Fishy Spaghetti Explanation

Cecil's Columns/Staff Reports
121

[QUOTE=mwbrooks]
I think the part that makes myself and others uncomfortable is that, for a noodle, a force in one direction seems to produce acceleration in a different direction. Otherwise it really looks like you’re pushing on a rope.
[/QUOTE]

It might look like that, but a correct summation of all the forces will be in the same direction that the acceleration is in. Forces are transferred through the noodle through internal stress, as I said back in post five, which I would be happy to answer any questions about.

In any case, an alternate explanation would also have to explain why the force imbalance due to pressure differences does not accelerate the spaghetti (or explain why there isn’t a force imbalance to begin with).

[QUOTE=mwbrooks]
There’s a pretty clear connection in the case of a solid object, or liquid sucked through a straw. But for the noodle case, I’m not good enough with math to find comfort in Maxwell’s equations, if they even apply. I turned to diameter change seeking a simple explanation that I can understand without resorting to either faith or hard work.

With the caveat, of course, that complex problems have simple, easy-to-understand, *wrong * answers.
[/QUOTE]
…which is what resorting to a diameter change explanation is. As a counter-example, imagine an anisotropic material which is circumferentially (and radially) stiff but longitudinally flexible. This would make it easy to bend (like a noodle) but difficult to compress radially (like a steel bar). A similar real-life engineered example of this would be dryer vent hose, if you’ve ever used that (but, of course, dryer vent hose is engineered to move air through it, so it’s not quite applicable here). Your theory would predict that it’s impossible to move this material with a pressure imbalance.

That’s pretty much the case, with that added explanation that the air pressure on the rest of the spaghetti surface (including the unused sin[symbol]q[/symbol] component on the surface within your cylinder) automatically cancels out.

However, if some portion of your spaghetti surface is far away from the mouth (as if you draped it over your fingers), then you get the “you can’t push on a rope!” objection, and we’re all the way back to the beginning of the discussion.

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[QUOTE=zut]
As a counter-example, imagine an anisotropic material which is circumferentially (and radially) stiff but longitudinally flexible. This would make it easy to bend (like a noodle) but difficult to compress radially (like a steel bar). A similar real-life engineered example of this would be dryer vent hose, if you’ve ever used that (but, of course, dryer vent hose is engineered to move air through it, so it’s not quite applicable here). Your theory would predict that it’s impossible to move this material with a pressure imbalance.

[/QUOTE]

I see that would be a problem, but I can’t get that far. I can’t imagine such a substance. When I try the dryer hose example in my head, the outside part collapses lengthwise until it acts more like a solid, and the inside part expands until it becomes rigid. And anyway the surface isn’t smooth enough, so you have an entirely different sucking mechanism (more Japanese).

The thing that’s fundamentally unique about a noodle is that the part inside your mouth just lies there. It doesn’t whack your uvula and stop the way a solid rod would, and it doesn’t pool up and present a top surface like a liquid. It gives every impression of being utterly inert and unaffected by any force except gravity. For that matter, the outer portion of the noodle does likewise, if you hold the plate up to your lips.

It’s just really hard for me to understand how seventeen inches of a noodle can be so utterly indifferent to what’s happening to one inch in its middle (more or less), unless there’s something significant about the forces acting on that one inch.

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[QUOTE=mwbrooks]
It’s just really hard for me to understand how seventeen inches of a noodle can be so utterly indifferent to what’s happening to one inch in its middle (more or less), unless there’s something significant about the forces acting on that one inch.
[/QUOTE]

There is something significant about the forces acting on that one inch in the middle.

What you’re missing is that there is a force on that one inch in the middle from the rest of the spaghetti, not just the air pressure.

The force on that one inch in the middle from the spaghetti inside your mouth is less than the force from the spaghetti outside your mouth. That’s significant, because the forces are not balanced, and the spaghetti accelerates.

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[QUOTE=zut]

That’s pretty much the case, with that added explanation that the air pressure on the rest of the spaghetti surface (including the unused sin[symbol]q[/symbol] component on the surface within your cylinder) automatically cancels out.

