by UncoveringTruths » Fri 31 Aug 2007, 16:00:13
$this->bbcode_second_pass_quote('', 'T')he "heavier on one side" seduction.
The most naive level of perpetual motion seduction is the notion that if a system has more mass on one side of the axle, then that side must swing downward. That notion is quickly dispelled by consideration of this symmetric arrangement of three equal mass balls on equal length arms. Clearly there's more mass on the left side of the axle. But just as clearly, the device will not turn of its own accord. Even worse, if given a push, it will not turn continually. It will come to a stop from dissipative forces just as any wheel would. This wheel is as likely to come to rest in one position as in any other, for it is perfectly balanced in any position. Persons who have little experience with mechanisms may think it would prefer to come to rest with one ball directly above the axle, and the other two below. That is not true. Our naive expectations are not the way nature works.
We can test its stability by turning the wheel to any position whatever. No matter what position it happens to be in at rest, it has no tendency to turn in either direction, and will not initiate motion by itself.
The earliest unbalanced wheel of Villard de Honnecort underwent countless modifications and embellishments over the years. But the seductive principle that motivated the inventors was that "If you can keep the wheel heavier on one side as it rotates, then it will continue rotating forever." Their overbalanced wheels had weights that moved, and in the static picture at least, there were always more weights on one side of the wheel axle. But, when the system is analyzed, one finds that the torques are balanced (add to zero). A wheel will not initiate motion unless the torques are greater in one direction than the other. If the net torque about an axis are zero, the system will not start turning by itself.
The situation is worse than that. Newton's third law ensures that all internal forces in a system sum to zero, and all internal torques do also. If the system is to move, some external source must supply force or torque. A system with unbalanced torque from external sources moves toward a position where the torques will become zero. That's a position where the system will be in static equilibrium. Typically the system will oscillate around that position, slowing down gradually to rest as its initial stored energy dissipates and it comes to rest.
Critical readers will note that the above comments assumed a uniform gravitational field. Actually the gravitational field decreases with height, and the field direction diverges from the center of the earth. These effects are negligible for a machine that would fit in a laboratory. But they would cause a slight preference for some positions of this wheel. Still, they won't provide any force that would cause a consistently preferred direction of motion through many cycles.
The Physical Principles of Unworkable Devices.
It's a cold cold world when a man has to pawn his shoes.