Don Kanner [Lane Tech HS Physics
Teacher] HighTech, LowTech
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 addons 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/sec^{2}) 
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:
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
Fred
freehandedly drew
a circle on the board, marked five points roughly equidistant on its
circumference, and connected
them to form a fivesided polygon, a pentagon or 5gon. 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° 
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 Rubbertired Metro: http://en.wikipedia.org/wiki/Rubbertired_metro. Interesting, Fred!
Arlyn VanEk [Illiana Christian HS,
physics] Rotational Mechanics
Arlyn 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 I_{c}=
mR^{2}, whereas for a disk of the same mass and radius the
corresponding moment of inertia is I_{c} = 1/2 mR^{2}.
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: I_{c} 

Ring  mR^{2} 
Hollow Sphere  2/3 mR^{2} 
Disk  1/2 mR^{2} 
Solid Sphere  2/5 mR^{2} 
Arlyn then balanced a (uniform) meter stick of weight W with a weight W_{0} 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 = W_{0} y = W_{0 }(0.5  x), or x = 0.5 W_{0} / (W_{0 }+ W). Note that the total weight to the left of the balance point, (0.5 +x ) W = 0.5W (2W_{0} + W) / (W_{0 }+ W), is not equal to the total weight to the right, W_{0 }+ (0.5  x) W = W_{0} + 0.5 W^{2} / (W_{0 }+ 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 lightfiber 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 LightUp FiberWand, see
the IdentityLinks
website http://www.identitylinks.com/lightup/lightupfiberwand.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