Fishy Spaghetti Explanation

Cecil's Columns/Staff Reports
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I don’t have the math skills to tell you a number. But I think the width of the band should be related the distance an average air molecule goes after striking a surface before it strikes another air molecule.

Sorry. My bad. I’ll happily restate my premise: The noodle’s motion results from the difference in momentum between molecules that strike the lip first and those that strike the noodle first.

I can’t follow the math, but I believe the article you cite says the air molecule loses momentum when it strikes a surface. Frankly how it does that without losing energy is beyond me, but if momentum is all it takes to exert force, that’s all we need, isn’t it?

Thanks for keeping after me on this, BTW. It’s fun for me trying to figure these things out. I’m sorry I don’t have time to get down and dirty learning the necessary math and whatnot to make a really good case.

62

As I suspected, you didn’t understand my explanation. If you don’t understand something, it’s not too difficult to ask for clarification rather than posting a snide remark misrepresenting my explanation.

The kinetic theory of gases explains what what causes “pressure” by what molecules actually do. “Pressure” acts perpendicularly to whatever surface it’s applied to, whether that be walls or floor or spaghetti. The pressure (or, rather, the differential pressure between the inside and outside of the mouth) is what ultimately drives the spaghetti into your mouth when you suck. Exactly how the forces are transferred through a rubbery piece of spaghetti is a little more convoluted, but I’d be happy to explain further. Unfortunately, I’m not sure if you don’t understand my explanation, or if you fundamentally don’t understand the physics.

63

Sure. Here’s the passage, with surrounding context:

First, note that the gas molecule “bounces off in the opposite direction with the same speed” as it had initially.

Next, note that momentum (like velocity, but UNlike energy or “speed”) is a vector quantity, meaning it has a magnitude and a direction. So the “momentum lost by the particle” is a little misleading, because the momentum is “lost” by the particle only in the sense that the direction changes. The magnitude of the particles momentum stays the same (it has to, because the mass and speed of the particle stay the same).

Oh, same here. A good question-and-answer session forces me to think about the issue and re-examine the fundamentals, which is worthwhile, and I come away with a deeper understanding at the end.

64

But when the article says the speed stays the same, doesn’t it make a point to limit the case to elastic substances? Aren’t lips and spaghetti somewhat inelastic?

In fact, aren’t truly elastic substances somewhat of an idealization, only to be found in the physics department, in the bin next to the frictionless wire?

65

Understood and duly noted.

In which case this thread blows.

It all seems quite convoluted beyond my humble air pressure differential contribution.

I agree with your assertment that bouncing air particles contribute greatly to the volatility of “things” e.g. keeping pneumatic tires inflated.

And concede partially that this kinetic motion contributes to the motion of the spaghetti (or to the rug in the tennis ball / rug / doorway system).

I am simply proposing that the difference in pressure between the two contained parts of the system (the mouth and the atmosphere) catalyzes the reaction concerning the pasta’s parade to the palate.

Air is a fluid (not a liquid, just a fluid) precisely because of the kinetic molecular action. It is this property of air that allows such dynamic changes in pressure, density, etc.

Space, while sparsely populated, is not empty but the pressure differential between the system space / spaghetti / mouth-under-one-atmosphere-of-pressure would be great enough that the spaghetti would be blown out of the mouth like a floppy javelin. Once this system has reached equilibrium however, the slight mechanical force applied by the tongue and cheeks would still change the internal versus external pressure and the noodle would be slurped the same as any where else.

I just think that the pushing does not occur on the external part of the air bound tip of the spaghetti but, much like a rocket, on the internal part of the mouth bound tip.

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Not elastic substances, elastic collisions. A perfectly elastic collision is one where the kinetic energy is the same before and after the collision. In the macroscopic world, where your intuition comes from, there’s no such thing as a “perfectly elastic” collision, because some of the energy is always bleeding away into other forms (heat, for the most part, ultimately). And, as you say, there are no macroscopic “perfectly elastic” objects.

