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terminal velocity in a vacuum?

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We are studying free fall, acceleration, terminal velocity, etc. this week in physics. Dd asked if it is possible to reach terminal velocity in a vacuum? I don't think so because terminal velocity needs air resistance. But, I don't know for sure.


Any physicists out there??

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In vacuum, there is no air resistance, so there would be no velocity dependent force slowing down a falling object. A falling object would accelerate with free-fall acceleration.


A nice demonstration was done by the Apollo 15 crew who dropped a feather and a hammer simultaneously on the moon. Both objects fall at the same rate, in absence of an atmosphere. Look for the video, it's on youtube.

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Regentrude, does this mean there is no terminal velocity in a vacuum? If there was a vacuum created in an infinitely long tube that theoretically isn't subjected to any outside forces, would a dropped item continue to accelerate indefinitely in a straight line?


If the tube was vertical, pointing straight away from Earth, an object released into the tube on top would accelerate until it hits the ground.

But the acceleration would not be constant in an infinite tube, because the gravitational force is approximately constant, causing a constant free-fall acceleration, only in the vicinity of the Earth's surface!

The gravitational force is not really constant, but goes with 1/r^2 where r is the distance from the center of the Earth (this formula is valid only outside of Earth, not in a tunnel into the Earth). If the distance from the surface is very small compared to the radius of the Earth, we can consider the force constant, and the object is under the influence of a constant downward acceleration.

If you make the tube very very long, the force and acceleration will vary. It will still always be pointing towards the center of the Earth, because gravity is attractive, but it will get larger as you approach Earth.


None of this changes the fact that in the absence of air, i.e. in vacuum, there will not be air resistance - and thus there will not be a terminal velocity.

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