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Balloon in an Elevator
A person is holding on to a helium balloon in an elevator. The elevator cable snaps, and at the exact same moment, the person lets go of the helium balloon. In the perspective of the person in the elevator, what happens to the balloon’s motion?
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guys, guys…. no one has actually considered the fact that the lift could be on the ground floor (ie not moving) … ;)
Thanks Whimbrel for the experimental demonstration.
So downy bill gave the correct answer in the 3rd comment. A few others (djkool, Jeffmo, dontgotaname, hacksoncode and isaacnewtonavatar) recognized that. Most of the rest of you fail and should stop answering physics questions if you can’t recognize a correct answer when it is given.
Why not just watch the answer?
http://www.youtube.com/watch?v=0NZSeTXDj6I
31 second you tube clip of this exact experiment, from NASA.
The intital condition has the elevator experiencing a force while restrained by the cable due to the Earth’s 1G acceleration, and the balloon experiencing a force while restrained by the string due due to the Earth’s 1G acceleration and due to its bouyancy in the 1G field due to the density difference between its internal volume (low density) and the air around it (higher density). In addition there is an air pressure gradient in the elevator due to the Earth’s 1G acceleration; the pressure is higher near the elevator floor.
When the cable snaps and the string is simultaneously released, three things happen:
1) The elevator is suddently in free fall in the Earth’s 1G field, no longer experiencing a force.
2) The balloon no longer experiences either a downward force due to the Earth’s 1G field, nor a buoyancy due to the density difference between its internal volume and the air, because the buoyancy was due to the presence of the 1G field now removed.
3) But the air pressure in the elevator quickly equalizes.
The net effect is that the air moves upward slightly with respect to the elevator walls, carrying the balloon upward slightly. The air then stops moving with respect to the elevator walls, and the balloon stops moving with respect to the elevator walls.
The elevator, balloon, and air (we ignore the relative motion of the person, which is a complex question) then proceed to fall without motion relative to one another until the elevator hits the basement floor. Assuming a rigid elevator structure which is not changed by the collision, at that time the person pancakes on the elevator floor, the air stops and re-establishes a pressure gradient, buoyancy of the balloon relative to the air returns, and the balloon floats upward relative to the elevator walls, stopping only when it reaches the elevator ceiling.
jesus’ magic breath will continue pushing the balloon toward heaven even if the elevator falls because balloons are pretty and jesus likes them. And when the people die from the elevator crashing, his magic breath will also push their souls up to heaven, except the non-christian people, who have heavy souls, so they go to hell
djkool14 is almost right. In an ideal elevator ignoring all the various things that upset this problem, it would do as he says (initially).
However, in a real elevator, first of all, the elevator can’t possibly freefall in an elevator shaft even if all the safety equipment fails. There’s a mass of air beneath it that becomes pressurized and cushions its fall, and there’s friction on the sides. If it were stated in the problem to ignore these effects, that would be a different matter.
Therefore the balloon rises, just because there’s still significant gravity felt by the occupants, including the air in the elevator.
He’s right in the sense that the air in the elevator will redistribute itself because the gravity is lower during the pseudo-freefall. That will help push the balloon up very slightly (the density difference across 10 feet is really very small, though, so this is likely lost in the noise… and is only relevant to the “ideal, ignore all the realities” version of the problem).
Even if it were a complete freefall, though, the balloon would still continue to rise, probably to the ceiling, because the effect djkool14 mentions will get it started moving, and inertia will keep it moving until air friction brings it to a halt. Of course, it’s impossible to predict exactly what will happen because convection is a chaotic process, and the movement of the screaming and thrashing passengers is likely to screw up the perfect ideal motions. It will wander about quite a bit.
To summarize: In a real elevator, it rises due to there still being some gravity creating bouyancy. In an ideal elevator that is allowed to come to a steady state where the air isn’t moving around, and the balloon has come to a stop from it’s initial movement upwards, it will come to a rest (eventually… but it’s almost impossible to predict when and where that will be).
Lets boil the problem down to this. If the elevator was in space and completely free of any gravity. What would the balloon do?
Acepincter is correct. It’s sort of a centrifugal force in which the denser air resting at the bottom of the elevator gets moved upwards due to the change in downward velocity.
You can do a similar experiment with a balloon in a car. Go fast, hit the brakes, the balloon moves towards the back of the car. You can find an explanation here.
http://www.teachersdomain.org/resource/phy03.sci.phys.matter.buocar/
Their reasoning is opposite my own (they sue acceleration instead of deceleration) but it’s still sound.
@endorphins This reply is just to avoid the possibility that someone seeing this might think I didn’t reply because I agreed that endorphin is correct.
This is a test of your physics reasoning ability. Read Endorphin’s comments and my comments carefully. If you understand physics, you will be able to pick out which of us is right. If that sounds like something your physics professor would say, it is probably for a good reason. :)
The balloon moves downward. Towards the person’s feet. Or, more precisely, AWAY FROM the denser, heavier air which will be forced to the top of the elevator by inertia.
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