Coffeefilter: how did my coffee wind up on the ceiling?
October 10, 2007 12:03 AM Subscribe
How did my spilled coffee wind up on the ceiling?
This could be the dumbest question you'll see all day, but I was never very good at physics so...
Yesterday in my early morning fog I walked into my kitchen carrying a plastic travel mug filled with about 200mL of coffee. The mug was about waist-high when it slipped out of my hand, falling straight down so that the bottom of the mug hit the floor straight on. Needless to say coffee went all over the kitchen, but I was surprised to see that some even made it up to the ceiling.
How is it possible that something dropped from height x wound up at height 3x with no additional propulsion? or was there?
This could be the dumbest question you'll see all day, but I was never very good at physics so...
Yesterday in my early morning fog I walked into my kitchen carrying a plastic travel mug filled with about 200mL of coffee. The mug was about waist-high when it slipped out of my hand, falling straight down so that the bottom of the mug hit the floor straight on. Needless to say coffee went all over the kitchen, but I was surprised to see that some even made it up to the ceiling.
How is it possible that something dropped from height x wound up at height 3x with no additional propulsion? or was there?
Think of it like the lottery-- a bunch of people contribute, but only a few walk away with a whole lot of money.
In this case though, 'people' are drops of coffee, and 'money' is energy.
When you held the cup in your hand, the coffee in the cup had some amount of energy which can be 'liberated' (not the official term) by moving it toward the floor. This is commonly called 'potential energy'. When you dropped the cup, this energy got converted into 'kinetic energy' as the cup approached the floor. When it hit the floor, the coffee essentially bounced, keeping the kinetic energy but changing direction. However, because of the cup shape and the way it was dropped (and the fluid dynamics and waves, etc.) some of the drops of coffee in the cup ended up with an unfair amount of the energy. Total energy was conserved, however (well, friction shaved some off the top, similar to the state lotto board in the above analogy.) Anyway, those lucky few drops, let's say 5% of the coffee in the cup, found themselves with 20 times as much energy as was 'liberated' from them when they dropped, at the expense of their neighbors. So, long story short, 20 times the energy means they can get to 20 times the height (again, neglecting friction as the coffee whizzes through the air.)
A whip works on a similar principle-- the thin end breaks the sound barrier, despite the fact that you are wagging the thick end at a much slower velocity.
posted by blenderfish at 12:46 AM on October 10, 2007 [3 favorites]
In this case though, 'people' are drops of coffee, and 'money' is energy.
When you held the cup in your hand, the coffee in the cup had some amount of energy which can be 'liberated' (not the official term) by moving it toward the floor. This is commonly called 'potential energy'. When you dropped the cup, this energy got converted into 'kinetic energy' as the cup approached the floor. When it hit the floor, the coffee essentially bounced, keeping the kinetic energy but changing direction. However, because of the cup shape and the way it was dropped (and the fluid dynamics and waves, etc.) some of the drops of coffee in the cup ended up with an unfair amount of the energy. Total energy was conserved, however (well, friction shaved some off the top, similar to the state lotto board in the above analogy.) Anyway, those lucky few drops, let's say 5% of the coffee in the cup, found themselves with 20 times as much energy as was 'liberated' from them when they dropped, at the expense of their neighbors. So, long story short, 20 times the energy means they can get to 20 times the height (again, neglecting friction as the coffee whizzes through the air.)
A whip works on a similar principle-- the thin end breaks the sound barrier, despite the fact that you are wagging the thick end at a much slower velocity.
posted by blenderfish at 12:46 AM on October 10, 2007 [3 favorites]
The plastic mug acted like the barrel of a gun, forcing the coffee upward in a focused direction rather dispersing it outward.
posted by quadog at 1:27 AM on October 10, 2007
posted by quadog at 1:27 AM on October 10, 2007
seconding quadog - but not about to test the theory.
posted by razzman at 1:29 AM on October 10, 2007
posted by razzman at 1:29 AM on October 10, 2007
I assume the lid came off. Coffee from being sloshed onto the lid was maybe flung upwards by centrifugal force of the lid spinning as it came off. (skipped most of physics class in high school, so no idea if this is feasible)
Or, unless still wet, maybe the drops were already there, and just now drawn to your attention. Moisture from the kitchen can combine with dust and stuff to result in drops of dirty water that then dry once the moisture level drops, such as the end of a dishwasher cycle.
