Asked • 02/10/20

Determining elastic force relationships of rubber band

In applying a general application of Hooke's law that demonstrates a linear relationship between the stretch of a band and its force output, such as looping one end of the band to a force gauge, and the other loop to a mass.


With respect to this classic experiment, what would be the relationship or force output of a 41 inch rubber band, if both loops where anchored to the floor with shackle mounts positioned one foot from each other, and the force gauge is situated above and between anchor points, which pulls the band upward and creates an isosceles triangle.


On the internet, some refer to this technique as double looping; however, it is observed that the full length or distance of the band (41 inches) is now divided into two, which are the hypotenuses of the two right triangles that make up the total isosceles triangle.


The question therefore, does the force output with this experiment double the force since the distance of the band between force gauge position and each anchor is 20.5 inches. An estimate is fine, no need to concern ourselves with friction or the circumference of shackle anchors or force gauge which are subtractive to the total distance of the rubberband.


P.S. This is not intended or part of an assignment or experiment, just mere curiosity only.


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Stanton D. answered • 02/10/20

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Hi Asked,

it's not clear exactly what you are asking. Are you trying to differentiate the setups which pull a single line up (with pulleys at each end to allow distribution of tension) from those which pull both lines up? If so, the relationship isn't a doubling - one band is unextended, the other forms triangles.

And anyway, as you perhaps have noted, you'll need to use trig functions to find the stretch distance, if you're measuring vertical position measurement only for the gauge (as I suspect you are?)

One further point: the Hooke's law range for common rubber bands isn't infinite, you may start maxing out somewhat before you snap the band. Examine your data judiciously!

--Cheers, -- Mr. d.

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Lance P.

The source that I am consulting is the following pdf paper: http://www.mistrongman.com/Misc%20Docs/CalculatingElasticBandTensions.pdf On page 6 of the document is how they configured the measurements, you will see that the loops of the band were secured by two metal shackles twelve inches apart mounted on the floor, which is a different setup than traditional rubberband physics experiments. Thus, does their setup of their experiment double the force output compared to the traditional setup. Page eight records the force data obtained. To put it a different way, is the total stretch of the band, the distance from one schackle to the next, or from shackle to the barbell? A similar analogy would be the difference of using one finger to hold one end of a rubberband fixed to the table, while using other hand and finger to pull other end straight up (vertical stretch model) versus using two fingers to hold both ends of rubberband fixed to a table, while using other hand and finger to pull straight up (isosceles triangular stretch model). If the force outputs are different, which one yields greater force production (vertical or triangular model)? Regards, Lance
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02/10/20

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