unrelated question

course phy 121

"My son is taking ""Technology Ed"" at the middle school. He had to build a tower out of one sheet of paper and 10 inches of tape. It had to be a min of 28 inches tall. I told him repeatedly that the triangle was the most stable and to build it out of triangles. He ultimately listened to mom's advice and build a three sided pyramid with x shaped supports (triangles). His tower reached 49 inches tall and he was very proud of the fact (told all his friends that they needed to start with a tripod). Today (Saturday) he is still tinkering with alternatives and trying to get higher. He decided to build a four sided pyramid, but it keeps crumpling. Besides the fact that it is too tall ( I think he also went to two sheets of paper) is there a reason associated with the four sides that might be contributing to the tower's demise? Why is a triangle more stable than a square or rectangle? Is the possible height related to the base? In other words, is there a point at which the height will become to big for the base and fall over (hey! I think I am asking a proportion question - which is the source of my frustration right now). For example, if the base is 16 inches square then is there way to determine a maximum height it can get to? Thomas wants to know which one could reach a greater height a triangular base, a square base, or a circular base? He won't listen to me :)

A triangle made of a rigid material is stable because if you change any of its angles, then at least one side must also change its length. If the material is rigid it isn't possible to change the length of a side (at least until you exceed the strength of the material).

This isn't the case with a square or rectangle. For example a square can easily be collapsed into a rhompus. This can be prevented by bracing its diagonals, which might help stabilize a square base.

The other factor is that paper is not rigid. It can't be stretched (a piece of paper can't be lengthened without the application of significant force), but it can easily bend or buckle, and therefore shorten. The more sides the pyramid has the more ways it has to buckle. I'm not sure that explains the collapse, since I haven't seen exactly how the structure collapses, but it's one thing to consider.

If you think of making the tower 20 ft. tall, with the same base, it will be clear that at some point it will begin behaving pretty much like a strip of paper that like a tower. It will buckle or bend along the seams, and as soon as this occurs it will collapse.