High School Mathematics Physics SMILE Meeting
03 December
Prepared by Porter Johnson
Bill Blunk [Joliet Central HS, Physics]     Jumping off the Table 
Bill began by climbing onto the laboratory table in front of the room, standing on it, and saying, with a SMILE on his face ... "I do this so that students can look up to me!"  He then asked why ballet dancers, gymnasts, and especially paratroopers always flex their legs as they land upon the ground.  To illustrate this, Bill stepped off the table, landing on the floor feet first, and flexing his body into a crouch as he came to rest. He then wrote down the following relation involving the (average) force F acting on a body over a time interval Dt, expressed in terms of the mass m of the body and its change in velocity Dv:
F Dt = m Dv

This relation, a direct consequence of Newton's Second Law, relates the Impulse (on the left side) to the change in momentum (on the right side). Bill pointed out that if he is the body, the mass m is constant. And since he falls through a given distance - the height of the table - his velocity, v, at contact with the floor is always the same. So Dv must  always be the same, since it is the reduction of v to zero while coming to rest on the floor. Thus, for Bill stepping off the given table and coming to rest on the floor, m Dv must be the same each time. And the change in momentum of Bill, the right side of the equation, is constant.

Using the notation popularized by Paul Hewitt [Conceptual Physics], a smaller force F acting over a longer time interval Dt produces the same impulse as a larger force F acting over a shorter time Dt :

F Dt = F Dt = m Dv = constant

By going into a crouch as he landed and slowed himself to rest, Bill increased the "landing time," and so lowered the average force on his body to a smaller value, F. If he had kept his legs stiff as he landed, he would have slowed to rest rather abruptly, greatly decreasing the time interval to Dt, and resulting in a much larger average force on his body, F!

To make this point in a more dramatic fashion, Bill said he would fall backwards off the table. But first he set up team of six of us (potential pall bearers?!) to catch him. The team was arranged into three pairs. Within a pair, each person faced the other. Each held his upper arm vertically at his sides, and forearms held forward and parallel to each other and the floor. Then - with hands facing down - each person grasped his own right wrist with his own left hand, and with his right hand he grasped the left wrist of his partner. The "people platform" thus formed by each pair can support much weight. (If you were a Scout, you probably know this!)

The three pairs then lined up in a row, perpendicular to the table, and Bill stood at the edge of the table, with his back to the row of these three "people platforms." Then he slowly tipped over backwards, keeping his body rigid, and falling right onto the "people platforms" - who were able to catch him before he might experience certain calamity! Everybody breathed sigh of relief, and Bill gave us the following pointers when attempting this feat:

It was suggested that one could practice the "rigid falling" component off the side of a swimming pool, preferably when the lifeguard wasn't looking directly at you. Bill pointed out that paratroopers make practice jumps from a height of about  3 meters [10 feet], corresponding to the speed at which they hit the ground during an actual jump [8 meters/sec or 15 mi/hour].  You really do have a jump on things, Bill.  Very nice!

Larry Alofs  [Kenwood Academy, Physics]      Diffraction versus Refraction
Larry produced a diffraction grating with 530 grating lines per millimeter, corresponding to a spacing d = 1.89 microns between lines.  He passed light from a standard red diode laser through this slit and onto the white board, showing 3 spots, which meet the grating condition d sin q = n l, the central spot corresponding to n = 0 and the two side spots for n = ±1. Larry pointed out that sin q = x / L = l, where x is the separation distance between spots, L is the distance from the grating to the board, and l is the wavelength of light.

As an extension of the exercise, Larry asked what would change if we replaced the red laser light source with a green one.  We decided that the wavelength l of light hitting the grating would be decreased, so that the distances between spots would also decrease.  Larry took out a green light solid state laser [http://www.harborfreight.com/cpi/ctaf/Displayitem.taf?itemnumber=43137] which has a 3 Volt power supply. He had ordered the light from a Harbor Freight Catalog [http://www.harborfreight.com/] for about $200, but it did not appear in their most recent catalog.  [By contrast, the green light laser manufactured by  MetrologicCorporation can be obtained for around $700.] He put the green laser on the same stand as the red one, so that both could pass through the slit.  We observed that the green side dots were about 20% closer to the center dot than for red. Very impressive, Larry!

