The magician's water glass

Classical Mechanics Level 2

A magician fills a glass with some water, lays a glossy postcard on top, and then flips the entire assembly while holding the postcard firm to the bottom of the glass. He then removes his hand and the postcard stays in place, keeping the water in the glass.

How is this possible?

Some water enters the postcard, which allows it to form hydrogen bonds with the water. The upward force on the postcard from the atmosphere exceeds the weight of the water. The glossy postcard is hydrophobic, and pushes the water back up into the glass. Some of the air in the glass dissolves into the water, creating a vacuum in the glass.

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Josh Silverman by Josh Silverman

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4 solutions

Andrew Tawfeek
May 7, 2015

One atmosphere is equal to 14 pounds per square inch, or ≈ \approx 101 kilonewtons per meter squared.

This is the conversion of 1 atm to Newtons per meter squared. Atm (short for atmosphere) is a unit used for pressure and it's the magnitude of the force exerted by Earth's atmosphere on one square meter.

So in this problem the force that is exerted on the paper is equal to the force of the gravitational pull the Earth is exerting on the water. The net force is zero, so there is no acceleration (or in simpler terms, gravity is having no noticeable effect.)

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But the air inside the glass is also at 14 psi. Shouldn't it counter-act the upward pressure on the postcard? There's something missing in your answer because it doesn't take into account the glass being closed.

Lawrence Kesteloot - 4 years, 4 months ago

The key principle here is knowing that fluid pressure is exerted from all spatial directions (and that the gases "flow" ). A pressure gauge will read the same in any orientation when immersed: http://faculty.wwu.edu/vawter/PhysicsNet/Topics/PressureProblems/SubmergedBlock/Gifs/Pressure41.gif

The water in the glass is actually "immersed" in the surrounding gaseous (but "fluid") atmosphere, which exerts fluid pressure from all directions on the glass and its contents.

Manjunath Sreedaran - 6 years, 1 month ago

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The pressure of the water and air in the cup is in equilibrium with the air pressure on the other side of the card. Technically this does not change with the orientation of the cup -- providing the mass of the card (including that beyond he lip of the cup) is not large enough to overcome the sliding friction of the interface. When turned over, such that the entire cup/card interface maintains a surface tension seal at that card-cup interface, there is no change in the force balance. Holding the cup at any angle where the water does not completely maintain that interface (or the weight of the card can cause it to slide off) will cause the air to enter the cup and break the equilibrium. If the cup was shaped like a boot and turned on it side so that the air was only in the toe - pointed up and containing all the air - the force that one would have to apply to the card is that which both maintains the surface tension interface and ensures the card-cup interface doesn't allow the sliding of the card that could break the interface. In this "boot cup" system there is a similar range of "inverted" angles that would require no pressure on the card to maintain the magician's illusion.

David Brown - 3 years, 11 months ago

This question ignores the fact the the air initially trapped in the cup would also be at atmospheric pressure and thus exert a downward force on the water in the overturned glass. However the correct solution would be to acknowledge the initial dynamic situation, followed by the water displacing slightly and increasing the volume containing a fixed mass of air. By the ideal gas law it can be concluded that the pressure of the air in the glass should drop until it's upward force on the water is such that the water stops moving the system comes to equilibrium.

Ev Grizz - 4 years, 4 months ago

This makes no sense.. atmospheric pressure pushes down due to gravity, not up..

Ariel Gershon - 5 years, 3 months ago
Siddharth Singh
May 6, 2015

The atmospheric pressure exceeds the fluid pressure inside the glass thus the postcard remains on its place but little later the postcard falls.

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what do you think would happen if the water was boiling when you performed this experiment?

vishnu c - 6 years, 1 month ago

It is a very famous middle school demonstration on atmospheric pressure and shows how one should not underestimate the effects of it, although we barely feel it due to our body accustomed to this. Atmospheric pressure is non intuitively very intense, enough to counteract the weight of the water in the glass to maintain equilibrium.

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Long Plays
Feb 22, 2018

1 atm is equal to 101325 Pa, which exceeds fluid pressure. If the water height is 16cm, then the pressure when flipped is around 1600 Pa only. Correct me if I'm wrong.

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