High School Math-Physics SMILE Meeting
08 December 1998
Notes Prepared by Alex Junievicz

Carol Zimmerman [Lane Tech HS]

Setup: 2 photo-gates and a cart with a mass to equal 2kg total, and twine connected through a pulley and a weight to accelerate he system... The times through the photo-gate with just enough mass to accelerate the system. Starting the acceleration as close as possible to the first photo-gate to effectively have it at 0 velocity. for 32cm distance times of 0.988 for 2kg, .682 for 3Kg, .599 for 4Kg cart masses would produce a slope of 1.4 where 2.0 was expected. Why?

In the discussion a point was brought up as the system mass was the Cart + Hanging mass therefore should the mass suspended be subtracted from the cart so that the total mass was 2kg. Since it was "physics" there were problems with the apparatus, and when it was fixed we ran out of time for discussion.

Professor John O'Leary [IIT Department of Civil Engineering]

```Bridge Design
Discussion on bending and shear
---------X--------
X                O Note: one end fixed and other on rollers to permit expansion

----------|
|----------     Stress moments ?
.
.   .
.         .
.               .
.                       .    Bending moments  ?
|           .
|
Force / area   = strain   \\no units   |     .    < /
|   .       / Young's
|  .   <  /modulus
|._________________

?  = E  e
-----------Geometry of Section-------------
.......
.     .               M l/2       Pl
.     .            =  _____   =  ----
.     .                I          4
.     .
.......
a factor of 8 is gained by making the height larger than girth.

.......                ..........
.     .                    .
.     .                    .
.     .    becomes         .        Thus maximum strength
.     .                    .         is obtained by a thin
.......                    .         taller structure with
..........    a top and bottom..
The "I" beam
Which also can translate to the truss
x...............x
.   .           .   .
.       .       .       .
.           .   .           .
x..............x...............x

spots labeled x are where members are joined
and provide the strongest points
( a good place for the load )

Note--Like a strip of paper it is strong in one plane and care must be made
to prevent buckling (twisting) failures Note: bridges often fail by twisting,
rather than from material failure.

New Rules-abutments are possible. Now the bottom (or resting surface) can be
fixed, as in the above one had to be variable, not it could be fixed and
allow less materials used to prevent stretching when using an arch.
---------Compression vs Tension ------------

Side view                   Comp   mass
of a beam    ________.______><_______.______________.
|      .   .           .   .          . |
|    .       .       .       .      .   |
|  .           .   .           .  .     |
|._______________.______<>______._______|
Tension
at the top there will be a force to compress; at the bottom there will be
In a cable system there will be tension

pull   >  .                                .  < pulling
.                          .
.    <> tension    .
.      .

The shape of the wire will itself determined by the load  and could be a
parabola and an arch will be sort of mirror
>< force compression
.       .
.                     .
.                             .
.                                   .
Force <> tension
a cable could be used
Interesting side Bar --after meeting
Load points should be junctions of members
_______x_________________x_______
.    .          *   .
.         *  .         .
.   *                .    .
________________________________

side view
.........
.      ..
. .  .  .
.  ..   .
. .  .  .    x members to help
..    . .        prevent twisting
.........        failures

```

References

• Why Buildings Stand up by Mario Salvodori
• Structures Daniel L Schodek 3rd Edition
• http://www.usma.edu [West Point Military Academy] has mechanical structures

Note: I saw an question someone had on a test where a locomotive 4 times the weight of a flat car hit and coupled, at 10Km/hr. My first thought was that there was a derailment and no conservation of movement on the tracks as they were dragged. I asked O'Leary's associate who seemed to be knowledgeable about Railroads....Coupling speed is done below 5 and at 10 damage may be result. I was interested in the comment that the power is much greater in toy trains that there may not be a realistic modeling.