinsic curvature) of the space around a mass. We are thus led to following the question: Assuming that the mouth of the bottle is analogous to a black hole, what portion of the area near the mouth of the bottle best fits Einstein's description of space-time distortion?
Now who says that you can't teach about black holes in high school? Don referred to the classic film Frames of Reference by Hume and Ivey. The following description is adapted from information on the website of the Department of Physics and Astronomy of the University of Victoria (BC, Canada), [http://www.phys.uvic.ca]:
FRAMES OF REFERENCE (Educational Services, Inc., 1960) 25 min, snd, b.w.
Professors Patterson Hume and Donald Ivey of the University of Toronto demonstrate the behavior of a body under the force of gravity as viewed from different frames of reference and the behavior of a frictionless puck on a rotating table in the laboratory. Two excerpts from this film are also available which present the above material in a condensed form:
1. "Excerpt 1", 7 min. QA839 F7. Shows gravitational effects.
2. "Excerpt 2", 5 1/2 min. QA839 F72. Shows rotational effects.
PJ Comment: The idea of "tunneling into the center of force" is very old. Isaac Newton criticized the Descartes model of the solar system, pointing out that this would be precisely the outcome of that mode. The Bohr Atomic Model was roundly criticized during the period 1915-1925, because electrons in atomic orbits would be expected to "wind down" into the center of the nucleus, in a time of about 10^{-9 }seconds, because of the total power radiated by a free point charge q experiencing an acceleration of magnitude a. According to the Larmor formula
Finally, Don had a modified version of Gary Guzdziol's vacuum disk [mp111803.html]. By reducing the internal plastic disk's diameter, it was used as a washer for a nut on the end of an eyebolt to which a heavy cord was attached. Without the worry of string breaking, Don appeared to lift a stool with the device but left us wondering which force really lifted the stool.
Don also posed the challenge of how to get all the marbles to stay on a paper plate when the plate is rotated, as an extension of the lesson given by Karlene Joseph at the last SMILE meeting [mp111803.html]. Go for it, Don --- you're on a roll!
Leticia Rodriguez [Peck Elementary
School] Chemical Tests
Leticia brought in a tray of materials which we were to
categorize by their physical
properties of form, color and texture. She had put various types
of food
coloring close to these samples, so that SMILE participants
(role-playing as third
graders) could more easily distinguish them. We were permitted to
see,
feel, hear, and smell them, after being assured that these
particular materials passed
relevant safety tests. Here is a table summarizing our
observations:
Observations of Properties of Unknown Solids | |||
Color | Description: | (secret identity) | |
Red | crystals, crunchy, rocky, clean, clear |
sugar | |
Yellow | transparent ,solid, dull, white, powder |
alum | |
Green | solid, white, smooth, dull, perfume scent |
talc | |
Blue | crystal, solid, white, cracking, no odor |
baking soda | |
Orange | powder, no odor | corn starch |
Fred Schaal [Lane Tech HS,
mathematics] Unleashing
Complex Numbers
Fred extended the consideration of zeroes of quadratic
functions; ax^{2 }+ bx + c = 0 , which he began at
the last SMILE
class. He wrote down the quadratic formula
and
asked what happens in the case (a, b, c) = (1, 2, 3)?, In that
case one
obtains x = -1 ± Ö(-2).
This case, as
well as many, many others, involves taking the square root of a
negative
number. By adopting the notation Ö(-1)
= i or i^{2} = -1, he introduced complex
numbers and
wrote the answer as x = -1 ± 2i.
He
then showed, using the algebra of complex numbers, that these two
complex
numbers satisfy the original quadratic formula:
1 - (± 4i ) -4 + 2 (± 2i) + 3 ^{?}=^{?} 0
0 = 0
All right! So, complex numbers are not so complex, after all! Thanks, Fred!
Porter Johnson mentioned that complex numbers were originally used merely to solve polynomial equations, after Gauss showed that every n-th order polynomial equation has n (possibly degenerate) complex roots. Much later, a mechanical engineer named Fourier made explicit use of the Euler formula, e^{ix} = cos x + i sin x, to develop Fourier series for the specific purpose of solving problems related to time-dependent heat flow in conductors. The electrical engineers introduced the complex impedance of a circuit as a means of analysis of time-dependent circuit behavior. In addition, complex numbers play a special role in descriptions of electromagnetic waves through Maxwell's Equations of electromagnetism. In 1925, the young physicists Schrödinger and Heisenberg independently developed Quantum Mechanics. For the first time, complex numbers played a central and unavoidable role in that theory, and in virtually all subsequent theoretical developments in physics. In effect, the central theoretical concept (wave function, probability amplitude, state of the system) cannot be measured directly, although its effects can be seen all over the universe! For additional information see these St Andrews University History of Mathematics pages: Quadratic, cubic, and Quartic Equations and The Fundamental Theorem of Algebra.