posted by hungrysquirrels at 1:48 AM on October 10, 2007
Or, unless still wet, maybe the drops were already there, and just now drawn to your attention. Moisture from the kitchen can combine with dust and stuff to result in drops of dirty water that then dry once the moisture level drops, such as the end of a dishwasher cycle.
posted by hungrysquirrels at 1:48 AM on October 10, 2007
I stand by what I said above (which addressed your skepticism that Physics allows this phenomenon to happen at all,) but I also offer the following speculation as to what is happening in the cup:
I wouldn't really quite say it is analogous to a gun. The mug of liquid hits the ground. The liquid inside wants to bounce upward in a uniform manner, but can't, because that would create a vacuum at the bottom of the cup. So, it crawls up the sides of the cup, since that is the path of least resistance due to surface tension. So now you have a cup with a bunch of liquid on the sides and a depression in the middle of the water. You essentially have the crest of a wave around the edge of the glass. Now, gravity takes over and pulls the wave down. Since it is in a round vessel, the waves propagate to the middle of the glass. So, you have this circular profile of crested wave growing smaller and smaller, so the wave must get higher and higher to compensate for its decreasing profile. Finally, when the crest of this continuous wave gets very near the center of the cup, the wave is gaining height very quickly; so quickly that the water breaks away from the rest of the water, and goes flying vertically into your ceiling.
Anyway, that's my theory, but I'm sure there are physicists around who specialize in this kind of thing.
posted by blenderfish at 1:56 AM on October 10, 2007
I wouldn't really quite say it is analogous to a gun. The mug of liquid hits the ground. The liquid inside wants to bounce upward in a uniform manner, but can't, because that would create a vacuum at the bottom of the cup. So, it crawls up the sides of the cup, since that is the path of least resistance due to surface tension. So now you have a cup with a bunch of liquid on the sides and a depression in the middle of the water. You essentially have the crest of a wave around the edge of the glass. Now, gravity takes over and pulls the wave down. Since it is in a round vessel, the waves propagate to the middle of the glass. So, you have this circular profile of crested wave growing smaller and smaller, so the wave must get higher and higher to compensate for its decreasing profile. Finally, when the crest of this continuous wave gets very near the center of the cup, the wave is gaining height very quickly; so quickly that the water breaks away from the rest of the water, and goes flying vertically into your ceiling.
Anyway, that's my theory, but I'm sure there are physicists around who specialize in this kind of thing.
posted by blenderfish at 1:56 AM on October 10, 2007
I'm certain that Bessel Functions are involved. Somehow.
posted by IvyMike at 2:43 AM on October 10, 2007
posted by IvyMike at 2:43 AM on October 10, 2007
This is likely the correct explanation. And yes, IAAP.
posted by fatllama at 2:46 AM on October 10, 2007 [2 favorites]
posted by fatllama at 2:46 AM on October 10, 2007 [2 favorites]
This may be related:
singularities in repeatedly oscillated cylindrical tanks of liquid
B. W. Zeff, B. Kleber, J. Feinberg, and D. P. Lathrop, "The Dynamics of Finite Time Singularities: Curvature Collapse and Jet Erruption on a Fluid Surface," Nature 403 401 (2000)
paper (pdf)
posted by sebastienbailard at 3:04 AM on October 10, 2007 [2 favorites]
singularities in repeatedly oscillated cylindrical tanks of liquid
B. W. Zeff, B. Kleber, J. Feinberg, and D. P. Lathrop, "The Dynamics of Finite Time Singularities: Curvature Collapse and Jet Erruption on a Fluid Surface," Nature 403 401 (2000)
paper (pdf)
posted by sebastienbailard at 3:04 AM on October 10, 2007 [2 favorites]
ummm... I'd like to interject: I don't think water can bounce, or at least not very well at this amount of energy input:
The question didn't state whether the coffee on the ceiling was directly above where the cup was dropped, though it was implied by saying 'straight on.' Did the travel mug tip over when it was dropped, if so the coffee could have been ' catapulted' onto the ceiling...
