Posted by Scott Ellis (126.96.36.199) on November 13, 2002 at 21:52:33:
There has been some discussion lately about swinging pendulums and moving pivot points. I wanted to take the opportunity to discuss some other related ideas.
One of the few straightforward remarks that Bessler ever made about the wheel was that the weights “gained force from their own swinging.” To me, this sounds a lot like the notion of pumping a swing. Plus, this would be an obvious place to look for a perpetual motion, since the phenomenon of resonance allows a tiny force applied with the right timing to cause a very large motion over time.
There are two main ways to pump a swing, and of course both require a net input of energy:
A. By lifting the mass at the bottom of a swing
B. By adding angular momentum to the system (rotating the mass during the swing)
A. Lifting the mass
If we lift the mass a little bit at the bottom of the swing, it reduces the swing radius . Based on the to the Conservation of Angular Momentum, this makes the mass swing faster. Thus it goes higher than it was before. We do this on a playground swing by pulling back on the chains and pressing the seat forward on the down-swing, and doing the reverse on the back-swing. This creates an angle in the chain, and therefore a reduction in the swing radius. We can also stand up on the swing as shown below:
Another way to pump a swing in the same manner is by lifting the pivot point just a little bit at the swing nadir. We can do this with a weight tied on a string by holding the end of the string and gently lifting with just the right timing.
B. Adding angular momentum
The other way to pump a swing is by adding angular momentum to the system. This is not very intuitive at all, but true nonetheless. Basically, since the angular momentum in the system is conserved, rotating the mass during the swing also causes it to rise higher. Any angular momentum that we put in must be recoverable in the system, so it gets converted into gravitational potential on the other side:
But how can we apply these principles? After all, they both require a net input of energy. I think the trick would be to capture and release the force of gravity in just the right way and with just the right timing to cause the pumping effect to occur.
Here's an idea based on the first principle (lifting the pivot point). Imagine the teeth of the gear must always be in one gear track or the other. That is, they cannot leave one without entering the other:
Another interesting thing about swinging pendulums is how the apparent weight of the mass changes over time. Depending on the various parameters (weight, swing radius, amplitude, etc.) the apparent weight of the mass can range anywhere between one third and two times the actual weight of the mass. That is, at the bottom of the swing, the mass seems much heavier than usual, and at the end points of the swing, the mass seems much lighter than usual.
Therefore, if swinging weights in a wheel were coordinated with one another and with the overall speed of the wheel, then it is possible to envision a scheme where the weights on one side of the wheel were always at their nadirs, and the weights on the other side of the wheel were always at their end points. Therefore, the wheel would always be lighter on one side than the other.
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