To distinguish the color separation produced by the grating [interference] from that obtained with a glass prism [refraction], he suspended a fairly large prism in front of the two laser light sources.  We could see that, indeed, green light was refracted more than red light, because the index of refraction for glass and many other materials is greater for green than red, but that the images shifted by about 1% of the amount observed previously with the diffraction grating. Beautiful!

Now we see the light, Larry!

Karlene Joseph [Lane Tech HS, Physics]    A Story of Science Excitement
Karlene showed her 4th grade daughter a variation of the SMILE demonstration of resistors in series and resistors in parallel, which her daughter described as way cool! A few days later her daughter went into the hospital for tests involving a pulse oxygen monitor, a heart monitor, and a a neural monitor.  The daughter was quite surprised when she learned that humans ALSO conduct electricity.  Karlene got her a CHIRPING CHICK toy, on which a chirping noise is produced whenever you touch the terminals and make a closed circuit.  At school the daughter's class got 26 people to form a "series circuit", through which electricity passed so that the bird would chirp. The resistance between two points of dry human skin is of order 100,000 Ohms, so that a current of 0.1 milli-Ampères would flow with a potential difference of 10 Volts. Children are never too young to begin to appreciate science.  Really way cool, Karlene!

Ann Brandon [Joliet West HS, Physics]    Energy of A Pendulum
Ann led us through the following experiment: Is mechanical energy conserved when a pendulum swings?

    Procedure:
  1. Hang a pendulum (wood block with two eye hooks at the top edge) from two strong strings, so that it will swing in a vertical plane.
  2. Measure the distance h2 from the floor to the center of the pendulum mass, as it hangs straight down.
  3. Set up the photo-timer so that the pendulum will break the beam at the bottom of its swing.
  4. Measure the thickness DD of the pendulum, front to back, and record it.
  5. Lift the pendulum to one side, and measure the distance up to the center of mass h1.
  6. Zero the timer.
  7. Let the pendulum swing ONCE through the beam.
  8. Record the time Dt on the timer.
    Analysis:
  1. Determine the mass m of your pendulum.
  2. Calculate the Initial Gravitational Potential Energy.
  3. Calculate the Gravitational Potential Energy at the bottom of the swing.
  4. Calculate the Velocity at the bottom of the swing.
  5. Calculate the Kinetic Energy at the bottom of the swing.
    Questions:
  1. What was the Total Mechanical Energy before the swing?
  2. What was the Total Mechanical Energy at the bottom of the swing?
  3. Was the Total Mechanical Energy conserved during one swing of the pendulum?
  4. What forces are acting on the pendulum during its swing?  Draw a picture of these forces.
  5. We know that any pendulum will eventually stop swinging.  Which force causes this to happen?
  6. What happens to the missing energy?
The experiment was done with the following photo-gate / light source, and timer: Thornton / DEC 102 APC 100 Power Supply, which records the beam interruption time in milliseconds on a digital display. We made measurements to determine: m =0.300 kg, h1 = 0.10 m, h2 = 0.86 m, Dt = 0.025 sec, and DD = 0.08 m.  We calculated the velocity at the bottom of the swing to be v = 0.08 m / 0.025 sec = 3.2 m / sec. The kinetic energy at the bottom is thus 1/2 mv2 = 1/2´0.3 ´ (3.2)2 = 1.54 Joules, and the change in potential energy is m g (h2 - h1) = 0.300 ´ 9.8 ´ (0.76) = 2.23 Joules.  We conclude that about 30% of the energy is lost in the swing, either through air resistance or other frictional losses, or flexing of the bar, which has one end attached on the table and the other tied to the strings. With a lighter, smaller steel ball or brass cylinder, the results are obtained in closer agreement with energy conservation.  A nice, swinging experiment, Ann!

