# Hooke's law (F=-kx)

1. Aug 7, 2009

### zcd

Do bungee cords and/or surgical tubing follow Hooke's law (F=-kx)? If not, are there any equations that give force in relation to length?

If I was to numerically test for change of length by hanging weights off of each elastic, would it be possible to derive an equation according to the numerical data? If so, how would I go about doing this?

2. Aug 7, 2009

### CFDFEAGURU

Re: Elastics

Hooke's Law does not hold for non-linear materials.

3. Aug 7, 2009

### Mapes

Re: Elastics

But nearly all materials are approximately linear elastic up to a point, and Hooke's law works well in this region.

4. Aug 7, 2009

### CFDFEAGURU

Re: Elastics

Yes, but how do you know when you have reached the point where linearity stops?

5. Aug 7, 2009

### Mapes

Re: Elastics

The stress-strain curve stops being a straight line (though the critical deviation is up to you; with metals, it's commonly taken to be 0.2% strain).

6. Aug 7, 2009

### FredGarvin

Re: Elastics

I know this is old data, but I think it may be helpful. I would think that bungees would be a good example of a linear spring assuming there are no weird properties in the lay up or design of the cord. It's easy enough to do this test though. All you need is a fish scale and a pad of paper.

Here is a load-deflection plot for a landing gear bungee cord from a US Army report.

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7. Aug 7, 2009

### CFDFEAGURU

Re: Elastics

I have had to model non-linear materials using ANSYS numerous times. I used the neo-hookean model for this type of material. Depending on the accuracy you are looking for maybe you can get away with using F=-kx but I don't recommend it.

8. Aug 7, 2009

### rcgldr

Re: Elastics

Latex tubing isn't linear, it's a curve. The data on this web site matches the data I measured myself using a different method, hanging various weights and mearuring length of stretch:

http://www.hollyday.com/rich/hd/sailplanes/rubberdata.htm [Broken]

This is the data I measured. Note that 50% means to increase lenght from 100% to 150%. The percentages show "pull" distance.

Code (Text):

strain versus tension: (strain == pull distance)

0% =   0 lb / in^2
50% =  70 lb / in^2
100% =  95 lb / in^2
150% = 115 lb / in^2
200% = 135 lb / in^2
250% = 160 lb / in^2
300% = 175 lb / in^2
350% = 195 lb / in^2
400% = 205 lb / in^2  (not recommended).

For example, I have latex tubing with 2/16 inch inner diameter and 7/16 inch outer diameter for a cross section of 0.13806 inch2, and it generates 26.9 lbs of tension at 350% pull.

Practical application example video (60 feet of tubing, 210 feet of fishing line, pull distance ~180 to 210 feet):

http://jeffareid.net/rc/jrartms.wmv

Last edited by a moderator: May 4, 2017
9. Aug 7, 2009

### zcd

Re: Elastics

Thank you for the replies. Would it be sufficient to model an equation of the data with a TI-83+'s exponential regression ability? The attachment given by FredGarvin looks like it behaves somewhat linearly at about a deflection of 1in (what is a deflection?), while the site given by Jeff Reid looks more continuously exponential. For the context, I am using this for a projectile launching competition that specifically prohibits use of counterweight and metal springs to provide launching force.

10. Aug 7, 2009

### rcgldr

Re: Elastics

Latex tubing is great for water balloon style launchers, if you have the room for a good pull. Bascially an oversized slingshot, using a large frame (window frames work if launching from a building).

For the more serious stuff, some pumpking tossing machines are pretty high end. At the top are the pressurized air cannons. There are also motorized spinning devices and catapults. However starting off with the simple latex based stuff:

So trebuchets (weighted) devices aren't allowed, but what about a ballista? Think of a cross bow using a leaf spring from a car for the bow.

Pressurized cannon:

Last edited: Aug 7, 2009
11. Aug 7, 2009

### FredGarvin

Re: Elastics

If you look at the data that Jeff posted, it looks very much like the graph I posted. It has a large non-linear portion and then, for all intents it goes close to linear.

12. Aug 7, 2009

### rcgldr

Re: Elastics

Link to website with rubber band hysteresis graph (rubber bands are "stiffer" than latex tubing):

"idealized" rubber band:

http://en.wikipedia.org/wiki/File:Elastic_Hysteresis.jpg [Broken]

Last edited by a moderator: May 4, 2017
13. Aug 7, 2009

Re: Elastics

I think bungee cords have a polymetric structure.They stretch easily at first but then become stiffer as the polymers straighten.Also,the unloading characteristics are different to the loading characteristics and the cords display something called hysteresis.
Impurities can have big effects on the elastic properties,for example rubber is vulcanised with sulphur to create links between the polymer chains,a process called vulcanisation which is used in the manufacture of tyres

14. Aug 7, 2009

### rcgldr

Re: Elastics

There are some latex polymer compounds that allow up to 700% stretch. These are closer to what FredGarvin mentioned, with a fairly long linear section in the middle part of the graph, but I haven't found an example graph yet. These are used in gloves and well a product that FredGarvin should be familiar with as part of his night job. However I'm not aware of any latex tubing that is made in such compounds, and although they can be stretched to about 500% or so of their original length, they will weaken from repeated stretching. 450% is about the limit (350% pull).

Last edited: Aug 7, 2009
15. Aug 9, 2009

### zcd

Re: Elastics

Air pressure isn't allowed either. My plan is to build the slingshot type for ease of calculations, because it's more of a precision contest than sheer distance. Judging from the information, it's sufficient to approximate the force linearly. As for wear over time, I think that problem can be addressed by using new sets at a reasonable rate. Thanks for the resources.