At the molecular scale, things are different–we’re talking about the interactions of single molecules and not the incredibly massive conglomerations of molecules (like a tennis ball) that squeeze and distort macroscopically. At the molecular scale, collisions between molecules are perfectly elastic, and are modelled that way in kinetic theory.

(caveat: actually, collisions between molecules are perfectly elastic on average, with some collisions resulting in less kinetic energy, and some in more kinetic energy, as some of the energy is transferred into internal energy in the molecule.) I fully admit that exactly how the energy is transferred here is waaaaay at the limit of what I personally understand. However, I’m perfectly comfortable with “molecular collisions are perfectly elastic, averaged statistically,” because that works to explain macroscopic behavior. Wikipedia again, this time with a cool animation.)

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Does this work better? If not, I’ll go create a photobucket account or something.

It’s a really crude sketch. But the point is I can’t understand zut’s argument that there are “as many outward bound particles as inward bound”. Or rather, if I’m understanding him correctly, then the argument isn’t right. Possibly I am not understanding him correctly.

Let me put it like this:
Suppose the mouth is to the right of the spaghetti strand. I’m interested in looking at the force on the segment of spaghetti that’s right next to the mouth, because that’s where I believe the horizontal force originates.

Some air particles strike the spaghetti moving directly to the right (towards the mouth) and then bounce off to the left.

Some particles strike the spaghetti moving upwards and to the right, and then bounce off moving upwards and to the left.

Some particles strike the spaghetti moving downwards and to the right, and then bounce off moving downwards and to the left. (These are the ones that start where the ones I described before ended up. I thought zut was saying these would exert an opposite force, but in fact they exert the same force as far as the horizontal component is concerned.)

The point is, any particle that originates to the left of the spaghetti (regardless of which way it’s moving in the other dimensions) exerts a force to the right when it hits the spaghetti. (The force may have other components, but the horizontal component is to the right.)

To counter this force, you’d have to have a particle originating on the side of the spaghetti where the mouth is. Before you start sucking, there would be air particles inside the mouth that hit the spaghetti and push it to the right, but after you start sucking there are fewer of these.

Zut says: “there are just as many outward-bound particles striking the noodle there.” If by outward bound he means the force is to the left (away from the mouth), then this is the statement I’m disagreeing with. I’d like to see him draw a picture to show what he means by inward and outward bound particles. All the particles (the black lines) that I drew push towards the mouth.

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Let me simplify what I’m saying:

I don’t think I understand what zut means by “inward moving and outward moving” particles. (A picture would be helpful.) I’ve rephrased things in terms of left and right.

(1) Assume the mouth is to the right of the spaghetti strand (obviously some of the strand extends into the mouth.)
(2) If the mouth is sucking, then we have a low-pressure zone inside the mouth (to the right of the spaghetti strand) and a higher pressure zone to the left of the spaghetti strand (outside the mouth.)
(3) Thus more particles hit the strand from the left than hit it from the right. Thus, the net force is to the right.

It seems like zut thinks that all particles that hit from the left bounce off to the right, and are countered by an equal number of particles that hit from the right and bounce off to the left. But in fact there are ones that hit from the left and are reflected back to the left, and these outnumber the ones that hit from the right and are reflected back to the right.

But maybe I’m misunderstanding zut, and anyway I’m not sure it matters. If we can agree: (1) that there is higher pressure on the left of the strand than on the right, (2) higher pressure on the left means that more particles striking the strand originate from the left than from the right, and (3) particles striking from the left push the strand to the right – then it seems clear that this pressure differential produces a force to the right.

If we don’t agree on those points, please highlight which one you think is controversial.

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I can see it, but I’m not sure how it helps. :slight_smile:

I think Zut’s argument is that particles bouncing off the lip first and then hitting the noodle impart as much force on the noodle as particles that come straight in and hit the noodle. This is where he and I seem to disagree, at least. We agree that there are as many particles hitting the noodle from any direction, but not that they hit with the same force.

