High School Mathematics-Physics SMILE Meeting
26 April 2005
Notes Prepared by Porter Johnson

Ann Brandon [Joliet West HS, physics]              Workshop on Standing Wave Machine
 Ann held a workshop in which 8 participants constructed the standing wave machine, which she showed us at the last SMILE meeting, mp041205.html.  Good job, everybody! Special thanks to Ann.

Fred Schaal [Lane Tech HS, mathematics]              Follow-up Questions on Book by Michio Kaku
 As a follow-up of his comments about this book at the last SMILE meeting mp041205.html, Fred asked two important questions concerning developments in twentieth century physics.  Here are his questions, as well as the answers, given on-the-spot by Porter Johnson.

  1. What is the Lorentz-Fitzgerald Contraction, and is it real?
    Maxwell and his contemporaries developed the theory of electromagnetism in analogy to the theory of sound being developed by Lord Rayleigh and his contemporaries.  Sound clearly propagates in a material medium --- air, water, steel, etc.  Maxwell thought of electromagnetic waves as vibrations in a mysterious ether that permeated all of space.  It was a material medium that permeated all of space, but it was either difficult or impossible to detect its presence directly.  Because sound travels differently in the wind, light should travel differently in the "ether wind".  A few years after Maxwell's death (1876),  Michelson conducted a series of experiments to detect the motion of the earth through the ether  (1887) --- and failed!  Lorentz and Fitzgerald (1902) proposed an explanation of this (and other) unsuccessful experiments to detect ether wind, as a physical contraction of moving bodies in the direction of their motion. They developed the Lorentz transformation (actually discovered by Volk in 1881, who didn't recognize its importance) to explain this point. In 1905 Einstein proposed a a different explanation for non-detection of ether wind -- the theory of relativity.  In relativity, events that are simultaneous in one frame are not simultaneous in another inertial frame -- in effect there is no global time variable.  In the words of Einstein:
    "There is no such thing as time -- only clocks"
  2. How is the Einstein-Podolsky-Rosen (EPR) paradox resolved in a manner consistent with the requirements of relativity?
    The essence of the EPR paradox involves the spontaneous decay of a particle at rest into two particles.  The standard pedagogical answer involves the neutral pi meson p0, which decays spontaneously into two photons (g1, g2) in about 10-15 seconds: p0 ® g1 + g2 . The p0  has spin (intrinsic angular momentum) zero, whereas the two photons are spin-one particles. In other words, the total angular momentum of the system in the rest frame starts at zero, and it must remain zero -- in the absence of interactions with the external world.  Each of  the gamma rays has an energy of about 70 MeV -- which is easily detectable. Suppose that each one travels freely for years before being detected by the LGM (little green men) on distant planets circulating around distant stars. Suppose that the LGM on one of the planets measure the photon spin (left or right circular polarization).  They  then know the spin that the LGM on the other planet would simultaneously measure.  But, relativity requires that information cannot travel faster than the speed of light, and it doesn't in this case, even though it may appear so..

    Einstein     was, in effect, attacking Bohr and Quantum Theory, and not his theories of relativity, through such a Gedanken Experiment.  Modern developments suggest the use of this "entanglement" of the states of decay products  to make a quantum telegraph, which would transmit signals that can only be received by one observer, and would then be erased.
Thanks, Fred!

Babatunde Taiwo [Dunbar HS]              Simple Electric Motors
Babatunde showed an electric motor that he had built according to the instructions obtained from Pasco Scientific Teacher Resource Guide [Investigation Seven:  Making a Model Motor from Scratch, pp T-285,286], using a D-cell battery, about 1.5 meters of magnetic wire, a battery holder, masking tape, a strong magnet, and a  two paper clips.  The following explanation is excerpted from that source:

"Stored chemical in the cell established an electric pressure difference which pushed charge through the coil -- but only if the coil is oriented so that scraped ends are in contact with the clips. (If the insulated half of one end is in contact with the clips, no charge can flow.) Using the Right Hand Rule for Motors (7.11), once can predict the direction of the force on the wire on the two sides of the coil, and therefore which way the coil will rotate."
His students were able to construct a simple electric motor, complete with field magnet, rotor, and commutator, in one class period by following these instructions.   For details on a very similar procedure, see the lesson given by Lee Slick in SMILE on 11 November 1997 [ph1111.htm], and those given by Ann Brandon in SMILE on 23 March 2004 [mp032304.html].

