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Re: [Phys-L] Impossible vehicles.

BTW, a *somewhat* similar effect is seen by pulling horizontally on the thread away from of a partially unwound spool of thread lying sideways on a flat surface. If the thread comes off the spool on the bottom (i.e. surface facing) side of the spool it will roll and *wind itself up* by rolling toward you *faster* than the pulled thread speed when you attempt to pull the thread toward you away from the spool. But if the thread comes off on the top (i.e. surface away) side of the spool the thread will unwind further, but the spool will move toward you slower than the speed of the pulled thread. This effect requires that the spool's outer edge radius contacting the surface be greater than radius of the thread's de-contact point where it comes off the spool, and it requires that the spool's contacts with the surface have enough tractive (i.e. static) friction to prevent significant slipping when the spool rolls.

OTOH, if the radius of the rolling contact is less than the radius of the thread pull off point (with sufficient surface/spool static friction) and the thread comes off the spool on the bottom side then the spool will roll *away* from you and unwind as you pull on the thread. And if the thread comes off the spool on the top side the spool will roll toward you at less than 1/2 of the speed at which the thread is pulled. In order for these last 2 cases to work and prevent interference between the surface and the thread where surface contact radius is less than the thread pull-off radius the surface may need to be modified so the thread is pulled off in a central slot under the surface and the spool rolls on a pair of relatively narrow rails instead of an overall flat surface.

In both of the bottom pull-off cases the spool speed *diverges* (either toward you, or away from you, depending on the radius ratio) in units of the pulled thread speed (relative to the surface) as the radius ratio approaches unity from either side. So if the radius ratio is sufficiently close to unity in the bottom pull-off cases either the spool will begin to slip for not having enough contact static friction or the thread will snap for lack of tensile strength. Slipping can be prevented by switching from rolling on a flat surface to turning a gear on a fixed linear rack. Snapping the thread may be delayed by going to stronger thread/cord/cable. For a sufficiently strong apparatus with a radius ratio sufficiently close to unity the thread/cable will not be able to be moved by pulling it with the maximum pulling tension available in the bottom pull-off cases.

A thermodynamically similar situation occurs with an absorption refrigerator, which has no moving parts (other than sealed self-convecting/evaporating/condensing/dissolving internal fluids contained inside various tubes and vessels), and is operated by *burning* a fuel such as propane/LPG/natural gas, or by using some other heat source. Absorption refrigerators are quite common in off-grid applications where electrical power is not available to operate a motor driving a compressor & fan used in a more conventional refrigerator.

An analogous electrical device is a transformer. Analogous mechanical devices are block & tackle, gearbox, and lever.

David Bowman