It has been reported that a wad of crumpled paper has a very interesting property: the tighter it is wadded the more it resists further compression (ref.). This is thought to be due to the fact that more and more of the paper is given over to being folded creases, each having stored up energy tending to straighten out again. While this seems rather obvious, the physicists who did this will not win any great awards because they have overlooked one major aspect: what are the implications of this. ALWAYS look for the implications of your work. Where can your newfound knowledge be applied?
In this case, the knowledge might be employed in intentionally crushable items such as resilient highway crash barriers or the padding in helmets.
Let us first take a look at highway crash barriers. There are three types commonly employed in the USA.
- Large plastic barrels of water, which when hit gush their contents up into the air. This requires a lot of energy to throw the massive amounts of water upwards, and the moving vehicle dissipates its own energy (slows down) as it adds energy to the water. Energy is dissipated in a linear fashion as each barrel in a line of them requires the same amount of energy to throw its 500 pounds of water upwards. To make the barriers more impenetrable, the barrels are usually placed in a triangle so that the deeped the vehicle penetrates the cluster, the more and more energy is absorbed.
- Foamed concrete blocks. While these look like ordinary concrete blocks, they are much lighter and crushable. Their value lies in the fact that they are permanent and resist the ravages of weathering, while the plastic barrels, above, become more and more brittle in the presence of sunlight's UV radiation. However, the "air-entrained" concrete blocks are at their greatest resistance to crushing at the beginning of the crush and then become weaker and weaker as the shock waves go through them.
- Accordianated steel barriers flex like springs to absorb the shock of a collision. However, these, like the foamed concrete blocks, are strongest at the beginning of impact, and lose resistance as the penetration continues.
Thus the idea of crumpled paper comes into play. It, like the triangle of water barrels, acquires more and more resistance the further the penetration. Of course, crushed paper barriers would not work in highway situations if for no other reason that they cannot stand up to moisture. They'd turn to pulp. What might be used are crumpled aluminum sheets, for example.
But paper is still useful for your own project analyses. What you need is a big wad of crumpled brown wrapping paper, a cylindrical container (perhaps a garbage can), a piston made of a sheet of wood that is slightly narrower than the cylinder, and some weights (perhaps some bricks).
- Figure out the volume of the paper sheet you wil be using. I'll let you figure out how to do this!
- Unfold (hint!) the paper and flatten it out (or get a similar sized piece of paper). Then wad it up into a loose ball.
- Place the wad into the cylinder so that it touches the bottom of the container, and measure the height of the wad.
- Weigh the piston, and place that atop the wad. Again measure the height of the wad. It should be slightly compressed by the weight of the piston.
- Add some weight to the top of the piston, and measure the height. Bricks might do for your weights. Add more bricks and keep measuring the decreasing height of the wad.
- Do this five times with other sheets of paper of the same dimensions.
- Make a graph of weight versus height for each of the five trials. (Teachers and judges love graphs!)
What sort of curve did you get on the graph? Does the wad become easier and easier to compress, or harder and harder? How much pressure did you have to exert to push the piston down 1 inch at the beginning, and how much for an inch later on? Does this look promising for a technology useful in crash protection when you want the collision to be first gently resisted and then stronger and stronger and stronger?
Other things you can do with this
It is obvious that the more crinkles you can force the paper to form as it is crushed, the better the "effect." So think of ways to make that happen. Here might be two ways:
- Rather than having a smooth-walled cylinder, have one with roughed sides so that the parts of the wad that touch the walls get caught in the crushing process and then must fold.
- Rather than one huge wad of paper in the cylinder, add many smaller wads of paper. (Instead of using one huge sheet of paper, take a sheet of the same size and cut it into smaller pieces and then wad them up loosely and add them to the cylinder.
Make comparison graphs using the above two strategies to see if they work. Ahhhh! More graphs: your teacher will love you! "A+" will not be a high enough grade.