High School  Mathematics-Physics SMILE Meeting
20 April 2004
Notes Prepared by Porter Johnson Marilynn Stone and Don Kanner  [Lane Tech HS, Physics]         Dropping Weights through Pipes
Marilynn took a brass weight, and held a copper pipe [about 2.5 cm in diameter and 1.5 meters long] vertically with the bottom just above the floor.  She dropped the brass weight through the pipe, and it hit the floor less than 1 second later, according to our estimates.  Then she dropped a strong magnet of about the same size through the pipe, and it took an estimated 8 seconds to hit the floor.  How come?  The slow-down was caused by eddy currents set up in the pipe by the moving magnet, which produced an upward force on the magnet.  She passed the magnet and pipe around the room, and we each looked down the pipe with fascination as the magnet slowly drifted down the pipe.  Don Kanner then asked whether the size and material constitution of the pipe made any difference in the motion. He dropped the weight through a slightly larger copper pipe, and we noticed that it got to the ground more quickly. He also dropped a cow magnet through the same pipe -- the cow magnet fell more quickly, because it produced a weaker field (in proportion to its weight) than the original magnet.  What about putting the smaller pipe concentrically inside the larger pipe?  We observed that the original magnet took longer to fall through the two pipe system, in comparison with falling through only one of the pipes.  Why?  The eddy currents induced in each pipe produced a stronger upward force on the magnet.  We next took these measurements for the various cases:
Case Time for Fall
Brass weight inside (2.5 cm) Cu pipe     0.58 sec
Cow Magnet inside (2.5cm) Cu pipe   0.6 sec
Cow Magnet inside concentric Cu pipes   1.7 sec
Strong magnet inside 4 cm Al pipe   3.0 sec
Strong magnet inside 2.5 cm Cu pipe   7.7 sec
Strong magnet inside concentric Cu pipes  11.3 sec

A "pipe drop" was preformed by the late Alex Juniewicz at the SMILE meeting of 30 September 1997:  ph930.htm.

Bill Blunk took an aluminum parking token [valid in parking meters throughout the mighty metropolis of Great Falls, Montana], and dropped it through the gap between the two small magnets. The token passed slowly through the field region, and then fell tot he floor.  Interesting!  For more details see the writeup of the the SMILE meeting of 08 September 1998:  ph090898.htm. 

Thanks for "dropping in", Marilynn and Don!

John Bozovsky [Chicago Discovery Academy: Bowen HS, Physics]         Rocket Altitude Measurement
John is a physics teacher who, for decades, has motivated his students' interest in physics by getting them involved with model rockets.  Why can design construct, and send a model rocket to the highest altitude, h?  Which raises the question:  how can students measure h for their rockets? (handout)  John explained that, in practice, it is rather difficult to measure h, since the rocket seldom goes straight up from the launch point, but tends to wander off in some direction or another.  With the aide of a colorful 3-D scale model to show the geometry of the situation clearly, he showed us how to find h using two observers, A and B, positioned at each end of a baseline of length AB, laid out on the floor (presumed level) ahead of time.  Two large circles (about 1.5 meter radius) are drawn on the floor centered at A and B at each end as well.  When the rocket reaches its highest altitude (zenith) at the position, Z, in space, observer A uses his Astrolabe [http://www.astrolabes.org/astrolab.htm] to record the angle, c, above floor level of the rocket, as shown: 

                               Z  (rocket zenith)       Z     
 (vertical plane)            . |                        | . (different vertical plane)
                           .   |                        |   .
                         .     |  h                 h   |     .
                       .   c   |                        |    d  .
                      A--------X                        X-------- B

(X is the point on the ground directly below Z. Similarly, observer B uses his astrolabe to record angle d.) Observer A -- immediately after recording the angle c on his astrolabe -- moves his astrolabe vertically downward to point toward X at floor level, and places a mark on his circle to enable measurement of angle a, with a protractor, which he does, as shown in the diagram below.  Similarly, B marks his circle and measures angle b. 
                              X         (projection of location of rocket
                             .   .       maximum height onto the ground)
                            .       .
 (plane of ground)         . a     b   . 
                          A--------------B

