and Garden Poles
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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
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 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.