Aha! This may be the crux of our disagreement, so to speak. I think I’m saying that there is a discontinuity at the lip/noodle interface at which the statistical average breaks down. If it were a corner in a solid object you could average the imparted force across the boundary, but it’s not. The fact that the noodle is able to move relative to the lip, well, lets the noodle move relative to the lip!

I think I was wrong, though, about particles losing more momentum (energy) when they hit the lip than when they hit the noodle. Assuming momentum must be preserved, it’s the particles hitting the noodle that lose their momentum. The noodle still moves because there are fewer air particles per area inside the mouth, and the lip still remains still because it’s got teeth behind it.

Now, back to how wide the boundary is. I still think the molecules that really do the work are the ones that hit near the lip. Molecules hitting farther away hold their end up, so to speak, but they don’t actually give up any momentum, do they?

To paraphrase something Alan Lightman wrote many years ago, you might not be able to measure it, but it’s always just right!

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Well, it’s not much of a drawing, but zut said something like “Think of the incoming particles and where they end up. Now think of the particles that start where they end up and go the opposite way. Those ones will exert a force in the opposite direction.” (That’s me summarizing how I understood zut, so maybe I’ve got his meaning wrong.

The black lines in my picture are supposed to be particle trajectories. My point was that some of the ones start on the left and end up on the left, so even the ones following that trajectory in reverse would start on the left and end on the left. In other words, both the particle and its opposite push the spaghetti to the right.

Now that I think about it, the more important point is this:

I disagree with both of you on this. Why should there be as many particles coming from the direction of the person’s face? You seem to be assuming some sort of left-right symmetry when the structures around the particle aren’t left-right symmetric.

Consider a different example: Imagine a coin suspended in the air so that its face is parallel to a wall. If the coin is far from the wall, then we expect air molecules to hit both sides of the coin at an equal rate. If the coin is touching the wall, we expect air molecules to hit only the side facing away from the wall. From these two end-points we can extrapolate that the ratio of particles hitting the wall-side to particles hitting the room-side decreases to zero as the coin approaches the wall. (I’m not saying it decreases linearly – it probably changes very little until you get close to the wall, and then drops rapidly to zero over the last inch or so.)

Likewise, I’d think there are more air molecules hitting the spaghetti from the “room side” than from the “mouth side”. The the net force pushes towards the mouth. Of course, within the mouth the situation is reversed, where there’s more pressure pushing out of the mouth. But there’s fewer total collisions inside the mouth due to the smaller pressure, so the force pushing it out of the mouth is less.

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Hold on. I said nothing about “exerting a force in the opposite direction.” Pressure force is exerted perpendicular to the surface. I was, as mwbrooks said in his post that you quoted, pointing out that, statistically, there should be particles coming from all directions.

There is no assumption of symmetry. There is just an assumtion of a random collection of molecules in the air. Why would there be any fewer particles originating from any particular direction? What’s different about the air there?

That’s provably false. If the number of particles colliding with the wall-side of the coin were less than the number of particles colliding with the room-side of the coin, the force on the coin would be unbalanced, and it would jump out of your hand toward the wall.

You seem to be saying here that this is a special case because the noodle is moving. A few issues with this: First, you still have to have enough force to start the noodle moving (a force which, in general, is non-zero). This force has to be developed before the noodle moves (by definition), so you can’t construct an explanation for noodle motion that relies on motion of the noodle. Second, I think you’re misconstruing the “statistical average” here. In the quoted passage, I was talking about how energy is stored within the molecule after a collision (and released on later collisions). What method would you propose that would skew the energy release to provide a force to drive the spaghetti into the mouth?

