The
television show had it right, but I can see why you didn't believe it.
After all, it's a half-cup of water if the cup is either upside down or
right side up. So, without a change, the pressure in the cup should be the
same, not less as the show claims. But there are a couple of
changes.
When you turn the cup upside down, a few drops of water may escape and
that makes a difference. Now there's less than a half cup of water
in the bottom of the cup and the air in the top of the cup expands to fill
the larger volume on top. When the air expands, its pressure drops.
This causes a pressure difference between the air outside and inside the
cup. The greater pressure outside pushes against the rigid plastic, which
keeps the water in the cup, and the trusting friend's head dry (except for
those few initial escaping drops of water).
Also, as the water tries to escape the upside-down cup, water molecules
stick to the rim of the cup. The water molecules adhering to the cup's rim
essentially "stretch" to extend the wall of the cup and thereby decrease the
volume of the water in the cup, which also acts to increase the air volume
in the top of the cup and reduce its pressure, emails physicist
Erik Ramberg of Fermilab.
But, like many seemingly simple puzzles, the TV show explanation does not
explain the entire phenomenon --- just as the Reader suspected.
Two forces are necessary to explain the inverted cup experiment:
- pressure difference, as the TV show mentioned, and
- surface tension.
"To hold up a whole glass full of water is too much for the weak surface
tension - air pressure does the trick - but the trick relies on the
stretchiness of water, due to its surface tension," emails Physicist
Erik Ramberg of Fermilab.
Ramberg ran some experiments and found when the weight of the water
was great (like a full glass of water), a pressure difference was needed to
hold the water in the inverted glass. But, when the amount of the
water was small (perhaps a quarter of an inch depth in a three-inch jar)
surface tension alone could support the water in the inverted glass.
Surface tension allows a film of water to form a seal around the rim of
the cup and blocks or, at least, greatly restricts replacement air from
entering the cup. Essentially no water can fall out of the cup because
no air can come into the cup to replace the falling water.
Water surface tension — caused by electrical bonds holding molecules
together — keeps the cup water (if it's a small amount) from falling.
Water molecules are slightly polarized. One end of a molecule is
more positive than the other end. So, water molecules throughout the
cup cling to their neighbors — the positive end of one molecule hanging on
to the negative end of another.
The molecules "don't act like just a bunch of marbles in a bag," Ramberg
says. Instead, more like "very, very weak magnets
in a bag. They will tend to stick together and resist pulling apart."
Like molecules (the water molecules in the cup) tend to stick
together. Moreover, unlike molecules (the water molecules and the
molecules that form the walls of the cup, for example) tend also to stick
together, but more strongly even than the cup water molecules.
Likewise, the water molecules and the unlike red plastic-lid molecules stick
together more strongly than the cup water molecules. So the
tightly-held water molecules along the rim of the cup and along the walls of
the cup form a barrier restricting or preventing the flow of air into the
inverted cup. The tightly-held molecules form a seal.
The seal prevents air from flowing in, which prevents water from falling
out.
The seal isn't perfect. A drop or two of water may ooze out.
Perhaps a small bubble of air may sneak its way into the cup through a crack
not filled by tightly-held water molecules. But the seal is good
enough to prevent small amounts of water from falling out of the cup ---
even with the top open to the outside so air pressure can equalize the
inside with outside pressures.
More Exploring:
How do insects walk on water?, WonderQuest
