How does a cup move on its own when pouring hot water into it?

[NickFoster]

Please bear with me because I'm not that great at physics. I witnessed something earlier today which was the most bizarre thing I have ever seen, and I'm looking for an explanation. I know this sounds contrived but this is exactly what happened without any embellishment: I was at work making two cups of coffee and I poured water from the kettle into the first cup and then as I was pouring water into the second cup, the first cup moved, entirely of its own accord and without me touching it. It turned through 180° whilst sliding to about 2 inches from where it started and was still moving when I grabbed it.

So what I think happened is: the kettle is not very good and when you pour the water always dribbles down the spout and pools on the table. So I think that the cup must have been planing on the surface of that water. I reckon the motion of the water inside the cup sloshing around after being poured must have somehow translated into moving the cup. Is this possible? It seems unlikely for something with the mass of a cup of coffee, but I can't think of any other explanation.

In case it is relevant: the surface it was on was a laminate kitchen worktop.

 

[Danger]

Welcome to PF, Nick.
I'm not sure if the liquid motion would account for it, but I suppose that it's possible. I have, however, experienced the exact same phenomenon when there was a vibration present in the (dry) surface. The source of that could be a microwave oven turntable motor out of balance, or even just the kettle itself trembling if it was still boiling. If you work in an industrial environment, it could even just be something transferred through the floor from a milling machine or suchlike, or from construction going on anywhere in your neighbourhood. The last time that it happened to me, they were digging up a sewer line almost a block away.
In those cases, I also saw concentric rings like tiny waves forming on the surface of the liquid. Do you notice anything like that?

 

[Mapes]

And I've also experienced the same thing myself. I concluded (at the time) that the hot liquid was heating the air under the mug (there was a slight recess, a small dome-shaped region, under the mug). As the hot air vented, the mug behaved like a little hovercraft, sliding and rotating on a smooth countertop with essentially no friction.

 

[NickFoster]

Thanks for the replies... I don't think the movement was caused by vibrations as there were none noticeable and it was a very smooth, gliding movement and I would imagine that vibrations would cause juddery motion. Mapes seems to be describing the same thing I saw, but if the cup is experiencing an essentially friction-free surface, would you not still have to apply a force for it to move? If that is the case and considering that only a very small force would be required then would the liquid motion be sufficient? If not, perhaps an uneven venting of the hot air?

 

[Mapes]

The force could come from venting, as you said, or the gravity component parallel to the countertop (which is never perfectly flat), the fluid momentum when you poured the liquid, air currents, etc. Don't know which was dominant in your case.

 

[Borg]

The spilled water is probably the reason. My mechanics professor considered putting this exact problem on a final exam. This was 25 years ago so I'm quite rusty on the details. I do remember that the suface tension of the water under the glass was something that we had to consider. With the right conditions, the cup actually floats on the water. Then, all you need is the slightest of forces to move it - could be a slosh or even a slight variation in the level of the counter.

 

[Danger]

I agree that the countertop was probably not level, and that the planing effect is quite plausible. One point of curiosity, Nick. You said that the cup rotated 180°. By any chance, was the handle facing away from the direction of travel when it started, and ended up facing toward it? That would be evidence for it traveling down a slope, since the handle side would be heavier.

 

[turbo]

That would be evidence for it traveling down a slope, since the handle side would be heavier.

Alternately, if expanding air needs to vent from under the cup, it would tend to vent out from under the lightest side of the cup. No slope needed if the counter-top and the bottom of the cup are smooth.

 

[Danger]

Good point, Turbo.

 

[berkeman]

Alternately, if expanding air needs to vent from under the cup, it would tend to vent out from under the lightest side of the cup. No slope needed if the counter-top and the bottom of the cup are smooth.

Hah! That's downright brilliant, Turbo.

 

[NickFoster]

Yes, that's right. The handle started facing away from the direction of travel and finished facing the same way.

 

[DaveC426913]

Yes, that's right. The handle started facing away from the direction of travel and finished facing the same way.

I thought you said it turned through 180 degrees?

Cuz I was going to theorize that it pivoted on a tiny bump on the bottom rim. Would explain both the rotation and the 2 inches of travel.

 

[NickFoster]

Err... that is 180 degrees?

 

[DaveC426913]

Err... that is 180 degrees?

If the handle started off facing away from the direction of travel and finished the same way, I interpret that as a net rotation of zero degrees.

To have rotated 180 degrees, the handle would have to end up facing toward the direction of travel.

 

[NickFoster]

Oh, I see... what I meant by 'the same way' was 'the same way as the direction of travel', not 'the same way as it started'. Sorry, I didn't make that very clear.

 

[gmax137]

My wife & I saw this several years ago in a Chinese restaurant - the small stainless steel teapot started moving across the glass-topped table. We still laugh about it whenever we get tea in a pot like that... I think the spout dripped a little hot tea and the table had a slight slope to it.

 

[sganesh88]

@Nick
So there was no rotation. only translation. right?

 

[DaveC426913]

@Nick
So there was no rotation. only translation. right?

Wrong. It rotated through 180 degrees. Handle started off pointing away from direction of travel and ended up pointing toward direction of travel.

