High School Physics Smile [12-09-97]

Notes Prepared by Porter Johnson

Professor John O’Leary [Civil and Architectural Engineering, IIT]

Professor O’Leary gave his annual lecture on principles of bridge-building.

He began by describing the forces on a typical bridge structure, with center loading and side supports:

```
Compression
---- >         < -----
__________________
/\                /\
/  \              /  \
/    \            /    \
/      \          /      \
/        \        /        \
/          \      /          \
/            \    /            \
/     < -----  \  /  ----- >     \
/________________\/________________\
/\             Expansion            /\
|                  |                |
|                  |                |
|                  |                |
Support Force             |                 Support Force
\/
```

The effect of the load, and the balance of "bending moments" [what Civil Engineers call "torques"] results in compression on the top members, and forces of expansion a the bottom.

The maximum stress [force per unit area] s max on a board of width b, and height h, and length L is proportional to the length L, inversely proportional to the width b, and inversely proportional to the square of the height h:

s max µ L / b h2

Furthermore, the bending displacement d at the center is proportional to the following:

d µ L3 / (b h3)

As a consequence, we can make s maxand d small by making the height h large.

The buckling formula obtained by Euler is

Pcritical = p 2 E /4 I/L2

where the parameter I for a rectangle is

I = b h3/12

A beam buckles under compression about the "weak axis", rather than the "strong" axis.

Another important design principle is that "triangulation" makes very stable structures, whereas non-triangular regions can more easily become deformed under stress.

There were several other presentations on this last day of the Fall 1997 SMILE program.

Estellvania Sanders [Chicago Vocational HS ]

She did a lesson on measuring and comparing weights of paper, plastic, and styrofoam cups filled with water, orange juice, and pop. The empty cups weighed 3-4 grams, whereas the full one weighed 60-120 grams, and the cups weighed the same, or perhaps a little more, after the liquid was poured out of them. She made the presentation to show how to teach students the concept of measurement and data taking. [She did "signing" for deaf student throughout her lectures, and elicited signing respo nses from the class.]

She did a lesson on magnetism using the electric motor as a device to deflect compasses from pointing "true North". It was not easy to measure secondary currents even using a micro-ammeter, although the primary current in the motor did cause a compass needle to deflect.

Angela Scott [Crane HS]

She did a presentation identifying the physical properties of chemical compounds, but categorizing their physical properties. Such a classification does not, in general, identify a chemical uniquely, but it is an important consideration in chemical an alysis.

Angela Patrick [Crown School]

She made craters like those on the moon and Mars by launching various projectiles into a pan filled with flour, corn meal, and grits [mercifully, the uncooked variety]. The projectiles dug out a hole, and caused elevations of material along the sides, and very much resembled the lunar/Martian variety. A NASA package suggested using dry sand, but since that was unavailable she improvised using more readily available materials.

Bill Lilly [Kenwood HS]

He showed a new calculator-based-ranger [CBR], which is used to detect motion and measure distance. It can be incorporated into programs on the calculator for automatic data-taking. The device represents an improvement on the older CBL devices. We r an out of time during Bill’s presentation, and we hope he can return to show it next year.

Happy holidays to all! See you next year!

### Addendum to Smile NOTES 12-9-97

Prepared by Alex Juneviecz

Estellvenia Sanders

Measurements and Comparison (Signing)

Vocabulary

Cup Water Juice Soda(pop)

Scale Empty Compare Pour

Same Record-Write Scale

Supplies

2 each plastic and styro-foam cups

quantity of 1. Water 2. Orange Juice 3. Soda

Procedure

Mass cup - partially fill cup - mass cup with liquid -

then empty cup and mass cup again.

Repeat for each type of liquid and cup

write comparison state hypothesis

-----------------------------------------------------------

J. O'Leary --- IIT Civil Engr ---

Showed that the bending of a meter stick depended upon direction

Showed the formulas for a beam that the element for height had a cubed and the

width has a square element. Thus the height was more important then the

width. Thus a tall beam was stronger, and that the elements in the center

were not very important. Am I form was much better as there are compression

at the top and stretching at the bottom.

Physics teacher call the bending torque, but civil engineers use the term

Moments. The term torque has a different application to civil engineers.

(Compression) Pressure

\/

-----------------------------------------------------------------

/\ O

P/2 l/2 l/2 P/2

Fixed end Moveable end

Helps prevent

sheering when

beam stretches

--------------------------------- especially due

| to temperature

|

Sheer vs Pressure /\ |--------------------------------

.

. .

. Pl/4 .

. .

. .

. .

Bending Moments /\

The problems in a bridge failure is usually twisting

and x cross members are used in the base, top and

entrance to the bridge

The top and bottom of an I beam is sometimes laminated

to add thickness providing more strength.

___________

| | _

|____ ____| O = 3/2 pl/bh**2

| |

| | Delta = P/4e l**2/bh**3

| |

| | h

| | e is a constant

| |

---| |--- steel = 3 x 10**7

| | Al = 12 x 10**6

|_________| wood = ? x 10**5

-b- Idea is to get the most mass as far

as possible from the center

Euler's Formulas

Showed that a foam stick when presses bend and broke

when pressure applied laterally

Pressure

\/ Critical Value

XX

XX .

XX . Bends at

XX . a certain pressure Pcr = Pi**2 e/4 I/l**2

XX

xxxxxxxxxxxxxxx

I = bh**2/12

Problem with tube bridges

xxxxx xxxxx

x x twisting x x

xxxxx xxxxx

-----------------------------------------------------------------

Jane

Magnets

Showed a galvanometer she made using a compass by

wrapping bell wire around.

A generator using a magnet and 20 turns of bell wire

--------------------------------

Angela Scott Crane Prep

Identifying Chemical Properties

3 known powders and they are to identify which is which

Physical Properties

Color

Shiny or Dull

Crystalline or powder

Chemical

Re-action to Silver Nitrate

HCL

--------------------------

Angela P Crown School

An activity that can be used with a variety of ages

Craters-

A pan full of power. Improvised by the use

of Flower, Corn Meal--covered with

Jello powder to give a layer of color.

Throw objects at various speeds and mass to see how creators

are created. Adapted from casual observation to detailed

analysis of rays, and measurement of results, etc.

---------------------

Bill Kenwood A.

Brought in a TI CBR. Used with TI82 etc. The CBR has programs

internally available and can be plugged into TI82 and transfer

the program.