Starting the arch might be easier if one person reads the directions out loud.
Raise the HINGED BASE against the LAYOUT BOARD.
Begin each side of the arch with block 1. Place the blocks on the drawing matching the positions of the green triangles and black lines.
Make sure the blocks are tight against each other and just cover the pattern.
Holding the HINGED BASE against the LAYOUT BOARD, use the handles to slowly raise the arch.
Holding the HINGED BASE against the table top, slowly lower the LAYOUT BOARD.
The shape of the arch copies the shape of the hanging chain. Gravity is pulling down on the chain. It does not fall because the eyebolt at the top of each post is pulling up, opposing gravity.
The chain is very flexible. Push on any link and what happens? The chain returns to the same shape. Why? In this shape, called a catenary curve, the two opposite pulls or forces are in balance, or at equilibrium. Because the chain is very flexible, it will move until the opposing forces are in balance. Nature is demonstrating a stable shape. The arch you built has the exact same shape as the hanging chain, only upside down. It copies what nature has shown to be a stable shape.
So, push gently on your arch to see how strong it is.
Utility wires alongside roads and streets form catenary curves between the supporting poles. Suspension bridge main support cables are also examples of catenary curves. The St. Louis Gateway Arch is another example of a catenary arch.
Cutting blocks of wood to make a catenary arch is hard. The ends of the blocks must be cut at special angles. But you can make your own catenary curve with any length of very flexible chain, including a necklace. Try holding two different chains side by side and see if their curves match.
Think about the arch you built. Gravity is pulling down on each of the blocks of wood. What is opposing gravity?
For the hanging chain, the eyebolts at the tops of the posts are pulling up, opposing gravity. When the wooden arch is standing, nothing is pulling up. However, the tabletop is pushing up on the bottom blocks.
The force of gravity on the moon is much less than the force of gravity on the earth. If this exhibit were placed on the moon, would the hanging chain take the same shape? Why or why not?
Would the wooden arch stand? Why or why not?
Although the pull of gravity is less on the moon, it is still a uniform force. The shape of the chain would be the same.
The arch would stand just as well in the moon's reduced gravity.
The arch you built is made of maple wood. Imagine blocks of the same shape and size made of balsa wood, which is much lighter than maple. Would a balsa wood arch stand as well as the maple wood arch? Why or why not?
The weight of the material used to build the arch is irrelevant. The catenary arch stands because the opposing forces are exactly equal along the curve. Gravity will exert more pull on heavier materials, so the table will have to push harder in opposition, but the forces will still be in equilibrium.
Look closely at the shape of the hanging chain. At the top, the chain is almost straight up and down (vertical); as you move down the side the curve starts flattening out; at the bottom of the chain the curve is flat (horizontal). Why?
Each link of the chain supports all of the links below it. Links near the center have only a few links below them, and thus little weight is pulling on them. Further up the chain, there is greater weight pulling on each link. The topmost links support all of the remaining links and thus support the greatest amount of weight.
Using the chain as a model, answer the following question. Will the wooden arch be able to support a set of car keys gently placed on top of block 11? Why or why not?
When any weight is placed upon the bottom link, the chain assumes a different shape, meaning that the original curve no longer balances out the opposing forces. Therefore one would not expect the wooden arch to be able to support such a point load. See how much of a point load your arch will support.
Picture one side of the arch made of lighter weight basswood and the other side made of much heavier hickory wood. If block 11 is made entirely of one or the other, would you expect the arch to stand? Block 11 could be divided into left and right halves, front and back halves or top and bottom halves. If one half of block 11 is made of basswood and the other half of hickory, would you expect the arch to stand? Would it make a difference how block 11 was divided?
Each side of the standing arch both pushes down upon the table and sideways against the other side of the arch. If the two sides have distinctly different weights the arch would not stand.
Block 11 is not part of either side of the arch. Gravity is pulling straight down on this block, but it is also pushing against each side. If block 11 were made of a substantially lighter material than the two sides, the arch should still stand. If block 11 were made of a substantially heavier material the arch probably would not stand.
If you place a sheet of paper on a smooth surface such as a kitchen counter, place your hand on the paper and push straight down onto the paper nothing happens; if you push down at an angle to the countertop rather than perpendicular, the paper (and your hand) slide sideways. In the arch you built, why is it important that the ends of the blocks are cut at very specific angles?
The ends of the blocks are cut at specific angles so that they are always perpendicular to the shape of the curve. This causes the opposing forces to be passed directly along the curve rather than inward or outward.
further information listing needed
This exhibit is described in the Exploratorium Cookbook series.
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