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