Mass hanging from more than two strings

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Discussion Overview

The discussion revolves around the problem of determining the tensions in a mass hanging from three strings arranged in a plane. Participants explore whether the system is solvable or indeterminate, particularly considering different configurations and the nature of the strings or springs involved.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that the system is statically indeterminate, particularly when considering the equilibrium position of the mass and the potential for different strings to be slack depending on the configuration.
  • Others argue that if the strings are replaced with springs, the problem becomes solvable due to the force constant associated with springs, allowing for the application of Hooke's Law.
  • A participant notes that in real-world scenarios, strings behave like springs, which may influence the determination of tensions in the system.
  • There is a suggestion that having strings of the same flexibility could potentially change an indeterminate problem into a determinate one, although the exact stiffness may not be crucial.
  • One participant seeks confirmation on the setup involving a spring and the application of Hooke's Law to determine the hanging length of the mass.

Areas of Agreement / Disagreement

Participants express differing views on whether the problem is solvable or indeterminate, particularly based on the materials used (strings vs. springs) and the conditions of the setup. No consensus is reached regarding the overall solvability of the problem.

Contextual Notes

The discussion highlights the complexity of the problem, including the assumptions about string behavior and the potential for different configurations to yield different results. The dependence on material properties and the specific arrangement of the strings or springs is also noted.

dimitri151
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Is there a way to solve for the tensions in a mass hanging from three strings all in a plane, say? Is it solvable or is it indeterminate?
 
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dimitri151 said:
Is there a way to solve for the tensions in a mass hanging from three strings all in a plane, say? Is it solvable or is it indeterminate?

Three strings, all in one plane... So, for instance, you would scribe a straight line on the ceiling, put three hooks on points on this line, take three strings, tie one to each hook, tie the all three free ends to a single mass and let the mass hang, eventually settling into an equilibrium position?

In the usual case, two strings will be taut and the third will be slack.

If the string lengths work out just right the result will be on a cusp between a solution where one string is slack and another solution where a different string is slack. In that case, the result will be indeterminate.
 
It is statically indeterminate. If you assume a force constant k, with F=k\Delta x, for each string, it can be solved.
 
Yes, jbriggs, that's exactly the setup. (I should have said it that way in the first place.)
Thanks, Meir. By force constant , you mean if you hang the mass from springs instead of strings, then it is solvable?
 
dimitri151 said:
By force constant , you mean if you hang the mass from springs instead of strings, then it is solvable?

Yes. Remember that in the real world, inextensible strings do not exist. Real strings always behave like "springs."

Sometimes, the fact that all the strings have the same flexibility (e.g. they are all made of the same material) is enough information to change an indeterminate problem to a determinate one, and the exact value of the stiffness is not important.
 
If you could just give a nod if my setup is done correctly.
If you hang a mass from one spring, the length of the spring with no force is L, the mass is m, the spring constant is k then you just apply Hooks Law so the mass will hang L+mg/k from the ceiling (since F=-kx)?
 

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