# Springs question - vertical versus horizontal stretching...

by 1ledzepplin1
Tags: horizontal, springs, stretching, versus, vertical
 P: 15 So I know hooke's law well enough and I understand the spring constant and it's vertical applications where force equals displacement times some constant. What I am unsure of is to what degree this all applies to a horizontal stretch of a string? For one scenario let's say our spring of constant k is bound at both ends and is stretch sideways, whats the relationship between the constants and the tensile force drawing the spring back? For the second scenario lets say we leave one end dangling of a slinky and pull it at 1/2 the length, how does the original spring constant change between the two divisions? Lastly, given a slinky, what effects on tension are we looking at if we twisted it? You can watch some pretty nifty tensile responses from coiling a slinky beyond what it's equilibrium state is and im very curious about this. What does it doto the spring constant? Are there localized regions of stress for any particular reason or is it manufacturer inconsistency?
 P: 1,411 Why should there be any difference in the spring constant dependant on orientation of the spring?
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P: 6,927
 Quote by 256bits Why should there be any difference in the spring constant dependant on orientation of the spring?
In a real horizontal spring, if you don't ignore gravity, the deformed shape will be a curve, the tension in the spring will not be uniform along its length, and the force at the ends will not obey Hooke's law.

You can ignore the above effects if the weight of the spring is small compared with the tension in it. For a slinky, you probably need to include them.

Actually, a complete model of a slinky might be even more complicated because the coils of the spring can't overlap, and therefore the maximum amount of curvature of the slinky at any point along its length under its own weight depends on the tension at that point.

 P: 1,411 Springs question - vertical versus horizontal stretching... I was assuming the ideal spring equation in textbooks was what the OP was asking about, where if it was a free standing (laying ) spring, the deflection due to gravity is ignored. The spring can lie upon a surface where the frictional effects can be also small, as would the case where the spring is guided by an interior rod. In the case of a large spring constant, small diameter, and long length, the sag would be visible as a catenary ( as seen on cables on bridges ), and the spring can be modeled as a wire.
 Engineering Sci Advisor HW Helper Thanks P: 6,927 The "classical" model that gives the catenary shape for suspension bridges etc assumes the cable is inextensible, and is longer than the distance between the supports. If the cable can stretch along its length, the shape of the curve is different. This (and the references in it) might be interesting: http://www.slac.stanford.edu/econf/C...papers/038.PDF
 P: 1,411 Thanks for the link. I didn't know they had it so much down to a science! where is the OP guy. I had this generic site for him to peruse. Well, more like generic equations of catenary and related curves, including elastic cable. http://www.digplanet.com/wiki/Catenary