Re: [math-fun] breaking spaghetti
ACW>If I were researching this seriously, I would advance on two fronts. First, I would build a robotic spaghetti-bender so that the forces were more reproducible between trials. There are a good fistful of variables in the way you put stress on the noodle: each hand exerts a translational force on the piece of noodle it's gripping, as well as a torque; the robotic jig ought to provide controls for at least some of those variables. Second, it is clear to me that a thousand frames per second is at least an order of magnitude too slow. Everything interesting to this problem happens between two adjacent frames: in one frame, the noodle is in one piece, and in the next, three breaks have occurred and two pieces are spinning away wildly into the air. We need to resolve the breaks into distinct frames to see what order they happen in; it seems likely that rebound from early breaks causes the late ones. ----------- Exactly. I withdraw my suggestion that it's a recoil effect. I think Nick Horn's MIT paper just covers varying the clamped endpoint angles and their relative positions. Presumably, one combination of these (for a given arc length) produces Warren's circular arc. But pages I've found seem to be saying (unclearly) that simply shoving the unclamped endpoints together (as with the wafer or Warren's strip) produces, for the strip, deflection described by a polynomial cubic in the absolute distance from the middle abscissa. --rwg I believe the Lehigh incident in my brother's inadvertent CC refers to our 1961 (pre-college) campus tour. Lehigh's pride and joy was a huge 5000000lbf destructive testing machine for, e.g., life-size bridge supports. For our amusement, it squashed lengthwise a wooden column that looked a foot square in cross-section.
I wrote Destin at "Smarter Every Day" about the problem and he responded that he was already working on an episode about it; he has completed filming and will publish it in December. He has previously used a camera fast enough to catch the shattering of a prince rupert's drop, so he's up to the challenge. (https://www.youtube.com/watch?v=xe-f4gokRBs) On Tue, Nov 25, 2014 at 11:51 AM, Bill Gosper <billgosper@gmail.com> wrote:
ACW>If I were researching this seriously, I would advance on two fronts. First, I would build a robotic spaghetti-bender so that the forces were more reproducible between trials. There are a good fistful of variables in the way you put stress on the noodle: each hand exerts a translational force on the piece of noodle it's gripping, as well as a torque; the robotic jig ought to provide controls for at least some of those variables. Second, it is clear to me that a thousand frames per second is at least an order of magnitude too slow. Everything interesting to this problem happens between two adjacent frames: in one frame, the noodle is in one piece, and in the next, three breaks have occurred and two pieces are spinning away wildly into the air. We need to resolve the breaks into distinct frames to see what order they happen in; it seems likely that rebound from early breaks causes the late ones. -----------
Exactly. I withdraw my suggestion that it's a recoil effect.
I think Nick Horn's MIT paper just covers varying the clamped endpoint angles and their relative positions. Presumably, one combination of these (for a given arc length) produces Warren's circular arc. But pages I've found seem to be saying (unclearly) that simply shoving the unclamped endpoints together (as with the wafer or Warren's strip) produces, for the strip, deflection described by a polynomial cubic in the absolute distance from the middle abscissa.
--rwg
I believe the Lehigh incident in my brother's inadvertent CC refers to our 1961 (pre-college) campus tour. Lehigh's pride and joy was a huge 5000000lbf destructive testing machine for, e.g., life-size bridge supports. For our amusement, it squashed lengthwise a wooden column that looked a foot square in cross-section. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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