However, if some portion of your spaghetti surface is far away from the mouth (as if you draped it over your fingers), then you get the “you can’t push on a rope!” objection, and we’re all the way back to the beginning of the discussion.

[/QUOTE]

Well, I can push on a rope under the right circumstances (or push a thread through the eye of a needle, or a piece of cooked spaghetti through the hole in a colander, etc., as long as my fingers are close enough to the hole). I also note that with this (proposed above) model, if the spaghetti were to bend while being pushed for whatever reason, the portion of the spaghetti that is effectively being pushed simply moves closer to the hole, so the system is self correcting.

Also, a difference in this case from the “pushing a rope” example is that the pushing force, per unit area, is not greater than the lateral force per unit area against the spaghetti, and the only non-canceled-out force is in exactly the right direction (I’m not sure what the precise conditions for inducing spaghetti buckling are; I’m merely pointing out that there are differences here).

125

[QUOTE=zut]

What you’re missing is that there is a force on that one inch in the middle from the rest of the spaghetti, not just the air pressure.

[/QUOTE]

You’re right. I am missing that. I can’t see it, no matter how hard I squint.

I can see it up to the first bend in the noodle. If I try to see it any farther, then I might look at two plates with noodles coiled on them and think it should be easier to suck the first inch of the longest noodle. If it’s easy to suck the end of a foot long noodle, then why doesn’t a 100-foot coil leap up at my face like an angry cobra?

Certainly I see that you’re right as far as liquids go. Neglecting surface tension, soda can’t move up a straw unless there’s a puddle of soda behind it, with a nice top surface and a column of air above to push. Obviously the force is transmitted through the liquid, because if you break the straw anywhere the liquid just runs out the bottom and you end up sucking air. (Neglecting, as I said, surface tension.)

Mind you, I’m not saying there isn’t air pressure on the entire noodle. I’m sure it’s fine pressure, and it should be proud of itself. You can even say it’s in the game, as far as that goes, but if it’s out past the first bend in the noodle, I just don’t think it’s in play.

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[QUOTE=mwbrooks]
I can see it up to the first bend in the noodle. If I try to see it any farther, then I might look at two plates with noodles coiled on them and think it should be easier to suck the first inch of the longest noodle. If it’s easy to suck the end of a foot long noodle, then why doesn’t a 100-foot coil leap up at my face like an angry cobra?
[/quote]
I’m completely at a loss here. What does “I might look at two plates with noodles coiled on them and think it should be easier to suck the first inch of the longest noodle” mean? Easier than what? Why is it easier? And why would spaghetti “leap up at [your] face like an angry cobra”? What does any of this have to do with what you quoted?

And, one more time, I explained the concept of internal stress within the spaghetti back in post number five; if you have any questions, I’d be happy to answer them.

127

[QUOTE=zut]
And, one more time, I explained the concept of internal stress within the spaghetti back in post number five; if you have any questions, I’d be happy to answer them.
[/QUOTE]

Yeah, post five still isn’t helping.

I’ll drop the irony and state my main question as simply as I can: How exactly does internal stress make a force acting on an immobile piece of noodle accelerate a different piece of the same noodle, even around a U-bend?

128

Yeah, the “irony” doesn’t help.

And I have no idea where you get this idea. If the piece of the noodle is immobile, then it doesn’t move, by definition. Why would it accelerate another part of the noodle? What would lead you to believe that?

OK, let’s back up a couple steps.

  1. *Unbalanced * forces cause motion, right? Or, more properly, they cause acceleration: F=ma.
  2. So if you have an object where the forces are unbalanced, it must accelerate.
  3. For the same reason, if an object is not accelerating, the forces applied to it must be balanced.
  4. This also applies to portions of objects. So, for example, if you pushed on the wall of your house, the force of your push must be canceled somewhere else, since the wall doesn’t accelerate. In fact, when you push on your wall, the “internal stresses” between the wall and the floor, and between the wall and the ceiling, increase until all the forces are perfectly balanced.

