I've already mentioned one of my favorite things to think about, the infinitely sticky substance (Fish!). Yesterday I came up with another one, an infinitely elastic object. Meaning that it bounces off of things perfectly. Now, I don't claim to understand collisions very well, but the first consideration that comes to mind is whether this object (let's say it's a ball) is hard or soft. If it were rubbery, it would absorb force and then use it to propel itself backwards on collision. If the rebound were perfect, it would bounce off with the same amount of force as it entered with. But on the other hand, if it were hard, it seems like it would bounce off better. The same way that a basketball bounces better than a ball of pizza dough.
On second thought, it would have to be rubbery. It has to deform slightly on impact with another object, doesn't it? Otherwise (and I'm just going on intuition here; I don't have any other tools to work with), it feels like it would shatter on impact, because the forces on the ball would have to go somewhere, cause some change. It has to do with impact, which is force times time. An infinitely hard ball would take no time at all to bounce, so the impact would also be zero. But that doesn't say anything about the force. It could be anything and still satisfy the equation. The other thing that impact is is the change in momentum, and the ball is certainly changing its momentum. After all, it's switching directions entirely. Hmm... I can't remember what kind of a proof that is-assuming one thing, finding that assumption's consequences, and finding a contradiction in them. Here, I assumed that the ball was infinitely hard, and had a contradiction in the magnitude of impact, so I can safely conclude that the ball is not infinitely hard. (I think that's a valid proof)
So we have a rubbery ball that is perfectly elastic and bounces off of things without slowing down in the slightest. If we dropped it to the floor, it would perpetually bounce up to the height we dropped it from and back down to the ground. In other words, there would be no loss of energy. Conclusion: perpetual motion!
The key to this substance is the perfect rebound. This, I suppose, means that it has to rebound in the same time it absorbed the force. It seems like it needs to have a very set shape which it wants to return to with all possible speed. Hmm...but that sounds a lot like a very hard substance. Shoot. I'll leave that question alone for a bit.
What would it be useful/annoying for? Certainly it would be useful for museum exhibits and scientific papers, simply because of its inherent weirdness, but without knowing a bit more about what it would actually be like (hard, soft, etc.), I don't know enough to really tell what it would likely be used for.
Another interesting thing about it is that it cannot possibly make any noise on impact. That is, the ball can't. The wall or floor it hits can. Unless that, too, is made of the elastic material. This is a weird material. I'm starting to see why physics would object to the existence of such matter.
I am thankful for my unbelievably awesome family.
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