Rubber band: More or less force to stretch at the beginning?

[MilleySill]

Since rubber band does not follow Hooke's Law, is it more force is needed at the beginning of the stretch, or less force is needed? There are 2 different Elongation vs Force graph in S-curve on the net. Even different AI bot give different answers on a same question, which one is true?

 

[.Scott]

So here's both stories:

1) Pro-Hooke's Law
The main ingredient in a "rubber band" is latex.
Here's a link to a section of a wiki article that discusses this.
When reading that article, I believe the phrase "The Flory theory of rubber elasticity suggests ..." can be misleading. There is a "Flory theory" regarding the molecular structure and arrangement of polymers - but I haven't found an elasticity article by Nobel Laureate Paul Flory himself. But in any case, the phrase is probably best interpreted as "A model of rubber elasticity based on the Flory theory suggests ...".
So, to summarize that particular wiki paragraph (not the whole section), a model of rubber elasticity based on the Flory theory suggests that latex (rubber bands) should be "spring-like" and follow Hooke's Law.

2) Anti Hooke's Law
Here is a link to an article that describes what was found when the elasticity of rubber bands was actually measured.
The bottom line is, no, they do not follow Hooke's Law.
In particular, if you look at the graph at the bottom of page 2 of that article (in the PDF), you will see that not only is rubber band elasticity non-linear, it also shows considerable hysteresis - different elasticity while being stretched than while being relaxed. In particular, for any given length, more pull while being stretched than while it is being relaxed.

 

[Lnewqban]

Welcome!

Please, see:
https://en.wikipedia.org/wiki/Hysteresis#Elastic_hysteresis

You can experiment yourself, and feel higher resistance at the beginning of a deformation induced by a force.

Motorcycle's tires do not like sudden applications of loads, according to my personal experience loosing traction at the wrong moment.

 

[A.T.]

The bottom line is, no, they do not follow Hooke's Law.
In particular, if you look at the graph at the bottom of page 2 of that article (in the PDF), you will see that not only is rubber band elasticity non-linear, it also shows considerable hysteresis - different elasticity while being stretched than while being relaxed. In particular, for any given length, more pull while being stretched than while it is being relaxed.

And the amount hysteresis depends on how quickly it is being stretched/relaxed. Also, when kept stretched at constant length the force might decrease over time. So it's all much more complicated than Hooke's Law.

Here another experimental study:
https://www.rose-hulman.edu/~moloney/Ph425/0143-0807_33_4_771RubberBands.pdf

 

[MilleySill]

So here's both stories:

1) Pro-Hooke's Law
The main ingredient in a "rubber band" is latex.
Here's a link to a section of a wiki article that discusses this.
When reading that article, I believe the phrase "The Flory theory of rubber elasticity suggests ..." can be misleading. There is a "Flory theory" regarding the molecular structure and arrangement of polymers - but I haven't found an elasticity article by Nobel Laureate Paul Flory himself. But in any case, the phrase is probably best interpreted as "A model of rubber elasticity based on the Flory theory suggests ...".
So, to summarize that particular wiki paragraph (not the whole section), a model of rubber elasticity based on the Flory theory suggests that latex (rubber bands) should be "spring-like" and follow Hooke's Law.

2) Anti Hooke's Law
Here is a link to an article that describes what was found when the elasticity of rubber bands was actually measured.
The bottom line is, no, they do not follow Hooke's Law.
In particular, if you look at the graph at the bottom of page 2 of that article (in the PDF), you will see that not only is rubber band elasticity non-linear, it also shows considerable hysteresis - different elasticity while being stretched than while being relaxed. In particular, for any given length, more pull while being stretched than while it is being relaxed.

Thank you, that clears the confusion

 

[MilleySill]

Thanks to all of you, I appreciate for all the replies. I am trying to understand how a rubber band behaves. It astonish me that a simple rubber band that I can see it in every day's life can lead to such complex physics and calculations behind. I find out the force required to pull the rubber band is not consistent, unless it is a spring? That means if I am applying a mechanical force to do the pulling job, it actually needs more motor power at the end of the rubber band stretching because I can hear it the motor "making more noise", trying to generate more torque when the rubber band is being pulled near to its end point. The pulling process is not smooth either, normal speed at the beginning and much slower at the end.

In the opposite, I am trying too, to understand how a rubber band behaves, the force when it is been released. The kinetic energy, how fast it takes to return back to its original state? Is it different if I pull half way and release it, or I pull it to the max and release it? I believe it is so, that's how the bow works.

How to measure the speed, when applying different load on it? Does it start with constant speed or any acceleration and de acceleration in between? Let's say if I want to apply a certain force to hit on a target, or an object to land on a certain range, how much should I pull the rubber band? Most of the videos for examples, are just interested to show how to get an arrow to land on a target board. It doesn't care how much force is in that arrow as long as it pierce the board. If I am trying to land an object to an area using rubber band, where the force should not be overexerted, how do I make the estimation? I am trying to survey on net, but perhaps the keywords I am using is incorrect, so far I couldn't find any related materials to refer from.

 

[A.T.]

It astonish me that a simple rubber band that I can see it in every day's life can lead to such complex physics and calculations behind.

The internal structure of rubber is more complex than that of a metal / regular crystal. That's what allows it to be stretched so far. But it also makes the behavior harder to predict. For practical purposes you should measure the properties of the rubber band you want to use.

 

[.Scott]

I find out the force required to pull the rubber band is not consistent, unless it is a spring?

To be clear, rubber bands based on latex will never act like exactly like an ideal spring. The simplified model of a rubber band based only on Flory's theory follows Hooke's Law. But that is only a model - an over-simplified description of what is really happening with the latex. With a little engineering, you might be able to create a latex sample that when stretched by a small amount would follow this model, but certainly not if you stretched it as far a rubber bands are commonly stretched.

More to the point, if an AI has reported to you that rubber bands follow Hooke's Law, that AI has misinterpreted discussions - likely the many discussions related to the limited Flory-based model. As a software engineer, I find it very easy to see how the AI could do this. Since AI's don't "understand" what they are reading, they cannot naturally "connect the dots". I have not seen the limitations of the Flory-based model clearly and explicitly stated in those other discussions - certainly not as clearly and explicitly as I am trying to do here. So we can expect AI's to be handicapped when venturing into this topic.

So long as you don't over-stretch or break a good metal spring, it will follow closely to Hooke's Law. Hooke's Law presumes that the spring itself does not permanently deform and that it will promptly return any energy it is holding under stress or compression (that it will "spring back").

The fact that latex does not respond this way means that more is going on with it than is described with the Flory model.
This additional "goings on" is likely the breaking of molecule-to-molecule bonds as the elastic is being stretched or remains stretched. This "breakage" not only explains the hysteresis but indicates that the latex is converting some of the mechanical work to something else - no doubt heat - perhaps some sound.

 

[Lnewqban]

Thanks to all of you, I appreciate for all the replies. I am trying to understand how a rubber band behaves.

Also, that behavior dramatically changes with age (exposition time to UV light and ozone) and temperature.
If some kind of friction is involved in the deformation, lubrication also changes the behavior much.