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Re: [armsrforclimbing] Spring constant of a rope:
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jt512
Oct 8, 2008, 12:50 AM
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Registered: Apr 12, 2001
Posts: 21895

armsrforclimbing wrote: It's late, I'm fresh off the debates and a glass or two of wine, so bear with me. Then we are in exactly the same position.
In reply to: The equation of a line is y=mx+b set b=0 and the line passes through the origin, you also end up with the equation y=mx (similar to that of the Hooke's Law without direction of force) Hooke's law describes the linear relationship of force and deformation in an idealized spring. So in concept, the slope of the line obtained from plotting force on the Y axis and the resulting deformation on the X axis results in k's (read: slope) units of force/unit length. "k" is referred to as the spring constant, if it were a force value, as used in rgolds paper, it would by nature of a slope (change in y/change in x) be required to change and cannot be constant. This is the Hooke's law I am familiar with. The "k" value derived in the paper does not represent a physical constant unique to a particular spring, rather a variable force, and will not work with other equations when used as such. Your model states that force is proportional to the absolute stretch in the spring, whereas rgold's states that force is proportional to the relative stretch, ie, the absolute stretch divided by the length of the spring. I don't know which one, if either, is the official Hooke's Law, but it is unimportant. What is important is that your model and his are different, if the models are considered to apply to springs of arbitrary length. If, regardless of the length of the spring, the force is proportional to the absolute stretch; then the force cannot be, in general, proportional to the relative stretch, and vice versa. On the other hand, given a fixed spring length, the two models are equivalent, differing only in whether the length of the spring is taken into account in k or x. If the relative stretch model holds for climbing ropes, it is the more convenient model, because it holds for any length rope. I don't know if that clears anything up, or not. If not, it's the wine's fault. Jay
(This post was edited by jt512 on Oct 8, 2008, 1:09 AM)


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