2

I have a finite length string that is equally strong in each point. The strength is finite. I slowly start to pull it apart by both sides. In which point(s) will this string snap? Will it extend indefinitely like a rubber band? Snap in all points at once? A pattern of snapping (e.g. from ends to center)?

Let's assume that clamping doesn't damage this ideal string.

Vladislavs Dovgalecs
  • 121
  • You are asking about the physical properties of something that does not exist. The physical properties of "ideal string" are whatever you define as "ideal" for your purposes. – Solomon Slow May 24 '18 at 17:20
  • The property of strength of a real and ideal strings are not the same. The strength of a real string is the strength in its one weakest point. The true ideal string (with no spontaneous symmetry breakdown) wouldn't break in one point, but in all points. The force would be applied equally to all points. You need to define the number of points the string has (e.g. the number of molecules) and calculate the total work and separating distance required to pull all of them apart. Dividing the work by the distance will give you the strength of the ideal string, much larger than one for a real string. – safesphere May 24 '18 at 17:57

1 Answers1

1

You have given no information to deduce where it will snap. So it cannot be calculated.

But just because it may be (nearly) uniform throughout, that doesn't make it magically elastic. Once the force on the string exceeds the yield strength, some (undefined) position will fail. That failure will reduce the forces elsewhere so only one break occurs.

BowlOfRed
  • 40,008
  • 1
    Your conclusion that the ideal string would break in one point is not logically justified. – safesphere May 24 '18 at 17:48
  • @safesphere, if it doesn't then the (slow) pull needs to supply the energy to break the bonds in multiple places simultaneously. That's the same problem as all the water in a pan turning to steam simultaneously during heating. – BowlOfRed May 24 '18 at 17:51
  • Exactly! See my comment above under the question :) – safesphere May 24 '18 at 18:03
  • I don't know that is true. Is there a definition of an ideal string that it's not made of molecules and molecular bonds, or just that it's free of flaws? Even if every bond were identical, you can't snap them all simultaneously. One will fail first and reduce the pressure on the rest. – BowlOfRed May 24 '18 at 18:14
  • The string must have a finite number of points, whether molecules or whatever, but conceptually nothing can be infinite, even in the ideal case. Secondly, sure you can snap them all at once ideally. Even in real life, I personally have observed a full bucket of liquid water freezing solid in an instant. I came to a country house in early winter and was thirsty. I took a mug and tried to get some water from a full bucket. Once I submerged the mug in water, crystal rays of ice exploded from the mug in all directions and the mug was instantly frozen solid in a bucket of solid ice. – safesphere May 24 '18 at 18:44
  • You should write an answer for the alternative view. But, the freezing you describe certainly started at one point and progressed, not at all points simultaneously. The water system was set so that an instability at one location favored crystallization. The string is set so that an instability at one location will cause a break there and relieve the stress. So the fracture has no mechanism to propagate. – BowlOfRed May 24 '18 at 20:09
  • The analogy with water was in the energy level, not in the propagation. All bucket was frozen instantly with no heat released (that would delay the process). This means the heat energy of the entire bucket was released in advance before any part of water was frozen. The string would break at one point in case a spontaneous symmetry breakdown is allowed, which is an additional logical condition. – safesphere May 24 '18 at 20:27
  • @BowlOfRed, You are using the word, "ideal" to mean something different from what a physicist means when saying it. The physicist isn't talking about a hypothetical piece of cotton twine that is free from every conceivable manufacturing defect or irregularity: The physicist is talking about some completely imaginary... thing with one or more string-like properties that are exactly described by simple mathematical equation(s). In other words, a spherical cow. – Solomon Slow May 24 '18 at 21:02
  • @jameslarge, I don't see any simple mathematical equation that governs fracturing of "ideal" materials. Simplification is fine where it makes sense. Again, I recommend those with alternative interpretations to create answers for this question. – BowlOfRed May 24 '18 at 21:16
  • @BowlOfRed, The OP is asking a question about the physics of ideal string. But there is no standard definition of what "ideal string" means. It's the OP's responsibility to specify (preferably, with equations) what the properties of "ideal string" are. If the OP would edit the question, and add equations that are relevant to the fracturing of his imaginary stuff, then maybe some kind physicist (not me though! I am no physicist), maybe some physicist would take interest and help the OP explore how his mathematical model evolves from whatever interesting initial conditions. – Solomon Slow May 24 '18 at 21:38