Spaghetti Physics

[Irishman]

Hi RM. The question that seems to remain open to you is where does the push act? I think my description above of pushing a rope through an eyelet is a pretty good description - it acts on the component of the noodle closest to the bit filling the opening.

Take a piece of cloth. It is soft and flexible. If you push the ends it likes to buckle. How do you push a piece of cloth through a hole? You spread the cloth across the hole, then push the part right at the hole. That part goes in, it drags the rest of the cloth with it.

You can push a soft, buckling string through a small hole the same way. Push the part right at the hole, it will go through the hole.

That is the effect with a noodle. The part right at the opening is being pushed.

I cannot draw a picture here. I thought Cecil did a good job of describing it:

After some discussion we concluded that whereas it is customary to think of air as pressing straight down, most individual air particles, in fact, strike the surface of the spaghetti obliquely. Those particles striking the spaghetti close to the point where it entered the mouth, and whose vector had some inward-pushing component, would force it in.

How does that differ from “entrainment”? Entrainment to me indicates that it is the air (or perhaps the sauce) that is receiving the pull of the pull. Thus air and/or fluid is freely passing through the opening, and the noodle is along for the ride. This would be like a canoe in a stream headed toward a waterfall. The water is the air/sauce that is flowing along, the canoe/noodle is just a passenger. This is not the case. The description in the other thread about entrainment was describing moving granular material like flour. Again, the main item getting moved was the air, with the dust just floating along for the ride. This is NOT the case for the noodle. To prove it, put the noodle into your lips but keep your mouth open, and suck the air. The noodle will not go into your mouth. You have to press your lips loosely against the noodle. This creates a seal, but not so tight as to create too much friction. Thus the moisture acts as a lubricant.

The noodle is getting pushed by the air particles outside hitting the area of noodle just outside the lips. These air molecules are striking the noodle in random directions. There are also air molecules striking from the bottom of the noodle, again in random directions. All these forces cancel out, until you start sucking. Then fewer air molecules are striking the noodle inside your mouth than outside. However, all the transverse collisions are still offset inside your mouth, so the noodle does not flop back and forth. But the net imbalance leaves a component of force acting on the noodle from outside to inside. It is not from the end of the noodle, even if you carefull hold the noodle straight. It is the sideways collisions near the mouth. Thus the air pushes the noodle at a region where the stiffness is enough to push the noodle and not lead to buckling. Slurp In goes the noodle.

That is the best I can describe it. The force acts on the sides of the noodle right outside the lips.

[zut]

*Originally posted by RM Mentock *
Where does the force act? That’s the original question. That’s why the original letter writer wrote to ask the question. I haven’t seen a good answer posted to the SDMB, although I may have missed it. As I said, I’m leaning away from entrainment myself.

If you look closely at Cecil’s answer, he says it is probably along the spaghetti, near the mouth. That’s actually entrainment of the spaghetti by the fluid (air or sauce), even though he claims later to have rejected that theory.

OK; I think I see your point. A few things to chew on:

First, I can see where Cecil’s answer looks a lot like entrainment. (Cecil’s answer was that “Those particles striking the spaghetti close to the point where it entered the mouth, and whose vector had some inward-pushing component, would force it in.”) However, this explanation is, well, silly. Any place on the surface where air particles strike has air particles striking in all directions. The force from any particle having an inward-pointing velocity is (statistically) canceled by a nearby particle having an outward-pointing velocity. So: forget this answer for the time being, and forget the entrainment.

Second, I think the confusion here arises because people tend to misapply their intuition (which is usually reliable) to this problem. Any thought of “forces” and “pushing” leads to the inevitable “you can’t push on a rope” argument. People forget that air pressure is not equevalent to a single force; it is a pressure exerted everywhere. So: forget your intuition for the time being.

Finally, where does the force act? Or, more properly, how does the force act? Thought experiment: an astronaut floats a piece of spaghetti in front of him in the Space Shuttle (no gravity = easier thought experiment). Does the spaghetti move? No; the air pressure forces are balanced (No Force, no massXacceleration). Now imagine a tiny cubic chunk of the surface of the spaghetti. There is air pressure on one side of the cube; the other sides are buried in the spaghetti. Does the cube move? No; the air pressure force is balanced by compressive forces within the spaghetti material.

