- #1
Tusike
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Homework Statement
We have a string with property D (I don't know the name in english, it's dimension is N/m, the force required to stretch it 1m), which is small enough so that if we put the spring on the ground, it'll be shorter than it's standard height. The question is, when will this spring stretch more; if we hang it down from somewhere, or if we hold it in a way that the two ends each are 45 degrees to the vertical (sort of like a smiley, \/, a chain that you hold on the two ends)
Homework Equations
G=mg
F(spring)=Dx
The Attempt at a Solution
My idea was the following, but I heard it isn't correct:
If the spring hangs from somewhere, F=G is pulling it from the top and keeping it stationary (SummaF=0), while G is pulling down the middle part. This can be thought of as if we were pulling each end with F/2=G/2 force, which means a force of mg/2 is stretching the spring.
If the spring is positioned the other way around, we have G pulling it in the middle, and two F's on each ends, and since the vertical components of the forces must equal each other, 2*(F*sinalpha)=mg, where alpha = 45, from which F=mg/(2sqr(2)/2)=mg/sqr(2) is stretching the spring. And since mg/sqr(2) > mg/2, the spring should be stretched more in the second position.
Thanks for any ideas! If my attempt wasn't clear I'll be happy to try and clarify it.
-Tusike