posted by geos at 5:30 AM on October 10, 2007
The question didn't state whether the coffee on the ceiling was directly above where the cup was dropped, though it was implied by saying 'straight on.' Did the travel mug tip over when it was dropped, if so the coffee could have been ' catapulted' onto the ceiling...
posted by geos at 5:30 AM on October 10, 2007
Mod note: few comments removed, if you DON'T KNOW, you don't need to answer the question
posted by jessamyn (staff) at 5:43 AM on October 10, 2007 [1 favorite]
posted by jessamyn (staff) at 5:43 AM on October 10, 2007 [1 favorite]
You focusing on the coffee as if it where a single object, but in facts its liquid and as zanni said some drops of the liquid recieved uneven distribution of force. Also the cup and fall had more "potential" energy already stored in it so when it was release it was like releasing a sling shot.. your only pulling back X but it travels 10x.
posted by crewshell at 5:59 AM on October 10, 2007
posted by crewshell at 5:59 AM on October 10, 2007
You can also think of this in terms of the propagation of the impact pressure wave; When you drop the mug, it and its contents acquire a certain velocity by the time the mug hits the floor. When the mug hits the floor, it stops and the coffee immediately above is compressed as it runs into the mug. This compression sets up a pressure wave which travels up the coffee until it reaches the surface, where if the wave has sufficient amplitude, it imparts sufficient kinetic energy to the water molecules at the surface to allow them to break free and fly upwards.
You should be able to achieve the same effect by tapping the bottom of a mug hard enough with a mallet. Try it if you've got a mug you don't mind accidentally breaking!
posted by pharm at 8:59 AM on October 10, 2007
You should be able to achieve the same effect by tapping the bottom of a mug hard enough with a mallet. Try it if you've got a mug you don't mind accidentally breaking!
posted by pharm at 8:59 AM on October 10, 2007
I like most of the other answers, but I think some simple properties of the lever (or teeter-totter, if you will) may be enough to explain DefendBrooklyn's observation.
Imagine a teeter-totter with one arm 3X longer than the other. If a heavy object falls onto the short arm, the long arm must rise three times as fast as the short arm goes down, which will almost the same as the speed of the heavy object when it hits. If a light object is sitting at the end of the longer arm, it will be flung upward at three times the speed at impact of the heavy object-- and that means it will rise to a height nine times as high as the heavy object was dropped from.
The falling cup has a kind of lever built into it. Even though the OP says it hit flat, it almost certainly was tilted slightly when it hit the floor, and so one point on the rim of the bottom of the cup made contact with the floor first. Just after that moment of impact, the point on the rim opposite the point of impact kept going at the original speed, of course, and the bottom of the cup constituted the short arm of a lever with the side of the cup as the long arm, as the cup began to rotate around the point of impact.
As a result, coffee on the side of the cup in the direction of the tilt will be flung off at a speed equal to the ratio of the height of the liquid on the side of the cup to the bottom diameter of the cup. If that liquid is flung straight up, it will rise to a height equal to the height the cup was dropped from times the square of that ratio.
posted by jamjam at 11:41 AM on October 10, 2007 [1 favorite]
Imagine a teeter-totter with one arm 3X longer than the other. If a heavy object falls onto the short arm, the long arm must rise three times as fast as the short arm goes down, which will almost the same as the speed of the heavy object when it hits. If a light object is sitting at the end of the longer arm, it will be flung upward at three times the speed at impact of the heavy object-- and that means it will rise to a height nine times as high as the heavy object was dropped from.
The falling cup has a kind of lever built into it. Even though the OP says it hit flat, it almost certainly was tilted slightly when it hit the floor, and so one point on the rim of the bottom of the cup made contact with the floor first. Just after that moment of impact, the point on the rim opposite the point of impact kept going at the original speed, of course, and the bottom of the cup constituted the short arm of a lever with the side of the cup as the long arm, as the cup began to rotate around the point of impact.
