The Impossibility of Flying Heavy Aircraft Without Training

You inject some gas into the cylinder below the disk. The disk will
rise until the pressure reduces to equal the weight of the disk. At
this point, the system is in equilibrium. What momentum transfer is
required at this point to maintain the weight of the disk?

The disk is constantly transferring momentum to the air below it, which
is transferring it right back after bouncing off of the floor. The disk
gets the momentum to transfer by beginning to fall down (due to gravity)
and that increases the pressure (the cumulative force of all the gas
molecules crashing into the disk).

If you remove gravity, the disk will start to accelerate upwards from
the pressure, due to transfer of momentum from the gas to the disk,
which is not counteracted by gravity. If the disk is massless, then the
same thing will happen.

If the temperature is lowered, the disk will fall because the molecules
will not have sufficient (thermal motion) momentum to counteract the
disk's force. The falling disk will impart momentum to the gas
molecules (increasing the temperature, or momentum per collision) and
will compress the gas in the cylinder (increasing the pressure, or
number of collisions per area) until equilibrium is once again attained,
at a lower altitude.

If the hollow cylinder has no bottom but is infinitely long, and the
disk still somehow has weight, then the disk will simply fall, imparting
its momentum to the gas molecules (which won't become compressed since
the volume is not increasing, and whose increase in temperature will be
dissipated over an infinite supply of gas. A terminal velocity will be
reached which will depend on the gas density.

Jose
--
Money: what you need when you run out of brains.
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