Building Scale Models to Predict Real Situations

• A wooden plank ten feet long is placed on two supports a distance apart. How does the plank deform as weight is placed in the center? What is the relationship between the deformation and the magnitude of the weight? Is it linear? As the support distance is changed and deformation vs. weight determined how does this scale? Why?

• What are the factors that determine the strength of the plank? We are going to use this plank to cross a river without getting wet. How heavy a person can this plank withstand and over what span?

• The object is to measure the deflection of a plank when different weights are applied to its center. A plot of weight vs. deflection will allow us to determine how to scale the system.

• Make a series of models of different scale sizes. For example, a 1 foot by 1 inch wide by 5/64" thick wood is a 1/10th scale model of the 10' plank. Record the deflection data (support distance in cm, weight in grams and deflection in cm) and the breaking weight for each of the models.

• Use a 10' x 8" x 3/4" plank and cinder blocks as supports. The weights to be used to test this plank may be bricks. A last experiment is to apply weights till the breaking point. Record this data.

• What are the relationships that have been measured? How do the various relationships scale? Are the large plank's deflections predicted by the models?

• Note that the unit of weight for the large plank were bricks. Bricks are not uniform and they are not a standard weight. Weigh a number of bricks (in grams) and determine an average weight for a brick and a deviation. That is, the average weight has associated with it a spread of values so that we only know approximately the weight of a particular brick.

• Since the top of the plank is under compression and the bottom under stress it stands to reason that just in the center is a point of zero stress and strain (a node). To each side of the plank nail a 10' x 2" x 3/4" strip of pine using 6 penny (6D) finishing nails. Nail into the center of the plank edge. Repeat the deflection vs. weight experiment.

• Make graphs of the data.
  Equipment:
  
  1. each team uses a different type of wood:
     
     1. pine
     2. oak
     3. hemlock
        
     4. ash
        
     5. poplar
        10' x 8" x 3/4" 3 ea.
  2. pine reienforcement boards: 10' x 2" x 3/4" 6 ea.
  3. finishing nails, 6D 1 lb..
  4. weights: bricks 200 lb. worth. (about 100 bricks)
  5. supports: cinder blocks 2 for each board.

On the basis of these data predict the largest weight for a given distance and construct a plank bridge to cross the stream-and try it!

Plank Dynamics-Vibrations

Invariances