As a result, coffee on the side of the cup in the direction of the tilt will be flung off at a speed equal to the ratio of the height of the liquid on the side of the cup to the bottom diameter of the cup. If that liquid is flung straight up, it will rise to a height equal to the height the cup was dropped from times the square of that ratio.
posted by jamjam at 11:41 AM on October 10, 2007 [1 favorite]
Clearly what we need here is someone to drop a mug in front of a high speed video camera in order to see what happens.
Experiments trump theory every time!
posted by pharm at 2:02 PM on October 10, 2007
Experiments trump theory every time!
posted by pharm at 2:02 PM on October 10, 2007
fatllama and sebastienbailard have it, I think.
posted by Opposite George at 2:36 PM on October 10, 2007
posted by Opposite George at 2:36 PM on October 10, 2007
Response by poster: Wow these are some incredible answers. It would indeed be interesting to see this with a high speed camera. Where are Adam and Jamie when you need them?
posted by DefendBrooklyn at 3:29 PM on October 10, 2007
posted by DefendBrooklyn at 3:29 PM on October 10, 2007
fatllama's got the right idea. The question is, what's providing the bounce? The liquid itself isn't really compressing, and mugs aren't too compressible, either.
There are weird effects you wouldn't expect due to atmospheric pressure, however. For example, if you take some liquids and drop some on the ground, you get a nice splash; reduce the ambient pressure by a factor of 2, and you might get a blob and no splash.
Similarly, if you drop a steel ball into a bucket of sand at atmospheric pressure, you get a stream of sand shooting up pretty high. Drop one into sand under low pressure, and you don't get much at all.
So, my guess--very small pockets of air develop during the fall, compress upon impact, and then release their energy, giving you the baseball/basketball effect that fatllama mentions.
I'm not really seeing the connection to the article sebastienbailard links. It seems like a stretch.
posted by dsword at 4:53 PM on October 10, 2007
There are weird effects you wouldn't expect due to atmospheric pressure, however. For example, if you take some liquids and drop some on the ground, you get a nice splash; reduce the ambient pressure by a factor of 2, and you might get a blob and no splash.
Similarly, if you drop a steel ball into a bucket of sand at atmospheric pressure, you get a stream of sand shooting up pretty high. Drop one into sand under low pressure, and you don't get much at all.
So, my guess--very small pockets of air develop during the fall, compress upon impact, and then release their energy, giving you the baseball/basketball effect that fatllama mentions.
I'm not really seeing the connection to the article sebastienbailard links. It seems like a stretch.
posted by dsword at 4:53 PM on October 10, 2007
dsword: There are other ways to store energy besides compression. In this case, the kinetic energy gained when falling towards the earth is transfered into waves on the surface. Because of the shape of the mug, the waves will reinforce each other at the center of the mug, causing liquid to separate and shoot off vertically, at a surprising velocity. That is sebastienbailard's link. Both are consistent with what I stated above. I do not believe it has anything to do with centrifugal force or leverage.
You can seriously just do this if you grab a round glass, put some water in it, then slam it down (gently) onto like a rubber mouse pad or something. You can see the wave build up in the center and everything.
posted by blenderfish at 5:11 PM on October 10, 2007
You can seriously just do this if you grab a round glass, put some water in it, then slam it down (gently) onto like a rubber mouse pad or something. You can see the wave build up in the center and everything.
posted by blenderfish at 5:11 PM on October 10, 2007
That is to say, fatllama's link is an excellent pratical demonstration of uneven distribution of kinetic energy and its effects, but I wouldn't take it entirely too seriously as a direct answer to the whole problem, since obviously coffee in a cup is not quite the same as a basketball and a baseball.
posted by blenderfish at 5:15 PM on October 10, 2007
posted by blenderfish at 5:15 PM on October 10, 2007
Yes, I fully understand that energy can be stored in waves.
The aforementioned researchers use a highly controlled set up in which they force a bucket of liquid up and down at a very specific frequency so as to create standing waves. As the waves all collapse at a single point, their energy is focused and you get a nice jet.
The OP dropped a cup of coffee.
