Mass hanging from more than two strings

[dimitri151]

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?

 

[jbriggs444]

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.

 

[Meir Achuz]

It is statically indeterminate. If you assume a force constant k, with F=k\Delta x, for each string, it can be solved.

 

[dimitri151]

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?

 

[AlephZero]

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.

 

[dimitri151]

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)?