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If you have a sealed container full of air in a closed system, say deep in intergalactic space, it will eventually cool to the temperature of the cosmic background radiation, which is about 2.7 Kelvin. Whenever an air molecule strikes the container, it transfers a bit of heat energy to the container and moves a bit slower. Meanwhile the container will spontaneously radiate heat energy in all directions. Since the outside surface is necessarily larger than the inside, over time all the heat energy will radiate away. Cosmic background radiation keeps it from ever reaching absolute zero.

Here on Earth, what happens instead with the same container is that it only cools to room temperature. Heat energy radiating away from the container is exactly matched by heat energy striking it from the outside, whether by atmospheric air or from random infrared photons from other objects.

So the question is this: Is the cooling of individual molecules enough to account for the force on the spaghetti? I don’t think it is. In any case, both the spaghetti and your lips are likely to be hotter than room temperature.

I think it’s more simple than that. The idea that air pressure only acts perpendicularly to any given surface is a generalization that only holds with a still body of air. Molecules move randomly; air pressure is a function of them striking a surface and each other. The likelyhood of a given molecule striking a surface exactly perpendicularly is actually extremely small. What actually happens is that the average effect of all the molecules adds up to a net perpendicular force across the entire surface. If the surface is flexible, like a balloon, then it forces the surface into something spherelike.

But with the spaghetti, we have a pressure differential, and therefore movement as the air molecules try to fill the area of lower pressure. Forget about the spaghetti for a moment. Imagine a supply of compressed gas: a helium tank, a can of air for cleaning your keyboard, a propane tank, whatever. When you open the valve, the gas rushes out through the opening, however small. Near that opening, the net force on the inside surface is not perpendicular anymore. More molecules are moving towards the opening than away from it, and so the net force is in that direction.

If you just suck in some air through your mouth, the same thing happens. Now add the spaghetti, and the only difference is that it gets carried along for the ride. There isn’t a sharply delineated zone wherein all air molecules striking inside that zone push the spaghetti into your mouth, and all those striking outside hit perpendicularly. Rather, it’s a gradient. Right at the lip-noodle junction, the net force is pointed most sharply inward. As you go farther back along the noodle, the net force returns to perpendicular.

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I think I see what you’re saying now. You’re not claiming the force is canceled by particles moving along the time-reversed trajectory, you’re claiming the force is canceled by particles hitting the opposite side of the spaghetti. Is that right?

I agree that pressure is exerted normal to the surface. So there’s two ways to calculate the horizontal force on a piece of surface:

(1) Find the vector normal to the piece of surface whose magnitude is given by the area of the piece times the pressure. Then take the horizontal component. There is a vector opposing this one, but its magnitude can be less due to the curvature of the spaghetti making the outward-facing area of that piece smaller. (I’m not saying the spaghetti surface stretches, I’m saying curvature reduces the segment’s outward-facing cross-section.) So there can be a net force into the mouth. Figure 1 This could be canceled by the force on the “endcap” inside the mouth, but not if the air pressure inside the mouth is reduced.

(2) Find the vertical cross-section of the piece of surface, and multiply it’s area by the pressure to compute the horizontal component directly. Here we would think the force is canceled by the piece whose vertical cross-section faces the opposite way. But while these cross-sections have equal area, one is inside the mouth so the pressure is less. Hence, it doesn’t completely cancel the horizontal force pushing into the mouth. Figure 2

My previous explanation may not have been so great, but I feel good about this one. :wink:

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OK, but now turn your face downwards so the noodle is hanging vertically, and lower your head until the lower end of the noodle is just touching a smooth, clean surface. There is no air immediately opposite your mouth to push the noodle in. Does this mean you can no longer suck the noodle? Hmmm.

Not at all. I’m saying it’s a special case because the noodle can move, or, rather, the noodle cannot transfer the momentum from a hit across the noodle/lip interface.