Don Kanner [Lane Tech HS, Physics]    Camera Obscura
Don began by describing a recent television program that explained the role of the Camera Obscura [http://brightbytes.com/cosite/what.html] in the late renaissance, in which the goal was to produce faithful images of portraits, rooms, and even landscape scenes.  The program highlighted the conclusions presented by David Hockney, Secret Knowledge: Rediscovering the Lost Techniques of the Old Masters [Viking Press 2001: ISBN 9-6700-30260].  Hockney has suggested that paintings such as da Vinci, Caravaggio, Velázquez, and van Eyck were actually created using optics and lenses; see http://www.acmi.net.au/AIC/CAMERA_OBSCURA.html..  The Flemish artist Jan Van Eyck [born in 1434] may have used a lens [http://www.ibiblio.org/wm/paint/auth/eyck/ and http://www.artchive.com/artchive/V/van_eyck.html] to produce the image of the little dog at the bottom of the painting Arnolfini Wedding Portrait.  Indeed, in a mirror behind the couple, we can see the wedding party, as well as a person covered with "black-out cloth" and looking through a hole.  Hockney does not consider his work an exposé of the great masters;  instead he feels that artists have always made use of the technology available to them in creating their images, and the Camera Obscura [or dark room!] may have been more widely used than previously thought.  The achievements of these artists stand as one of the greatest monuments to artistic genius of all time.  In the modern age, the dominant mode of art consists of digital images, which are more flexible and adaptable than the traditional easel, canvas, brushes, and paint.

One could produce images suitable for tracing onto paper using (1) a small hole to form a pinhole camera, (2) a lens to focus light, or (3) a spherical mirror to focus light.  Since the first method produces very dim images, even inside a darkened room, and since the technology to produce high-quality large images has been available only for about two centuries, Fred thought that curved mirrors would work best.  He brought a large spherical mirror about 50 cm in diameter, with a radius of curvature of about R ~ 2 meters, corresponding to a focal length of  f = R/2 ~ 1 meter.  On a screen we could see the inverted, blurred  image of a person standing in front of the white board, by reflection off the spherical mirror.

Porter mentioned the film Artemisia [1997; French language], which deals with the life of Artemisia Gentileschi (1593-1653), [http://www.u.arizona.edu/ic/mcbride/ws200/gentil.htm] one of the first well-known female painters.  In that film the artists view landscape scenes through a small hole, placed about a meter behind a 6 ´ 6 lattice network that lies in a vertical plane, to set the correct perspective while laying out an image.   Don mentioned that  Albrecht Dürer of Nürnberg also made sketches using a gadget with strings and a grid.  At last we see the light!  Thought-provoking and interesting, Don! 

Richard Goberville [Joliet Central, Physics]    Physics Toys and Cartoons
Richard passed around a Shock Pen, a Piezoelectric device that produces a high Voltage when one presses  its cap.  It is available from Johnson-Smith Catalog, http://www.johnsonsmith.com,where it is listed as item #26074, available for around $13.  Here is the blurb:

If "office thieves" are bugging you, here's the cure. The Shock Pen's hair-raising jolt is guaranteed to stop the "borrowing." Please do not use with young children, or anyone with a medical condition. Uses one "AAA" battery, not included.
Richard also passed around a "floating globe", which he obtained at a Hobby Lobby Store for about $50. A similar device is described and shown at the websites http://www.WorldGlobes.com and http://www.tradekey.com/product_view/id/69699.htm.  There is a permanent magnet on the North Pole of the globe and a piece of metal at the South Pole.  What holds the globe up? Richard also passed around some interesting cartoons from Garfield, Over the Hedge, BC, and The Far Side, showing important concepts in  mechanics. Don't forget about The Laws of Cartoon Physics: http://funnies.paco.to/cartoon.html. You've got us thinking, Richard! 

Michelle Gattuso, Lee Slick, Fred Schaal, and Bill Shanks were unable to do their presentations due to lack of time, but will be scheduled for 10 December, our next meeting.

Notes taken by Porter Johnson