OK, now, the spaghetti.

  1. When the spaghetti is just lying on your plate, all the forces on it are balanced. You know that because it’s not accelerating.
  2. (One of those forces is gravity. Let’s ignore that one for now; it doesn’t change the following, but just makes it more complicated.)
  3. Take a close look at the very tip of the spaghetti. The very last 1/8", say, or the last 1/100", or the last micron, if you want. It’s roughly shaped like a circular cylinder, and has air pressure on the circular end and around the circumference.
  4. The very tip of the spaghetti doesn’t accelerate. Therefore, the forces on it must be balanced. However, there’s one circular face that’s *inside * the spaghetti, not exposed to air pressure.
  5. The only way this tip could be balanced is if there was an “internal pressure” of some sort on the “inside face” that exactly counteracted the air pressure on the outside face.
  6. And, as a matter of fact, there is. “Internal stress,” let’s call it. This internal stress is everywhere in the spaghetti, and is equal in magnitude to the air pressure, and acts in every direction.

OK, now what happens when you suck on the spaghetti?

  1. Let’s assume, just for fun, you have a length of spaghetti inside your mouth and another length outside. When you reduce the air pressure inside your mouth, the internal stress in that portion of the spaghetti decreases.
  2. Now look at the short section of the strand that’s between your lips. Think of it as a stubby cylinder.
  3. (I’ll ignore friction here; again, it makes the following more complicated without actually changing the argument.)
  4. The stubby cylinder has air pressure on the circumference; the air pressure changes along the length, but the foce from this circumferential pressure balances out everywhere.
  5. The stubby cylinder *also * has an internal stress applied on its circular ends. The stress applied on the end *inside * your mouth is *less * than the stress applied on the end outside your mouth.
  6. These stress forces do *not * balance. If forces do not balance, there must be an acceleration, and indeed this stubby cylinder will accelerate.
  7. Since the stubby cylinder between your lips is connected to the rest of the spaghetti, the entire strand is pulled along for the ride.
  8. (Because the moving spaghetti pulls on the rest of the strand, transferring a force along it through the internal stress.)
129

[QUOTE=tim314]
…

  • If we treat the inside of your mouth as a vacuum, the only segment of the spaghetti strand that experiences a net horizontal force due to air pressure is the segment right in front of your mouth… would force it in."
    [/QUOTE]

What if you’re on a treadmill?

130

It’s impossible to eat spaghetti on a treadmill. I read it on a Snapple cap.

131

[QUOTE=zut]

  1. The stubby cylinder *also * has an internal stress applied on its circular ends. The stress applied on the end *inside * your mouth is *less * than the stress applied on the end outside your mouth.
  2. These stress forces do *not * balance. If forces do not balance, there must be an acceleration, and indeed this stubby cylinder will accelerate.
  3. Since the stubby cylinder between your lips is connected to the rest of the spaghetti, the entire strand is pulled along for the ride.
  4. (Because the moving spaghetti pulls on the rest of the strand, transferring a force along it through the internal stress.)
    [/QUOTE]

OK. So back closer to the original question, where does the compressive stress that pushes the noodle come from? Close to the lips, or farther out?

Or is the stress all in tension, arising entirely within the mouth?

132

It “comes from” the air pressure, which is everywhere.

The question is a little misleading, because the implication is that you could take a pen and circle some area on the spaghetti and say, “this is where the compressive stress comes from.”

Doesn’t quite work like that. The stress is there because the air pressure is everywhere. Now, at any given instant, you can look at the spaghetti strand as a whole and identify where the unbalanced force component is applied. That’s what BenjaminLewis was doing in his analysis.

But that doesn’t explain how that unbalanced force is transferred through the spaghetti to cause acceleration, and thinking strictly of “where does the force come from” is misleading. The spaghetti problem is not like pushing on a rope.

Or, to put it another way: Let me turn the question around.