Arlyn VanEk [Illiana Christian HS,
physics] Air Resistance of
Swinging Block
Arlyn VanEk set up a bifilar pendulum in front of us. He explained
that he had done this in his classroom. He used a wooden block (with
two eye screws) on its top edge for its bob, and suspended it from the
ceiling using light, inelastic cord tied to the eyes screws. He then
swung the bob back in an arc, keeping the cord taut to make angle to
the vertical. Then he released the bob from rest, and measured the time
for it to pass through a Pasco® (http://www.pasco.com) timing gate at
the bottom of its swing. Knowing the width of the block, its speed
could be calculated. From this kinetic energy could be calculated at
the bottom of its swing, and its gravitational potential energy could
be calculated by measuring the decrease in altitude from the beginning
to the bottom of its swing.
Assuming air friction is nil and noting that the motion of the block should not depend upon its mass, when he did careful measurements, he found that energy was not being conserved! Thinking that this might be due to air friction, Arlyn made a second block with a streamlined shape, resembling the head of a doubled-bladed axe. Repeating the experiment with this bob, he found this time that it had more energy at the bottom of its swing than it had potential energy at the beginning! How could this be?!
Ann Brandon and Larry Alofs remarked that the separation of
kinetic
energy of a moving body into rotational
and translational motion can be made only corresponding to a
translation of the
center of mass, and rotation with respect to the center of mass.
One may thus apply the principle of conservation of energy using that
principle. Correspondingly, it is crucial to be certain that the
center of
mass of the pendulum moves through a circular arc, and that
translational speeds
are measured for the motion of that center mass. The standard
arrangement
for a ballistic pendulum is to suspend a wooden block by four
strings, attached on the top side on
locations symmetric with respect to the front, back, left, and right
edges. One thereby makes a bifilar pendulum, with the desired
properties. PJ
also mentioned that an aerodynamic shape should more properly
represent an
aircraft wing --- sharp in the front and smooth in the back, rather
than being
front-back symmetric. He pointed out that the winning athletes in
the
platform ski jumps in the 2002 Winter Olympics (in addition to
being
anorexic) held their skis- cross-pointed at the front, to reduce
air
resistance, rather than in the standard
railroad track position, to reduce air resistance.
As a sequel, Arlyn showed that two steel balls collide almost elastically when one rolls into the other at rest on a smooth table. However, if the balls smash against one another in mid-flight and stay together, all the mechanical energy must be converted into heat. How do we know this? Arlyn took two solid steel balls [mass of about 500 grams each; about 5 cm in diameter], and smashed them together while a sheet of ordinary paper was held between them. It was quite plain to see that a small hole had been burned through the paper with each encounter. Furthermore, when the experiment was repeated in a darkened room, we could see flashes of light with each collision. Also, the smell of burnt paper was unmistakable Remarkable!
Finally, on a non-destructive note, Arlyn held up a Thumb Drive Flash Memory Stick with a capacity of 64 MB that can be inserted into the USB plug on his fairly new computer. He is using this small memory stick (normally used for a digital camera) to transfer data from the school computer to his computer at home -- the hard drive recognizes it as a formatted [ROM] disc, so that files can be moved to and fro. Neato!
Arlyn, you showed us how it really is! Thanks!
Fred Farnell [Lane Tech HS,
physics] Rocket Balloons
Fred took a long,
collapsed balloon, and inflated it by inserting a special straw and
blowing.
Then he released it into the
air. It zoomed around the room, making a "screaming"
sound.
Just for amusement and edification, he sent off several more balloons,
with
similar effect --- except for the one that exploded during
inflation. This
is an ideal party favor, which Fred had obtained from The
Party
Corner®, in
Orland Park Shopping Center. It was described on the package
as follows:
Referring to his presentation at a previous SMILE meeting [mp111803.html], Fred promised that he would bring his daughter's old tennis shoes to SMILE in the near future, since she is nearly ready to donate them to us for scientific study. And, it's about time for her to wear winter shoes!
Those rockets really took off! Thanks for showing us, Fred.
Bill Shanks [retired physics teacher & member,
Joliet Junior Chorale]
Clothes Pins
that Light Up
Bill showed us the perfect "party gag" gift ---
a pack of 50 plastic clothes pins, complete with (LED) bulbs,
which light
when you use the clothes pin to clamp the LED leads to make
contact with
electrodes on a small "dime shaped" Lithium cell, such as CL 2016,
2025, or 2032, which are rated at 2.8 Volts.
PJ
Comment: A red or
green LED can be lighted with a single cell, since a photon of
energy 2.8
eV corresponds to a wavelength
How could you use this in class?
Bill, you must be the life of the party! Very nice!
Karlene Joseph [Lane Tech HS,
physics] Crash and Burn
Website
Karlene showed us some video images of collisions of automobiles
in
which "crash dummies", as well as stunt drivers were sitting in
the
automobiles. The frame-by-frame sequence of images is quite
fascinating. It was
clear to all of us that, in fact, Newton's Laws fully explain
the
occurrences during the crash. In particular, when we saw the
impact and
damage when the head of the unrestrained occupant hit the dashboard,
the warning "wear
your seatbelts" was justified in graphic detail. These images
were
located on the website of The Center for Injury Control, School
of Public Health, Emory University [http://www.sph.emory.edu/]
on the Motor Vehicle Crash Video page.
Those daredevils and dummies showed how Newton's laws determine the course of collisions! Thanks, Karlene!
Notes taken by Porter Johnson