• A meeting announcement was passed around about  the Michiana Physics Teachers Group, operated by Mike McFarland of Notre Dame University.  For more details about this organization, you may contact him at (574) 631-7057, or by email at mmcfarla@nd.edu. 
• A new exhibit on Albert Einstein is opening at the American Museum of Natural History in New York.  To obtain more information, see their website, http://www.amnh.org.
• Information on the website It's About Time http://www.its-about-time.com was distributed. This group develops curricula in Earth Science, Physics and Math curricula for middle school through high school students
• The website http://www.humorsphere.com/fun/color.php contains an interactive test, in which you are to identify the colors themselves,  rather than names of colors. For example, if you see the word "BLUE", written  with red letters, you should answer "red", rather than "blue". Check it out, to see how long it takes you to master the puzzle! Thanks to Rudy Keil for this!

As a modern variant of this standard demonstration, Betty used her digital camera, a Sony Mavica Model FD-88 with an 8X lens. It records 5, 10, or 15 second video images directly onto the 1.44 MB diskette that serves as the "film".  She recorded the video sequence before class, and then played it back on her MacIntosh computer, using the "freeze frame" option to show that the ball left the cart, went up, "stopped" in mid-air, and returned to the cart.  She used a grid on a transparency sheet to obtain quantitative information on the position of the cart at various time intervals.  To show us how simple this is, she played her recorded image back to us on our large TV Monitor, with impressive results. It was suggested that she could relate the "frame rep rate" to real time by recording the image of the second hand of a clock with her camera, either separately or as part of the apparatus.  You showed us how it really should be done,  Betty!

Fred Schaal [Lane Tech High School, Mathematics]      Coding / Decoding and Matrices
Fred showed us how to code and decode a message, based upon matrix multiplication.  He illustrated the procedure for encoding and decoding, using the following highly significant message:

    B =   | 6  3 |
          | 5  2 |

    [ 7 15 ] | 6  3 |  =  [ 117 51]   AND  [ 0 12 ]  | 6  3 | = [ 60 24]
             | 5  2 |                                | 5  2 |

A =  | -2/3   1  | = B-1  
     |  5/3  -2  |

    [ 117 51 ] | -2/3  1 |  =   [7 15]     AND  [ 60 24 ] |-2/3  1 | = [ 0 12]
               |  5/3 -2 |                                | 5/3 -2 |

Professor Eduardo De Santiago [Civil and Architectural Engineering, IIT]    Bridge Design
Eduardo De Santiago made his fourth annual presentation before SMILE and guest students and teachers on "How to be a structural engineer in one lesson"! He began by posing the following difficult question:

• To design a bridge for center loading, an optimal bridge will be symmetric about the center; that is, if your bridge is not symmetric, you are wasting material. In general, you should have a good understanding of the points at which the bridge may be loaded.
• When a bridge is supporting an external load, internal forces are developed in various parts of the bridge. Civil engineers analyze these forces in terms of  bending moments and internal shear forces. A shear force tends to sever a beam, whereas a bending moment induces a deformation of the beam into a "smile" or a "frown". In general, bending moments are more significant than shears for bridge design.
• If you place a load on a horizontal plank placed between two abutments, the plank bows downward. In this situation the top part of the plank is under compression, and the bottom part of the plank is under tension. The "neutral axis" running horizontally along the center of the plank is under relatively weak internal forces. This idea is the basis for the "I beam" [transverse cross-section shaped like an I], in which the material is located primarily at the top and bottom of the beam, where the greatest internal stresses are found.
• Suppose we make a bridge that looks like a ladder turned on its side:
  
  This bridge will be resist bending, but will be very vulnerable to shear. We use trusses [diagonals] to handle shear forces efficiently.
• Here is a typical truss bridge panel
  
  The two good things about trusses are (1) that they can handle shear forces efficiently, and (2) that truss bridges --- assuming  ideal "pin connections" --- are completely solvable, as well as generally strong structures. Note that the "triangulation" provides strength by preventing "buckling" of the bridge. [Since the ends of the bridge are supported by the abutment and do not experience a bending moment, a triangular portion at each end, being unnecessary, is removed.]
• A truss bridge is made by connecting two side panels, with cross-bracing and connections to provide triangulation at the top. In addition, portal bracing is required at the top to eliminate side-sway.
• As a material, wood is strong under tension, but has a strong tendency toward buckling under compression.  Long, thin pieces of wood may be laminated by gluing them together along their entire length.  This is especially important for the bottom members of  the bridge.
• You should minimize the total number of joints, and be sure that the joints fit together snugly without gaps, before gluing them.  Remember that you are trying to obtain strength through triangulation.  Alignment of joints is critical for building strong contest bridges. 
• In practice, gusset plates may be used  for strengthening joints in steel truss bridges, but these are probably not practical for contest bridges.
• It is better to have "butt joints" with the full member resting on top of the piece below, so that the wood, rather than merely the glue, is helping to support the weight of the bridge.
• You have to be sure that your weight platforms will support the weight by themselves, since there is the possibility of a "punch out", in which the bridge remains largely intact, while the platform punches through to release the weights.
• Some experimentation in the Seattle area has suggested that the best glue for contest bridges is ordinary wood glue [Elmer's Glue™?] , rather than the more expensive varieties.
• If weight must be supported below the roadbed, you can build an inverted truss. It is important to have bracing below ground level at the abutments. Remember that the Romans understood the arching effect, and also learned [sometimes the hard way] that you must have the arch well attached to prevent buckling. You can build an inverted arch, as well as the usual kind.
• Structural engineers are required to over-design bridges by safety factors, so that a 1000 kg load bridge will actually support 1500 kg, etc. Such caution is, or course, a sure way to lose bridge contests. The perfect contest bridge would resemble the legendary One Horse Shay [For details see THE DEACON'S MASTERPIECE OR, THE WONDERFUL "ONE-HOSS SHAY": A LOGICAL STORY by Oliver Wendell Holmes http://www.bartleby.com/102/103.html] That is, it would shatter to smithereens when it failed, since all its members would be equally pushed to the limit.
• Truss bridges are limited as to the distances they can span. For longer spans, either cable stay bridges or suspension bridges are required.
• Good luck to one and all on your bridge building!

Ann Brandon, Larry Alofs and Bill Blunk were unable to do their presentations due to lack of time, but will be scheduled for next time.  See you then!

Notes taken by Porter Johnson