Springs question - vertical versus horizontal stretching

In summary, the conversation discusses the differences between vertical and horizontal stretching in springs and the relationship between spring constants and tensile force. It also mentions the effects of twisting a spring and how the shape and orientation of a spring can affect its tension and spring constant. The conversation references mathematical equations for catenary curves and discusses the complexities of overcoiled springs and the formation of loops or kinks in cables. The conversation ends with a request for resources on the topic.
  • #1
1ledzepplin1
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Springs question -- vertical versus horizontal stretching...

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, what's the relationship between the constants and the tensile force drawing the spring back?

For the second scenario let's 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 I am 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?
 
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  • #2
Why should there be any difference in the spring constant dependant on orientation of the spring?
 
  • #3
256bits said:
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.
 
  • #4
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.
 
  • #5
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/C04100411/papers/038.PDF
 
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  • #6
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 [Broken]
 
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  • #7
Thanks 256bits and AlephZero for each of your valuable links. Both contained precisely the information I was looking for and I'm pleased to see that it's as complicated and interesting as I had thought it was from direct observation. I was once told by my college physics professor that her christmas list, along with many other physicists she cited, had only wishes for more slinkys each year and I have a growing appreciation for this as I've learned more about complex tensile forces and the like.

I do however have one question still that one of you may have already answered but i didn't see it in the links.
I am looking not for just the mathematics of a stretch caternary, but i want to know anything and everything mathematical about an over-coiled spring and its caternary and curve redistribution.

If I'm not yet making sense, consider a slinky fixed at both ends and stretched to a forearms width. Now keep one end fixed and coil the other end in the direction the slinky is wound such that it is overcoiled.
The result will be a single locus of tension that, in a confined region, forms a twist resembling a cubic function.
The interesting thing is that this cubic-function stress shape moves freely across the length of the spring given nearly any form of orientational change whatsoever.
Any ideas or resources, friends?
 
  • #8
Not too much knowledge on that from me.

If I read you right, what you are describing is a loop or kink in the slinky.

This happens when a cable is unwound from a spool. Under no tension loops can form in the cable. With sufficient tension on the cable, the loops can be taken up and removed, as long as the loops are not too small.
One sees that all the time when unraveling an electrical extension cable, or even a telephone handset cord.

Slinky probably has more in common with a telephone handset cord than a regular cable, since the telephone cord has already a preformed coil just like a slinky.
 

1. What is the difference between vertical and horizontal stretching of springs?

Vertical stretching of a spring refers to stretching it in a straight, up-and-down direction, while horizontal stretching refers to stretching it in a side-to-side direction. This changes the orientation of the spring and can affect its behavior and properties.

2. Which type of stretching is better for a spring?

The type of stretching that is better for a spring depends on its intended use. Vertical stretching is better for applications where the spring needs to support weight or resist gravity, while horizontal stretching may be better for applications where the spring needs to provide tension or resistance.

3. How does vertical stretching affect the stiffness of a spring?

Vertical stretching can increase the stiffness of a spring, making it harder to stretch and requiring more force to do so. This is due to the change in orientation and alignment of the spring's coils, which affects its ability to store and release energy.

4. Can you use both vertical and horizontal stretching on the same spring?

Yes, it is possible to use both types of stretching on the same spring. This can be achieved by applying force in multiple directions or by using different attachment points on the spring. However, this may alter the spring's behavior and should be done carefully.

5. Are there any safety concerns when stretching a spring vertically or horizontally?

There are potential safety concerns when stretching a spring, regardless of the direction. The force applied to the spring can cause it to snap or break, which can be dangerous. It is important to follow proper safety precautions and techniques when stretching a spring to avoid injury.

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