Late last week, I ran across a spectacular video of a man being completely awesome: http://www.youtube.com/watch?v=BZwNLWgsUMg The video shows Christophe Hamel jumping/falling/hurtling off of walls, landing on a trampoline, and then bouncing up to land back on top of the wall -- sometimes in a handstand in case there was a risk you wouldn't be impressed enough otherwise [seen at 1:50+]. My first thought on seeing this video was "It's gotta be really hard for his mom to watch this." My second thought was, "Is it really possible for a trampoline to conserve energy that well?" Here's the problem. In introductory physics, you learn that when something falls in a gravitational field, it turns gravitational potential energy into kinetic energy (i.e., falls down, goes faster). If that same something then bounces, it proceeds to do the reverse. To get back to exactly the same height, there cannot be any energy lost from the object -- no energy lost to air resistance, or to internal motions in the object. However, in pretty much every aspect of our real world experience, we know that this perfect energy conservation doesn't occur, leading to the following:
If you're talking about a bouncing ball, and you lose some energy deforming the ball during the bounce, no harm, no foul. But, if you've just fallen 2 stories and are trying to bounce back up to the same height, then you'd better conserve every last possible bit of energy you possibly can. I've spent more time than I care to admit watching this guy, trying to figure out if trampolines are really that efficient at changing a person's direction without significant energy loss. I think that to first order, yeah, they must be. At first I thought that he might be extracting energy out of his muscles at the turnaround, but in most of the tricks, he's pretty much dead dropping on his curled back, not pushing off with his legs. My second thought was that maybe he was extracting energy from his initial rotation, but in a number of the tricks he's coming back with more rotation than he left with (although frequently in a tighter tuck, so it's not clear what's actually happening with his angular momentum -- i.e., I've watched, but have not done math). The one thing that has convinced me that he does not have an invisible jet pack is that he doesn't really come back to exactly the same height. His feet do (eventually), but he usually starts the trick from a tall position, frequently with an arm stretched vertically, or with a jump to get some extra height. Then, when he comes back up, he's frequently in a tuck or a dive, such that his center of mass is indeed lower than when he took off (though granted, not by much!). Here's a couple of examples right from the beginning of the film, with the takeoff on the left and the return on the right:
I'm relieved that energy conservation is still with us, despite this man's very fine attempts to do away with it.