Posted by Joel L. Lewis (24.197.38.131) on May 29, 2003 at 15:40:12:
I promised myself I'd stop posting every idea that pops into my head without testing things out more, but I can't resist with this one. Appolagies if I start to sound like I'm belaboring some simple point below, but I want to make sure I'm clear about what I'm REALLY suggesting, as it might initially look like I'm suggesting the old failure of trying to make a falling weight 'lift itself' higher than it fell from. The idea's pretty simple, though. Well, here goes...
While a ballanced lever will be in equilibrium at any position, equal weights hung equidistant from the axle/falcrum, one on each end, will place the center of gravity below the center of rotation and cause the lever to always come to rest at a horizontal, level position. This will also be the case regardless of the distance below the lever that the weights are hung. For instance, the right weight may be 6 inches below the center of rotation(the axle/falcrum)and the weight on the left 12, or vice versa, but provided the weights are equal and connect on a line with and equidistant from the falcrum, the lever will always be at exquilibrium when and only when it is level. Now, this has some interesting consequences.
Let's say that the lever is at a 45 degree angle, and both weights are the same distance below their respective connections to the lever. Imagine a line midway between the levels of the two weights, and you will see that as the lever moves to reach equilibrium, the two weights, being an equal distance below the lever, eventually converge at that level, the total movement of the weight that began at the low end having been to rise to that level, and the total movement of the other weight having been to fall, the same distance, to that level.
Now, let's imagine a second scenerio; the lever is once again at a 45 degree angle, out of equilibrium. However, this time the weights are suspended so that with the lever at this position the weights are at the same level. So, once again, place an imaginary line at that level. This time, as the lever moves to reach equilibrium, something different happens to the weights; when the lever comes to rest at level, the total movement of the weight connected to the high end of the lever will have been to fall, away from that level, and the total movement of that connected to the lower end will have been rise the same distance, also away from that level. And now, in fact, it is the weights that are at a 45 degree angle from level.
And now comes the big question-what if we imagine a second lever, sharing the same falcrum, but also at a 45 degree angle, and what if the weights were to dissengage the first lever and engage it? The weights, being on the same angle as the lever, would now both be the same distance below their respective connecting points. The lever would move to reach equilibrium. The lower weight would move up. The higher weight would move down. They would end up at the same level. The level at which they began. Thus completing the loop. And there's even energy to spare.
If there is some simple fact that I'm overlooking, my apolagies. If anybody that really UNDERSTANDS what I'm trying to say sees a basic problem that I'm overlooking, then of course don't hessitate to correct me. But I've got a good feeling on this one.(Yeah, I know, that's not new for me here, either!:-D) :-)