  1. If you apply air pressure to an object, is it clear that there must be some internal stress in that object, caused by the air pressure?
  2. Is it clear that the internal stress is equal in every direction, and is equal in magnitude to the pressure?
  3. Is it clear that reducing the pressure will reduce the internal stress?
  4. Is it clear that changing the stress on one end of the object will change the balance of forces?
133

[QUOTE=zut]
It “comes from” the air pressure, which is everywhere.

The question is a little misleading, because the implication is that you could take a pen and circle some area on the spaghetti and say, “this is where the compressive stress comes from.”

[/QUOTE]

Hmmm. Let my try another question and see if it’s less misleading. I’ll need to set it up:

[ul]
[li]Presumably, forces are balanced throughout those parts of the noodle that are not either accelerating through the lips or being dragged by other parts of the noodle.[/li][li]There is, I think we agree, a stress imbalance between inside (lower pressure) and outside (higher pressure) portions of the noodle.[/li][/ul]

Does the imbalance occur as a single point along the noodle, or is there a stress gradient somewhere between the low pressure and high pressure segments?

If it’s a point, where is it? If it’s a gradient, what is the extent of that gradient?

134

[QUOTE=zut]

  1. If you apply air pressure to an object, is it clear that there must be some internal stress in that object, caused by the air pressure?

[/QUOTE]

Yes.

[QUOTE=zut]

  1. Is it clear that the internal stress is equal in every direction, and is equal in magnitude to the pressure?

[/QUOTE]

Yes, if the system is at equilibrium.

[QUOTE=zut]

  1. Is it clear that reducing the pressure will reduce the internal stress?

[/QUOTE]

Yes.

[QUOTE=zut]

  1. Is it clear that changing the stress on one end of the object will change the balance of forces?
    [/QUOTE]

Yes. Furthermore, I submit that the internal pressure will no longer be equal everywhere, and in particular, it will be smaller mainly within the cylinder I spoke of earlier.

It’s sort of like pressing a spring from both ends, and then letting go of one end. I would still say that the remaining constraint on the other end is “most responsible for the spring’s motion”, but “pushing the spring” doesn’t seem like a very good description of what is occurring.

135

[QUOTE=mwbrooks]
Hmmm. Let my try another question and see if it’s less misleading. I’ll need to set it up:

[ul]
[li]Presumably, forces are balanced throughout those parts of the noodle that are not either accelerating through the lips or being dragged by other parts of the noodle.[/li][li]There is, I think we agree, a stress imbalance between inside (lower pressure) and outside (higher pressure) portions of the noodle.[/li][/ul]
[/quote]
OK, I’m with you on this.

[QUOTE=mwbrooks]
Does the imbalance occur as a single point along the noodle, or is there a stress gradient somewhere between the low pressure and high pressure segments?

If it’s a point, where is it? If it’s a gradient, what is the extent of that gradient?
[/QUOTE]
Good question. There’s definitely a stress gradient.

Part of that is due to what, exactly, is going on at your lips. The spaghetti is contacting your lips over some length; what is the pressure profile over that length? A linear pressure change between inside and outside is probably a good approximation, although likely not exactly accurate.

Ignoring that, though, there is going to be a gradient (a three-dimensional gradient, actually) as the stress change “fades away” into the bulk of the spaghetti. My sense is the stress would have substantially changed over the length of about 1/2 diameter, and be very close to the constant stress after about a full diameter.

136

Thank you. This was really bugging me. In retrospect it was due to my failure to grasp what other people had already said on the topic, but your analogy couldn’t have been clearer. It now seems obvious. Feel a bit silly for doubting it.

137

Which analogy convinced you?

138

Sorry, that was my first ever post on here and I wasn’t sure how to use the quote function. It was the explanation by Zut near the beginning.

139

Welcome, Mike. I should point out this discussion is from 2008, and took 3 pages to hammer into submission, so your comment is a bit out of the blue.

Take a look around, you may find something else to read about. Like treadmills, or driving on parkways and parking on driveways, or the three words that end in -gry. Or possibly “The whole nine yards”.

140

Yep, like I say, I was new to this. Haven’t revived any ancient threads since. Sorry about that. Thanks for the welcome.