High School Mathematics-Physics SMILE Meeting
27 January 2004
Notes Prepared by Porter Johnson

Don Kanner  [Lane Tech HS Physics Teacher]       High-Tech, Low-Tech Physics with Microsoft Train Simulator®
Don received this simulator for Christmas last year, but was unable to install it until he obtained a new computer, since it required 2 GB of ROM and 256 MB of RAM for proper operation.  For details concerning the program see the Microsoft website http://www.microsoft.com/games/trainsimulator/.  This simulator has certainly captured the imagination of the railroading community, and a number of additional add-ons are available.

Don found this program to be quite valuable for various aspects of physics instruction, such as making up problems, preparing for ACT exams, giving alternate assignments, and raising open questions.  The program seemed to incorporate GPS data, and to have quite realistic images of its various tracks, such as the Northeastern corridor of the United States, the Odakyu Electric Railway (Japan:  Tokyo & Kanagawa Prefectures), etc.With the computer set up and running in front of us, Don set up the program so that we could determine the time necessary to hit a particular speed; 60 km/hr or 16.6 meters/second, for various throttle settings.  The acceleration a could then be determined from the formula a = [16.6 (m/sec)]  / t( sec), where t is the time required to reach the speed.  We obtained the following data:

Throttle Setting   t (sec)   a( m/sec2
0 ¥ 0
20 % 79 0.21
40 % 35 0.47
60 % 23 0.72
80 % 15 1.11
100 % 13 1.28

Don pointed out that the radius of curvature R of the track could be determined by measuring the time T required for the train moving with speed V to go through an arc length s corresponding to turn angle q:

R = s / q (radians) = V ´ T /q (radians) = V ´ T [180° / p ] / q (degrees)
That should work!  Don explained the elaborate braking system on trains, with individual cars, connected by air lines running through the train, containing storage tanks.  Unless the storage tanks are pressurized, the brakes will not work and the train will not stop!

Don has written directly to Mr Bill Gates, founder of Microsoft Corporation®, complimenting him for developing the program, and making certain suggestions as to how this program might be more useful for instruction.  For example, the information on track inclination is not directly accessible, and it would be convenient to have a "display box" containing all current operating parameters in a single location on the screen.  Don is (fairly) patiently awaiting a reply!

Go for it, Don --- and keep 'em rolling!

Fred Schaal [Lane Tech HS, mathematics]        Innies and Outies
freehandedly drew a circle on the board, marked five points roughly equidistant on its circumference, and connected them to form a five-sided polygon, a pentagon or 5-gon. He then measured the interior and exterior vertex angles with a large wooden protractor, obtaining the following results:

Vertex   Interior angle   Exterior Angle
A 104°  76°
B  98°  82°
C 116°  64°
D 115°  65°
E 115°  75°
TOTAL 548° 352°
These totals are close to the expected results, 540° and 360°, respectively. Fred then relocated the vertex point C to a point close to the center of the circle, C', drew the new 5-gon, and obtained the following results:
Vertex   Interior angle   Exterior Angle
A 104°   76°
B  55°  135°
C' 210°  150°
D  70° 110°
E 115°   75°
TOTAL 554° 546°

The expected relation no longer works, because the sum of the angles for vertex C' is now close to  540°, rather than 360°.  If we had taken the exterior angle for C' to be -30°, we would have obtained 346°, which is more consistent with expectations.

Finally, Fred asked whether the rubber wheels on the Montreal and Paris METRO rail systems represent a practical means of noise reduction, or in fact are they too inefficient because of increased friction. Does anybody know the answer?  [It was mentioned that rubber wheels were once used in Chicago years ago.]  For additional information see the website Rubber-tired Metrohttp://en.wikipedia.org/wiki/Rubber-tired_metroInteresting, Fred!

Arlyn VanEk [Illiana Christian HS, physics]        Rotational Mechanics
first set up a race between a solid metal disk and a hollow ring (masses and diameters approximately equal), which were released from rest and rolled down the same inclined plane.  The solid disk won the race because it has a smaller rotational intertia than the hollow ring.  [Equivalently, it requires less energy for the solid disk to produce a given rotational speed than for the hollow ring.]  Arlyn explained that the distribution of mass, as well as the amount of mass, is relevant for rotational dynamics.  Arlyn pointed out that the moment of inertia of the ring (mass m; radius R) about its center is Ic= mR2, whereas for a disk of the same mass and radius the corresponding moment of inertia is Ic = 1/2 mR2.  At this point Earl Zwicker scurried out of the room, and he came back shortly with two meter sticks, each having two 100g masses taped to them.  For the stick with masses taped at its ends, it is more difficult to twist the stick back and forth about its center, than  for the stick with masses taped at its center. Very convincing, Earl!  Arlyn then rolled a small, light disk down the plane along with a large, heavy disk --- they rolled down at about the same rate.  He concluded from this and other experiments that the mass and radius of the object are unimportant, whereas the distribution of mass is crucial for winning the race. Arlyn then showed that a solid (metal) sphere is faster than a disk, whereas a hollow sphere (tennis ball) is slower than the disk, but faster than the ring.  These conclusions are consistent with the following table of moments of inertia (mass m, radius R) about the symmetry axis:

Moments of Inertia: Ic  

Ring       mR2
Hollow Sphere   2/3 mR2
Disk  1/2 mR2
Solid Sphere  2/5 mR2
Arlyn then illustrated that a hard-boiled egg spins nicely on the table, whereas a raw egg quickly stops spinning, because of internal dissipation of the rotational energy.  That's certainly one way to tell if your eggs have been cooked! 

Arlyn then balanced a (uniform) meter stick of weight W with a weight W0 attached to an end.  He showed that balance occurred at a distance x from the center of the stick, the weight at the end being a distance y = (0.5 m)  - x from the balance point.  Since the net torque about the balance point must be zero, W x = W0 y = W0 (0.5 - x), or x = 0.5 W0 / (W0 + W).  Note that the total weight to the left of the balance point, (0.5 +x ) W = 0.5W (2W0 + W) / (W0 + W), is not equal to the total weight to the right, W0 + (0.5 - x) W = W0  + 0.5 W2 / (W0 + W).  Balance occurs because torques balance at left and right, and not because there are equal amounts of weights on the right and left sides.  Arlyn also pointed out that, in "pumping" a swing, a person is putting energy into the system by systematically adjusting his/her center of mass

Arlyn, you showed some good stuff!  Thanks!

Bill Shanks [retired physics teacher, Joliet Central]        "LED"ing You On
Continuing in his unofficial role as MR LED MAN, Bill showed us his latest LED acquisition. First he reminded us of his older system, with separate red, green, and blue LED lights.  Then he showed us the new light-fiber pen, obtained at no great personal expense from Walgreen's, in which light from LED sources is partially reflected in the filamentary fibers fanning out from the end of the pen.  Thus, you can see the colors through the sides as well as at the ends of the fibers.  When he turned out the lights and waved the pen in the air, we could see remarkable images, illustrating persistence of vision, color mixing, and the like.  [For information on a Light-Up Fiber-Wand, see the Identity-Links website http://www.identity-links.com/light-up/light-up-fiber-wand.html] It was a very fascinating visual display, and we thank you greatly for showing it to us.  Nice work, Bill!

The next SMILE meeting, held on 10 February 2004,  will be held in the Hermann Union Building, in connection with the Chicago Regional Bridge Building Contest.  See you There!

 Notes taken by Porter Johnson