By just glancing at the graph in the paper, you can see that, even if you suppose the coffee formed such waves, if the wave height was more than 15% away from the critical height, it's a no-go as far as explaining coffee on the ceiling. In other words, it takes quite a bit of fine tuning to get this sort of effect. Nevermind that the cup probably falls a little on its side, there's no periodic forcing, there are air bubbles ("the entrainment of even very small bubbles decreases the jet velocity significantly"), coffee has a low viscosity, and so on and so on.
It's a stretch, putting it kindly.
It's not that complicated. fatllama had it right.
posted by dsword at 7:06 AM on October 11, 2007
The aforementioned researchers use a highly controlled set up in which they force a bucket of liquid up and down at a very specific frequency so as to create standing waves. As the waves all collapse at a single point, their energy is focused and you get a nice jet.
The OP dropped a cup of coffee.
By just glancing at the graph in the paper, you can see that, even if you suppose the coffee formed such waves, if the wave height was more than 15% away from the critical height, it's a no-go as far as explaining coffee on the ceiling. In other words, it takes quite a bit of fine tuning to get this sort of effect. Nevermind that the cup probably falls a little on its side, there's no periodic forcing, there are air bubbles ("the entrainment of even very small bubbles decreases the jet velocity significantly"), coffee has a low viscosity, and so on and so on.
It's a stretch, putting it kindly.
It's not that complicated. fatllama had it right.
posted by dsword at 7:06 AM on October 11, 2007
dsword: Take a round cup of water. Drop a ball in the middle of it. Watch what happens. The ball causes a depression in the middle of the water, causing the sides to raise. The sides then come back down, propagating as a wave toward the center, which then rises rapidly and shoots some liquid in the air.
You can also (and I have) take the round cup of water, and slam it into a surface straight down. Watch what happens. At least to me, it looks like the center of the water is rising very rapidly. It's very possible I'm wrong, though, and it's just some kind of newton's cradle-type effect, or the liquid is getting compressed slightly. *shrug* Ideally, someone could find or perform this exact experiment.
posted by blenderfish at 11:28 AM on October 11, 2007
You can also (and I have) take the round cup of water, and slam it into a surface straight down. Watch what happens. At least to me, it looks like the center of the water is rising very rapidly. It's very possible I'm wrong, though, and it's just some kind of newton's cradle-type effect, or the liquid is getting compressed slightly. *shrug* Ideally, someone could find or perform this exact experiment.
posted by blenderfish at 11:28 AM on October 11, 2007
Tsk. Useless the lot of you.
It's not as if this is a difficult experiment to try: I've just gone and banged a few glasses for my own edification.
Here's a video of a typical trial. Even though the camera only records at 15 frames / s it seems to me that you can see two things reasonably clearly: 1) the water is thrown up out of the glass and 2) the water is thrown up the side of the glass. Freeze framing may help with the latter.
You may all now continue pontificating while I work out a way to hold a glass in such a way that I can whack it on the bottom with a mallet :)
posted by pharm at 2:33 PM on October 11, 2007
It's not as if this is a difficult experiment to try: I've just gone and banged a few glasses for my own edification.
Here's a video of a typical trial. Even though the camera only records at 15 frames / s it seems to me that you can see two things reasonably clearly: 1) the water is thrown up out of the glass and 2) the water is thrown up the side of the glass. Freeze framing may help with the latter.
You may all now continue pontificating while I work out a way to hold a glass in such a way that I can whack it on the bottom with a mallet :)
posted by pharm at 2:33 PM on October 11, 2007
pharm: I salute your enterprising spirit. I really can replicate the wave coming up the middle of the water, but unfortunately this margin is too small to contain I don't have a video camera.
posted by blenderfish at 5:18 PM on October 11, 2007
posted by blenderfish at 5:18 PM on October 11, 2007
I just used the video mode of my Canon Powershot -- which is why it's only 15fps.
The wave meeting in the middle theory is plausible, but my little experiment does suggest that the theory proposed by jamjam upthread may have some merit to it.
posted by pharm at 1:09 AM on October 12, 2007
The wave meeting in the middle theory is plausible, but my little experiment does suggest that the theory proposed by jamjam upthread may have some merit to it.
posted by pharm at 1:09 AM on October 12, 2007
This thread is closed to new comments.
posted by zanni at 12:29 AM on October 10, 2007 [1 favorite]