Under air pressure (a hydrostatic load), these compressive forces (stresses, really) are equal in all directions within the spaghetti. You can slice the strand in any place at any angle, and the internal stresses are all equal to the air pressure. You can prove this by another thought experiment: The aforementioned astronaut cuts the spaghetti in some random place at some random angle. Do the two halves fly apart? No; the forces still balance; the air pressure now between the two halves is equal to the internal stress that was there before the cut.

Now, for the sucking of the spaghetti. Another thought experiment: The astronaut gently places the strand in his mouth and lightly closes it. Air pressure everywhere is constant; internal stresses are constant. Cut the spaghetti just outside the astronaut’s mouth. There’s no change except air pressure has now replaced internal stresses in one plane. But, here’s the key: There is no place in the spaghetti strand that is affected by the cut. All the forces are still the same.

It should now be intuitively obvious that when the astronaut starts sucking, the very very short strand of spaghetti will be pushed into his mouth by the difference in air pressure. And this case having a short strand is equivalent to the case of a long strand.

Or, if you prefer, it’s the difference in compressive stresses outside and inside the lips that causes the strand to suck in: the stresses are caused by the air pressure.

Does that make sense? The explanation is perhaps a little more convoluted than Cecil’s, but it is (ahem) correct.

[jb_farley]

As long as we’re doing though experiments:

I have a rope that’s fifty feet long. Every6 inches is a lightweight disk, perhaps some sort of nerf device. The nerf circles (or nerfles, as we shall call them) are, oh, 10 inches in diameter.

I have a box with an air pump inside. On the bottom of the box is a hole of ten inches. The nerfles and the hole have been lubricated with generous amounts of glycerine or tomato sauce. You decide.

I turn the pump on, creating a pretty strong partial vacuum inside the box. I then place the topmost nerfle onto the hole. What will happen?

I’m guessing that the rope/nerfle thing will be pulled into the box, so long as the pump is pumping. This seems rather german to the discussion. If it isn’t, how does the metaphor break down?

jb

[zut]

*Originally posted by jb_farley *

I’m guessing that the rope/nerfle thing will be pulled into the box, so long as the pump is pumping.

I agree; yes it will.

I think it’s a little easier to understand the mechanics of your thought experiment than it is to understand the original spaghetti problem. In this case, you can easily see that there is a pressure difference from one side of the “nerfle” to the other, causing the rope to be pushed into the evacuated box.

Of course, the pressure difference is analogous to the internal compressive stresses (in the spaghetti) that I was talking about, but that’s much less intuitive.

[ZenBeam]

Zut’s explanation is the clearest I’ve seen on this subject. I’d like to propose one experiment (which I haven’t performed) which could dismiss the idea of entrainment. Suck on the spaghetti while holding the end. If entrainment were the explanation, you should feel a tug only while sauce is entering you mouth between your lips and the spaghetti. If air pressure is the explanation, you should feel a tug as log as there is a pressure differential between you mouth and the spaghetti, even if no sauce is entering your mouth.

I have to say, I can’t imagine how sucking could pull the sauce into your mouth, and not pull on the spaghetti as well.

[zut]

*Originally posted by ZenBeam *
Zut’s explanation is the clearest I’ve seen on this subject.

Well, shucks. Thanks. I wasn’t sure it was understandable, because the basic argument (“The effects of two different tractions on an object are indistinguishable, if the two tractions cause the same internal stresses”) is really a graduate-level mechanical engineering argument.

And I’ll second your experiment. I was tryin’ to think of a good experiment that would separate out the effects of entrainment from suction, but I couldn’t come up with one. I like yours.

[Irishman]

I am a little unclear on the nerf-ring rope description. The long rope has a 10" ring every 6 inches, what, a half inch thick? Is the ring a solid all the way to the rope, or a collar on spokes? Assuming it is a disk and not a wheel…

The first nerf ring will be pulled into the box (assuming enough pressure to counter the gravity pulling the rope out of the box). Now then, once the first ring gets through the hole, am I to take it that the next ring is entering the hole? In other words, the box has a long opening about 6 inches long? If so, then the rope will continue to feed into the box. If not, then once the first nerfle clears the opening, then the suction will be free flowing around the rope, and the rope will no longer feed into the box. Instead, it will dangle on the first nerfle, perhaps bobbing around to let air pass.

Unless you greatly increase the pressure difference to something like half an atmosphere. Then perhaps entrainment will come into play. Of course then you have the hole quickly become clogged with other objects in the vicinity. Unless the box wall ruptures.