Earl Zwicker informed us that descriptions of both of these experiments have appeared in The Physics Teacher TPT:

  1. Spinning Loop by Rudy Keil TPT: Vol 23, p 308 (May 1985).
  2. Spinning Screw/battery/magnet/wire by Chris Chiaverina TPT: Vol 40, p 553 (Dec 2004).
Fred Farnell [Lane Tech HS, physics]              Rolling, Falling, Rolling
Fred brought in a defunct classroom white board (about 1 meter by 1.5 meter in size), which he carefully clamped  to the desk in front of us, so that it formed a broad inclined plane sloping slightly down toward us.  He then brought out a plastic ruler of length about 30 cm with a groove down the center, which he attached to near the top  right edge of the white board, with the groove on the top side; the ruler tilted upward from the board about 10°. He carefully attached the ruler so that a marble released from rest at a point on its groove would roll down it, and then go smoothly onto the white board.  He was able to adjust the initial direction of  motion of the marble on the white board to be horizontal and parallel to its top edge.  We watched as it rolled on the white board along a parabolic path, till falling off the bottom of the board.  Fred had thus created a system for studying two dimensional motion.  He varied the release height H of the marble above the ruler's lowest end, and we took several measurements of the time T required for the marble to roll off the bottom edge of the board.  Here are the data:
H
Release Height		 T
Average Rolling Time
05 cm 2.25 sec
10 cm 2.36 sec
15 cm 2.18 sec
18 cm 2.18 sec
Surpr-i-i-i-se, surpr-i-i-i-se! The times are all the same, to within experimental uncertainty. How come? Perhaps the horizontal and vertical motions are independent of one another in this case. Shouldn't they be?

So far, so trivial!  Fred assumed that the marble was perfectly round, and that it rolled without slipping down the inclined plane. Under these conditions, the component of acceleration down the plane, which is inclined at angle q above the horizontal, is

ay = 5 / 7 g sin q 
Using this formula, Fred obtained a "roll time" of 1.90 seconds ---- which is significantly smaller than the measured value. Now, just why do things happen this way? One possible explanation is that the connection between rotational angular velocity and translational speed is different for a marble riding along a groove from what it would be on a planar surface. Thus, the marble would slip somewhat when it goes onto the plane. At first it would slide across the plane, losing mechanical energy through friction --- like a bowling ball going down the lane! Maybe that is the reason!

An related question posed by Porter Johnson:

Q: What happens when a tire is rolled without slipping at an oblique angle down an inclined plane?"
A excellent experiment to challenge physics understanding. Thanks, Fred!

Don Kanner and Bill Blunk [Joliet West HS, physics]              You Can't Win at Tug-of-War just by Pulling Harder
Don and Bill stood  facing each other, each holding one end of his own spring scales.  The other ends of the scales were then hooked together between them.  They pulled in opposite directions, Don attempting to get and maintain a scale reading of 50 Newtons (about 12 pounds) and Bill tried to maintain 100 Newtons (about 24 pounds).  Don merely chased Bill across the room with increasing speed -- or did Bill pull Don! They always had about the same scale reading, despite their efforts.  It may have been an exercise in frustration for them, but it was quite entertaining for us.  Why did they fail?  Isaac Newton and his laws of motion have something to say about this. Don't they?

It was an excellent Katzenjammer Kinderen comedy routine, which served  to illustrate the consequences of  Newton's Laws. 

By chance, are you twins? Thanks, Don and Bill.

Bill Shanks [Joliet Central, physics -- retired]                           Meeting of the Board + A One Watt Flashlight
Bill recently was driving North on Interstate 75 in Georgia, on a quiet section between Macon and the metropolitan Atlanta traffic snarl.  Suddenly, he saw a large wooden board moving through the air in front of him, coming right at him.  Fortunately, he was able to swerve to avoid major impact, receiving only a minor dent on the right front bumper.  After this moment of terror had passed, Bill began to wonder whether he had just been lucky, or whether there had been time to react to the situation.  Aha!  Another good physics question!  The board might have been lying on the road initially, where it would be struck by a big truck and knocked high into the air.  If it rose to an approximate height h = 3 meters above the roof of the car before Bill saw it and it began to descend, a time t ~ 0.8 seconds would elapse before it came down to the level of the roof:

h = 1/2 g t2 ~ 1/2 ´ 10 ´ (0.8)2 = 3.2 meters

Bill might might have had time to react!

Excellent real-life physics experience! Thanks, Bill.

Comment by Porter Johnson: By contrast, an object dropped from a viaduct above the road is even more dangerous, since you probably won't see it until somewhat after it is dropped, and at that point it is moving more quickly through the field of view.

Bill showed his newest flashlight acquisition -- a one-watt LED diode white light flashlight that he had obtained at Sam's Club Joliet (about $13). After we darkened the room, Bill turned on the light, which seemed to be quite bright. He removed its lens and reflector to expose the bare LED, practically a point source.  We looked at the light through the "slits" formed by our fingers, and were able to see diffraction patterns, with the red, green, and blue colors separated!

Nifty gadget! Thanks, Bill

See you at our final meeting of the year,  10 May 2005. 

Notes prepared by Porter Johnson