- #1
phantomvommand
- 249
- 39
- Homework Statement
- See picture below
- Relevant Equations
- F = kx
Resolving forces?
Is this even solvable? I don't know where to begin.
Judging from the diagram, the spring starts compact, i.e. it cannot be compressed (much).phantomvommand said:Homework Statement:: See picture below
Relevant Equations:: F = kx
Resolving forces?
View attachment 322080
Is this even solvable? I don't know where to begin.
Are you suggesting that the diameter of the semicircle is (D + 2L/pi)?haruspex said:Judging from the diagram, the spring starts compact, i.e. it cannot be compressed (much).
Consider the outermost parts of the spring in the curved position. What length is that now?
Yes, it is non obvious.phantomvommand said:understanding how a vertical tension in the string even arises
Nearly right… think that through again.phantomvommand said:the diameter of the semicircle is (D + 2L/pi)?
The thing is, as the picture shows, that bent spring will not take the shape of a semicircle.phantomvommand said:Homework Statement:: See picture below
Relevant Equations:: F = kx
Resolving forces?Is this even solvable? I don't know where to begin.
True, but the question explicitly states it is to be taken to be a semicircle.Lnewqban said:that bent spring will not take the shape of a semicircle.
If I am understanding correctly, you are suggesting that assuming the spring is not stretched much, it's inner circumference is L, which gives an outer perimeter length of (L + D*pi).haruspex said:Yes, it is non obvious.
When a helical spring is stretched, each small cylindrical element of the wire is twisted about its axis. So it involves shear moments, like a torsion wire. (Confusingly, a "torsion spring" works through bending moments.)
However, you are probably not expected to get into such detail.Nearly right… think that through again.
But it is not the diameter that is of direct relevance; as I asked, what is the distance around the outer perimeter of the curved spring? Hence, how much has the spring been stretched on that side?
Not quite. As you note, that is only for the most stretched arc through the spring. What would it be on average? Bear in mind the circular nature of each coil of the spring.phantomvommand said:Are you suggesting that the tension is then kD*pi?
The next step would be to consider moments.phantomvommand said:how such a tension translates into a net vertical tension required at the ends with the string
A spring does not behave like a rubber band.phantomvommand said:I think I need help with understanding how a vertical tension in the string even arises. It is obvious intuitively, but when I break the spring down into an infinitesimal element I cannot figure out why.
… What gives rise to a necessary upward force which the downward string tension must balance?
If my method of analysis above is incorrect, I'd be happy to hear how else the tension in the string arises.
As I wrote in post #2, it doesn’t look that way to me (except near the ends, where the moment from the string is weak).Lnewqban said:As I can see spaces between the coils still in the bent position
A moment had to be applied whether or not the coils are touching their neighbours on the inside of the curve.Lnewqban said:If that is true, at each end of the spring, a moment had to be applied
Lnewqban said:the spring can’t keep the semicircular shape
I don't understand those last two points. The sequence you described seems to beLnewqban said:the spring is in repose
My post was directed to the OP, who stated he needs help understanding the reason for the string tension (please, see selected header quote in my last post).haruspex said:As I wrote in post #2, it doesn’t look that way to me (except near the ends, where the moment from the string is weak).
A moment had to be applied whether or not the coils are touching their neighbours on the inside of the curve.I don't understand those last two points. The sequence you described seems to be
That last step does not mean the spring is now relaxed.
- manually bending the spring into the arc
- attaching the string
- releasing the spring so that the string is in tension