Need help on rubber band and Hooke's Law

[yokan]

This has caused me to be very confused because at one time i did an experiment, the rubber band followed Hooke's Law, but at another time, it does not.
When I search the internet, some websites state that such experiments are only correctly done when the force is linear with the extension, while some other websites states that rubber bands don't even have a spring constant
I am thinking whether this is due to rubber bands have very low elastic limit?
That's the only explanation I could come up to sort of "fit" the two contradicting theories.
One more question, if the elastic limit does exist, around how big is it? 100N, 200N? I'd like to have an approximate, just a rough approximation will do fine so that i can re-plan a more accurate experiment

 

[quantumdude]

Because the make and model of a rubber band does not appear on the band itself, you will have to determine the spring constant k by experimentation. Just don't go too far outside the linear region, or else the rubber band will not be of any use to you in the future.

So I'd use incremented masses and add them on until the displacement is no longer directly proportional to the load.

 

[yokan]

Thx for your help
I was using increments of 50g and realized that the data points outline a fit curve with a decreasing slope right from the beginning. I was not very succesfully in finding a linear part...
So perhaps can you give me a rough idea of where the limit is?

Another very interesting phenomenon is that the curve has a decreasing slope up to ~500g of mass and continue onwards with a increasing slope, giving the whole curve a very special shape. Any thoughts on that?
Thx again in advance

Left out sth, a very very important question. If all things go right, the curve on a graph with Force against the change in length should have a decreasing or increasing slope?

 

[HallsofIvy]

"Hook's Law" is, like most physics laws, is a "linearization".

We know from very simple experiments that the force, if there is 0 "stretch", then there is 0 force. We also know that is the force opposite to the strectch. No matter what the "true" formula is, we can approximate it by the linear function.

That is, whatever the "true" force function is, we can approximate it by F= -km where k is the derivative of the true force function at x= 0

 

[yokan]

I see, so I can determine the "spring constant" by find the derivative of the curve at a specific point.
But in general, will the curve for the rubber have a decreasing slope or increasing slope on a graph of force against change in length?
Thx again for everyone's help

 

[HallsofIvy]

That depends upon the spring. If I remember correctly, springs for which the slope is increasing (so that the "spring constant" increases slightly with length) are called "hard" springs and springs for which the slope is decreasing are "soft" springs.

 

[yokan]

Can rubber band be divided into "hard" springs and "soft" springs?