Ye Olde Anti-Gravity Cup Experiment

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Forum Viking
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Ye Olde Anti-Gravity Cup Experiment

Hark! Physics majors assemble!

OK so what we have is the classics index-card-stuck-to-a-cup experiment. You fill up a cup mostly with water, then hold an index card tightly over it, then flip it over quickly. When you remove your hand, it stays in place. So the question is, of course, why? The forces at play here are these, I believe:
1. The atmospheric pressure on the bottom of the card is greater than the pressure provided by the water inside the cup: in this case, the water just provides a seal to keep the atmosphere out and maintain that pressure differential.
a. If so, then the smallest amount of water possible would work best (just wetting the edge of the cup does work, by the way, but probably not "best"). I don't think this is it, although I think it is the standard explanation, unless a greater amount of water provides a better seal or something.
2. The water inside the cup wants to escape, but in order to do so, the air must expand to n-times it's original volume. The potential energy of the water is too small to overcome the co/adhesion of the index card to the water and also provide the amount of work needed to expand the system, so nothing can get out. In this case either a) a completely full cup would work best, because the water would have to expand infinitely, or b) you have to balance the added weight of the extra water with the added suction of the smaller volume of air, meaning that that shit can be optimized (in a more complicated way than just empty or full), which is always good.

I was using a 3*5 inch notecard and a cup of radius .041m and volume about 325 mL. Naturally convert to metric and use Pascals if you have any mathematical solutions or anything.

It might be interesting to test this again using oil instead of water and comparing those results.
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Kow
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Re: Ye Olde Anit-Gravity Cup Experiment

Forum Viking wrote:2. The water inside the cup wants to escape, but in order to do so, the air must expand to n-times it's original volume. The potential energy of the water is too small to overcome the co/adhesion of the index card to the water and also provide the amount of work needed to expand the system, so nothing can get out. In this case either a) a completely full cup would work best, because the water would have to expand infinitely, or b) you have to balance the added weight of the extra water with the added suction of the smaller volume of air, meaning that that shit can be optimized (in a more complicated way than just empty or full), which is always good.

Kinda sorta this. The way you described it was kinda confusing but here I go in my attempt at explaining this.

The water wants to expand, but water (or liquids in general, iirc) doesn't really expand like a gas would. The seal created by the index card and water is tight enough that no air can get in to replace the lost water if it were to escape, therefore it doesn't. If you force the card off the cup, you'll notice an air bubble rise immediately to the top (base) of the cup. It's this action that allows the water to leave.

mr-mitch
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Re: Ye Olde Anit-Gravity Cup Experiment

The principle is similar to holding your finger over a straw filled with water.

Twistar
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Re: Ye Olde Anit-Gravity Cup Experiment

does the card cover the entire opening of the cup?

Kow
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Re: Ye Olde Anit-Gravity Cup Experiment

Twistar wrote:does the card cover the entire opening of the cup?

Yes. It wont work otherwise unless the surface tension is high enough. Like was said before, it's like having a straw with your finger over the top. The water can't fall down because the "seal" created by the surface tension (plus a card if you're using a cup) is stronger than the force of the water on it. With a big enough straw or cup, it will fail because the force down by gravity is stronger than the "seal".

gmalivuk
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Re: Ye Olde Anti-Gravity Cup Experiment

Forum Viking wrote: you have to balance the added weight of the extra water with the added suction of the smaller volume of air, meaning that that shit can be optimized (in a more complicated way than just empty or full), which is always good.

I don't think it can. If there's both air and water in the cup, then the weight of the water can expand the air just enough to push the card away from the rim of the glass.
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antonfire
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Re: Ye Olde Anti-Gravity Cup Experiment

I'm pretty sure I've seen the experiment done with a bit of air left at the bottom (top?). Apparently it doesn't expand enough. For 5cm of water, the volume of the air only has to change by only .5% or so to compensate for the added force of the water, which isn't too hard to do without breaking the seal. In fact, I just tried it and it works.
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TaintedDeity
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Re: Ye Olde Anti-Gravity Cup Experiment

I wasn't aware the cup had to be completely full of water until now and I've done it before.
Admittedly, it didn't stay up for very long...
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gmalivuk
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Re: Ye Olde Anti-Gravity Cup Experiment

Yeah, it'll work with different amounts of water. I guess I'm not really sure what "optimal" means in this context, actually. Presumably it's how much force it could support, right? In which case I think the completely full cup is still the optimum.
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Re: Ye Olde Anit-Gravity Cup Experiment

[quote"=gmalivuk"]Presumably it's how much force it could support, right? In which case I think the completely full cup is still the optimum.[/quote] I think that the force of adhesion is constant, as per:
Kow wrote:
Twistar wrote:does the card cover the entire opening of the cup?
With a big enough straw or cup, it will fail because the force down by gravity is stronger than the "seal".
If we had a longer cup, or some PVC pipe with a cap, then we could see if there's a point where adding water doesn't create enough additional suction to balance the added weight of water, so the constant (presumably) force of adhesion holding the cup is overcome and the card falls.
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antonfire
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Re: Ye Olde Anti-Gravity Cup Experiment

Yeah, there should be such a depth. Water is not perfectly incompressible, and at any rate it will boil when the pressure at the top is low enough. Siphons don't work when the height difference is greater than 10 meters or so for this reason.

Of course, the point at which the card dips enough to make the seal break is probably less than this. At 10 meters, the compressibility of water alone would allow the card to drop down about half a millimeter (I may be off by a factor of 2 or 3 in this I think), which is probably enough to break the seal.
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Carnildo
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Re: Ye Olde Anti-Gravity Cup Experiment

At ten meters (or so), even perfectly incompressable, boil-proof water would fall out: the pressure exerted by the water column would be greater than atmospheric pressure, and the water would generate a vacuum at the top of the pipe.

antonfire
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Re: Ye Olde Anti-Gravity Cup Experiment

Ah, yes, you're right, the boiling doesn't have much to do with it.
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?

Fossa
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Re: Ye Olde Anti-Gravity Cup Experiment

The shorter the column of water the greater the force it would take to dislodge the card. However, I believe that for any given column of water that will hold the optimal volume of water is still going to be 100% of the pipe. Well, this isn't entirely accurate, actually. This is assuming the alternative to water is air at ambient pressure. If we could remove water without introducing something at 1 atm (or whatever the pressure is where the setup is located) that would potentially increase the force holding the card in place...

gmalivuk
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Re: Ye Olde Anti-Gravity Cup Experiment

Fossa wrote:If we could remove water without introducing something at 1 atm (or whatever the pressure is where the setup is located) that would potentially increase the force holding the card in place...

Well right. In some sense the optimal situation is a pipe filled with neither water nor air nor anything else. Then there's the full 101325 Pa pushing up on the card with nothing to counter it.
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