For example, I whack a Tee ball with a bat. The bat’s momentum is transferred to the ball and the ball moves. That’s a molecule hitting the noodle. Now someone nails the next Tee ball to the tee (which is unusually rigid in this case). When I whack the second ball, it stays still and returns all the imparted momentum to the bat, which I drop with a cry of pain and dismay. That’s a molecule hitting the lip.

All of the common examples of air pressure involve solid objects, closed containers, volumes of liquid, and other situations where no one air molecule can ever get the upper hand. I think that’s precisely because nobody wants to try to explain the hydraulics of a floppy piston. After all, most readers of this thread are probably bored to tears by now!

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Yep, that’s pretty much it. I think people wouldn’t have such a hard time with this if it were just a short stiff cork (or a coin, if you like), but the “floppiness” of the spaghetti defeats people’s intuition.

I think you’re supposing an individual molecule imparts far more momentum than it actually does. And this still doesn’t address why the spaghetti would move in one direction and not the other.

You’re supposing a bulk flow of air into one’s mouth. That’s not the way I slurp in spaghetti. Or, more to the point: this isn’t what causese the spaghetti to move in a normal case.

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Well, if the noodle was like a vertical stick with one end exactly at the plate, I’m not sure you could suck it straight up. But realistically, the noodle is usually going to be longer than the distance to the plate, meaning there’s a little space directly below it where it curves onto the plate. Or, if it’s the exact right length, then the slightest upward movement of your head creates space beneath it (since it’s pressed between your lips).

I think even having a micrometer of air in between the noodle and the plate would be more than enough to exert air pressure. I realize now that’s what was wrong with me previously saying there’s a pressure difference just because you get close to your face. The average spacing between air particles at standard temperature and pressure is on the order of a nanometer, so as long as you’ve got well over a nanometer of space between the spaghetti and the plate there’s plenty of room for air to get in there and push against it.

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Not exactly. I’m saying that what would be the force of the bulk flow of air absent the spaghetti is instead transferred to the spaghetti. Imagine putting a piece of plastic wrap over your mouth and sucking in. (Don’t try this at home, kids!) The pressure differential causes the plastic to bulge inwards, even though no air is entering your mouth. The pressure vectors on the plastic are not normal to the surface until the system reaches equilibrium and the plastic stops deforming.

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Before you start sucking, the pressure exerted by the air outside your mouth is normal to the surface. Are you telling me that reducing the pressure inside your mouth changes the direction of the pressure vectors pushing from outside your mouth? That doesn’t make sense to me.

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Either one of our arguments will require a large number of molecules. As to direction I think we agree that the spaghetti moves towards the vacuum. You’re saying the only air molecules that matter are those that hit directly opposite the mouth opening, and I’m saying the ones near the mouth impart a shear force.

Let’s try another experiment. Forget the noodle. Build two machines, each with a vacuum pump and a chamber designed to “suck” on, say, a 1" round plastic rod. The machines are bolted to the floor with their orifices facing each other. If you stick a rod partway into just one orifice and turn on the pump on that side, the chamber sucks in the rod. OK. Now turn the pump off, stick the other end of the rod partway into the other orifice, and turn on both pumps.

So both ends of the rod are in an equally hard vacuum, with only “side” surfaces exposed to the air pressure in between.

Now, is there any strain on the rod? As I see it, if my arguments are correct, yes. If yours are correct, no.

This is tricky, though. If you break the rod and insert a strain gauge, you’ve got to do it so you don’t insert any perpendicular area between the machines, right? Even cutting a groove in the rod will let air in to push the end pieces apart.

I’m curious about what happens if you put one machine on rollers. I think it will get sucked towards the other, but is the rod pulling it, or is it being pushed by the air on its other side? How does the presence of the rod engender a force without transmitting it?

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There is necessarily a delay between the pressure drop inside your mouth, the stretching of the plastic film from the force of the air, and more air molecules moving in to fill the extra volume. As long as things are still moving and stretching, the net force at any given point on the film is going to be at an angle, simply because the air molecules cannot instantaneously move around.