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Q & A: perpetuum mobile

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Most recent answer: 10/22/2007
Q:
Is it possible to create perpetual motion on earth or in space? If you put a pendulum in a complete vacuum and swung it, would it create perpetual motion?
- Adam (age 13)
Massachusetts
A:
When people talk about íperpetual motion machinesí they usually mean machines from which useful work can be extracted forever. That would violate the laws of thermodynamics.

What you mean is something that would just keep oscillating forever, without providing any work. Thatís still impossible.

In your example, if there were absolutely no air in contact with the pendulum, and if it had a perfectly frictionless pivot, you might wonder where its energy could go. Because it has a mass which keeps accelerating, it will radiate gravitational waves, and gradually lose energy and slow down.

OK, that will take a long time. But a process exactly like that happens with some astronomical objects, for which the slowing due to gravitational radiation is measured.


Mike W.

Quantum-mechanical systems in their lowest energy states (think atoms with electrons in their orbits) still have kinetic energy which never goes away, but also from which no energy can be extracted (there is no lower energy state than the lowest one). The electrons have energies, meaning that the average square of the momentum of the electrons does not vanish. That's true even though at any time the average momentum is zero.

Tom

(published on 10/22/2007)

Follow-Up #1: gravitational radiation

Q:
Mike W. answered the question, in part, with: "...if there were absolutely no air in contact with the pendulum, and if it had a perfectly frictionless pivot, you might wonder where its energy could go. Because it has a mass which keeps accelerating, it will radiate gravitational waves, and gradually lose energy and slow down." Gravitational waves are generated by a non-zero second time-derivative of the quadrupole moment of the stress-energy tensor. What component of a frictionless pendulum in motion would possess that requirement? In other words, how is it mechanically identical to a spinning dumbbell?
- Richard R. (age 24)
Chicago, IL, USA
A:
Itís not mechanically equivalent to a spinning dumbbell, but thatís hardly the only configuration which radiates, because it's not the only one with a second time derivative of the mass distribution.

 The pendulum is very far from spherical. Its mass distribution about the pivot has both dipole and quadrupole components. As it swings back and forth, thereís a second time  derivative to the orientation of these moments.

Mike W.

p.s. To be precise, if you include the earth as part of the system, the dipole term as seen from a distance is zero. However, the local part of the field still generates tidal fields from which some energy is extracted by friction in the resulting tides.


(published on 10/22/2007)

Follow-up on this answer.