Note that, from the Law of Sines,
AB/ [sin (a+ b)] = AX / [sin  b] = XB/ [sin a] 
Now the height h may be computed in two ways:
h = AX [tan c]= AB [sin b] {tan c] / [sin (a+b)]  ;
h = AX [tan d] = AB [sin a] {tan d] / [sin (a+b)] .
On the scale model brought in by John, we measured the following quantities:  AB = 58 cm; a = 21°; b = 54° ; c = 49°; d = 69°.  We calculated h = 56 cm using each of the formulas.  This redundancy provides a check of consistency for the data obtained.  With a meter stick, we measured h and observed it to be 56 cm.  Great!

Information on the Astrolabe is given on the Encyclopædia Britannica website:  http://www.britannica.com/clockworks/astrolabe.html.  Seel also A Treatise on the Astrolabe by Geoffrey Chaucer [http://art-bin.com/art/oastro.html], which is considered to be the oldest technical manual in English.

The Estes Rocket Kits, which include the astrolabe (angle measuring device) may be ordered at the following URL:  [http://www.hobbyconnection.com/estes.htm].This rocket launcher is part of the Physics Van demonstration exercises being developed at Chicago State University for delivery to and use in local high schools.  for details contact John Bozovsky via email at jbozovsky@aol.com, or call Prof Mike Mimnaugh at Chicago State University (773) 995-2180. 

John, this really is about rocket science!  Thanks!

Monica Seelman [ST James Elementary School]         Bubble Trumpets and Bubble Recipes
Monica pulled out a Bubble Trumpet, which she had obtained from Tangent Toy Company: http://www.tangenttoy.com/trumpet.html. (3 page handout)  She had learned about this device from the article Playthings of Science by Fred Guterl, which appeared in the December 1996 issue of Discover Magazine: http://www.discover.com/issues/dec-96/. When she dipped this device into the bubble solution, and then held it up and blew hard on the mouthpiece, a froth filled with bubbles was produced.  By contrast, when she repeated the procedure and blew slowly but steadily, a single large bubble came out of the trumpet.  She then asked the following questions:

Monica provided us with several recipes for the bubble solution, which she had obtained from The Bubblesphere website:  http://www.bubbles.org/html/solutions/formulae.htm.  She all passed around Soap Bubbles by Ron Hipschmann, which appears on the Exploratorium [SF] website:  http://www.exploratorium.edu/ronh/bubbles/bubbles.html.

Thanks for delving into the mysteries of bubble science, Monica!

Babatunde Taiwo [Dunbar HS, Physics]         Vernier Force Plate with Graphing Calculator
Babatunde had recently obtained the Force Plate from Vernier Corporation: [http://www.vernier.com/probes/probes.html?fp-bta&template-standard.html].  He had used this apparatus to do various experiments involving impulses generated by jumping onto the plates, as well as the distribution of weight when one stands on two plates.  He illustrated the operations by having Bill Shanks stand on the force plate, and then jump into the air, and then land on the plate again.  Babatunde showed the recorded images of force on the plate versus time.  When Bill stood on the plate, the force on the plate had a steady value of about 800 Newtons.  As he jumped the force spiked upward. and then went quickly down to zero.  It remained at zero while he was in the air, for about 0.2 seconds.  When he returned to the table there was another spike, similar to the first one.  Babatunde then determined the total impulse over the jump period from data by numerical integration, and obtained about 700 Newton-seconds.  Babatunde then investigated how the force and impulse would change from these values (natural lant here were more oscillations in the force in these two cases.  In addition, the net impulse was less for the crouch landing (500 N-s) and the rigid landing (300 N-s) than for the natural landing (700 N-s).  Also, Don Kanner, the rigid jumper, could feel the difference in his bones!

A very nice display of impacts, there for all to see! Thanks, Babatunde!!

We ran out of time before these participants could show their lessons:

They, as well as anybody who has not yet made a presentation this semester, will present first at our last SMILE meeting of the semester, Tuesday, 04 May 2004.  See you there!

Notes taken by Porter Johnson.