Elevator paradox (water)

:This article refers to the elevator paradox as it relates to water. For the elevator paradox as it relates to the transportation device the elevator, see elevator paradox

Related Topics:
Elevator - Elevator paradox

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The elevator paradox, in terms of water, relates to the position of a hydrometer floating in water, which, in a classic demonstration, remains at an equilibrium position as the entire system is placed in an elevator which moves up and down, changing the air pressure.

Related Topics:
Water - Hydrometer - Equilibrium - Air pressure

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This is due to the fact that the change in air pressure is applied to the entire hydrometer flask; the underwater portion of the flask receives a transmitted force through the water, thus the flask receives no net force due to the change in air pressure. A cartesian diver, on the other hand, has an air space which, unlike a hydrometer, is not sealed, and thus can change its displacement as increasing external air pressure compresses the air in the diver. It should be noted that not all closed containers are immune from this change; a non-rigid container like a toy balloon will be changed, as will the rib cage of a human SCUBA diver, and such systems will vary in buoyancy. A glass hydrometer is rigid under normal pressure, for all practical purposes.

Related Topics:
Cartesian diver - SCUBA

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If a cartesian diver (instead of being in the classic plastic bottle) were placed in a beaker in an elevator, and the elevator could be lowered or raised enough to significantly change the volume of the air, the diver would respond.

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It is interesting to note that the upward or downward acceleration of the elevator, as long as the net force is directed downward, will not change the equilibrium point either - the force due to acceleration acts on the hydrometer exactly as it would on an equal mass of water.

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