Skewers and Garden Poles

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Building on two scales gives clear examples of how some relationships of physical properties change with scale and others remain the same. On both scales, triangular elements were the most stable. However, structures seem less rigid and more ready to twist on the larger scale.

The proportions of the skewers and the garden poles were the same. (This means that if the skewers are 200 times as long as they are thick, then the garden poles are also 200 times as long as they are thick.) The linear dimensions of the garden poles are 6 times the size of the corresponding linear dimensions of the skewers. This means garden pole areas are 36 (6 to the 2nd) times larger than the skewer areas. Garden pole volume is 216 (6 to the second) times larger than the skewer volume. The physical consequences of this are dramatic. Strength depends on cross-sectional area. This means garden poles are 36 times as strong as skewers. However, weight depends on volume. Garden poles weigh 216 times as much as skewers. Garden pole structures have to support greater weight for their strength and are therefore more floppy.

This effect is exaggerated in cantilevers. Since cantilevers are built out from a support, the distance of the weight from the support acting on the structure becomes a dominant factor. For the garden pole cantilevers, not only are they heavier than their skewer counterparts, but their center-of-mass is farther out from the support, creating proportionally greater torque. This adds to the bending that can be seen in these structures.

• Tie-in to the Straw and Pins-Building Out activity: This activity can be scaled up significantly by using plastic golf tubes and nails or wire. Plastic golf tubes are sold in some shops that carry golf supplies. They have 1-inch diameters and are as long as the shaft of a golf club. A set of these is rather expensive, so if you use them, you will probably just get one set for the class. To get repeated use, try putting holes in the tubes with a hole punch and joining the tubes with wire. This activity can be scaled down by using cocktail straws and the smallest pins available at a sewing store. The scale change is not large but the effects are still noticeable.

• Tie-in to the Clay Bridges activity: This activity can lend itself to illustrating the effects of scale on structure simply by trying to build bridges with different amounts of clay. Can you build a bridge twice as long with twice as much clay? How much clay do you need to build a bridge half as long? Have your students test their predictions. (See the Clay Beams and Columns activity for more on scaling with clay.)

• Tie-in to the Paper Bridges activity: Experimentation with larger sheets of heavier paper or smaller sheets of onionskin' paper can lead to scale comparisons here. The findings here are much more qualitative since scaling, especially for paper thickness, is much less controlled.