 

[sganesh88]

oh i now see it. But i have a doubt. How can the water poured down on the cup explain the apparently gliding motion? Since the water molecules at the time of collision with the cup should be having only a vertical component of velocity, the cup and water as a system cannot have a net horizontal velocity. I think that brings us to the theory of reduced friction brought out by the heated air; just like dry ice sublimation reducing the friction in this video helping the flea to carry the heavy load.

 

[DaveC426913]

oh i now see it. But i have a doubt. How can the water poured down on the cup explain the apparently gliding motion? Since the water molecules at the time of collision with the cup should be having only a vertical component of velocity, the cup and water as a system cannot have a net horizontal velocity.

I don't think anyone is suggesting that.

The movement of the cup is almost arbitrary, the idea here is that the water and/or heated air is reducing the friction to zero. Once friction is zero, the cup can move easily with virtually no provocation whatever.

 

[sganesh88]

I don't think anyone is suggesting that.

If you think no one attributed the gliding motion to the water poured onto the cup, i think you didn't read the thread properly.

I reckon the motion of the water inside the cup sloshing around after being poured must have somehow translated into moving the cup.

I'm not sure if the liquid motion would account for it, but I suppose that it's possible

The force could come from venting, as you said, or the gravity component parallel to the countertop (which is never perfectly flat), the fluid momentum when you poured the liquid, air currents, etc

The spilled water is probably the reason.

 

[Danger]

the water molecules at the time of collision with the cup should be having only a vertical component of velocity

Since when has anyone every poured liquid straight down into a cup? It's going off to one side every time.

 

[DaveC426913]

If you think no one attributed the gliding motion to the water poured onto the cup, i think you didn't read the thread properly.

Conceded. I had been interpreting those comments as more about incidental components than about direct causitive components.

 

[sganesh88]

Since when has anyone every poured liquid straight down into a cup? It's going off to one side every time.

Is it? I haven't seen much of a deviation.

 

[Danger]

Is it? I haven't seen much of a deviation.

I didn't mean that it necessarily hits the side of the cup, but it does enter with a lateral component to its flow. When it comes out of the kettle, unless you pour very slowly and carefully, the stream falls away rather than just dropping straight down from the spout. If you pour right-handed, it will be moving leftward and thus impart some force in that direction to the cup.

 

[sganesh88]

Oh. So this component along with reduction of friction by the hot air resulted in gliding. Can the situation be mathematically represented?

 

[Danger]

Oh. So this component along with reduction of friction by the hot air resulted in gliding. Can the situation be mathematically represented?

If the hot air was indeed involved, rather than some other mechanism (which has not yet been firmly established). Regardless, the lateral component would contribute. I'm sure that there is some way to represent it mathematically, but there are a lot of variables involved. You would have to know everything about the incoming flow, the amount of friction involved, etc.. I can't begin to help you with that, though; I have absolutely no understanding of math.

 

[Hessami]

I love vietnamese food, and this occurs quite frequently at my local restaraunt, where they use those small asian style teacups to serve hot (and sometimes cold) tea.

These cups are significantly lighter than your average coffee mug.

I have noticed that there is always water that has dribbled down the side of the cup when it occurs. And

These cups have no handles, so i doubt that it's to do with the weight distribution of the cup, though that is a great concept!

I am fairly certain i have seen it occur with a cold cup of tea as well, so I'm not sure whether or not it has anything to do with the heated air, although the heated air expanding in the gap below the cup could well result in reduced friction, and surely could only aid the process.

Could air be sealed under the cup by the water at the edges, allowing the cup to float on the thin film of water?

I would have to agree with the wonky table theory, the tables in this restaraunt are NEVER very flat. Haha.

 

[redargon]

whoah... I thought I'd do a rough calculation to see if the hot air theory is feasible and i was surprised. Ok, it's very rough, but still...

I assume ideal gases and use P1*V1/T1=P2*V2/T2
So that initial pressure is atmospheric, initial Temperature is 21°C and the volume of the dome under the cup remains constant.
From this, if the air temperature in the dome rises to, say, 70°C, the pressure increase is almost 17% or 0.1666bar.
The force generated by the pressure difference under the dome and outside the dome is F=deltaP*A
Assuming the Area of the applied force (area of bottom of cup) is calculated with a diameter of, say, 45mm (i just measured my coffee mug here at work), Then the force generated by the 0.1666bar on this area is around 26N! that's around 2.5kg! A temperature of 40°C will give you around 10N, almost 1kg. This would be plenty to get a filled cup up and moving. I want to test this at home

I'll check my zeroes, because I'm still a bit amazed, but i think it gives you a rough idea. The dripped water on the surface under the cup probably helps to seal the dome, allowing the pressure to build up.

cool!

 

[Hessami]

A temperature of 40°C will give you around 10N, almost 1kg

Checked those calcs... they seem to hold up. Wouldn't have thought the pressure would build up so much.

I am definitely going to try to recreate this.

 

[mgb_phys]

You use the same principal in oil bearings. A small oil pump pressurizes the oil and the load floats on an almost frictionless film of oil.
You can push a 200ton telescope around with your hand.

 

[rainnw]

Here is the phenomena in action:



This always happens at a certain asian restaurant we visit, and takes everyone by surprise.

I finally was able to reproduce it by putting in very hot tea and letting it sit for a while. Its a good party trick.