How Can You Determine the Elastic Limit of a Spring Without Causing Damage?

[foofoo]

Hi everybody.

First of all, sorry for my English. It's not my mother tongue.

We made the Hooke's Law experiment at school (high school). Everything worked out great. We had to find the spring constant and we did. But our teacher gave us an assignment for extra credits! We have to find the elastic limit of our springs without damaging it. I know we could get lots of springs and test them with know weigths (trial and error), but I don't think that's what she wants.

I've been googling and I've found some websites that talk about the elastic limit of springs and show plots where you can identify the elastic limit point. They talk about plastic deformation and how stuff crack in different ways. I've found topics about stress and strain, but I haven't found a specific example applied to what I need. I found a site that talked about if we stretch a wire, the amount it stretches by depends on its length, its diameter and the material it’s made of. I think something similar applies to springs.

Could anyone tell me which concept I should look for? A book's reference would be great? Does anyone know a book where I could find an example like this?

Thanks all.

 

[lightgrav]

The important point is that the Hooke's Law linear relation (L = Lo + k F),
which is reversible, is only valid for "small" deformations.
Larger deformations will be non-linear, and not reversible.
That is, if you increase Force little-by-little, and plot the slope as you go,
the slope (dL / dF) will change just as the elastic limit is reached.

This WILL make a permanent change in the spring.
But if that change is small enough, next year's students won't notice that your spring is different from the springs that were not abused this year.

 

[kyle8921]

Hello,

Thank you for sharing your experience with the Hooke's Law experiment and your assignment to find the elastic limit of your springs without damaging them. It's great to see students taking an interest in further exploring a topic beyond what is covered in class.

To answer your question, the concept you should be looking for is called the "yield strength" of a material. This is the maximum stress (force per unit area) that a material can withstand before it starts to permanently deform or break. In the case of a spring, the yield strength would be the point at which it can no longer return to its original shape after being stretched or compressed.

As you mentioned, this can be determined by plotting stress (force per unit area) versus strain (change in length/ original length) and identifying the point at which the curve deviates from a linear relationship (i.e. the elastic limit). This can also be found by performing a tensile test on a sample of the material and measuring the point at which it starts to permanently deform.

I would recommend looking for resources on materials science and engineering, as this is the field that studies the properties and behavior of different materials. A textbook such as "Materials Science and Engineering: An Introduction" by William D. Callister Jr. and David G. Rethwisch may be helpful in understanding the concepts of yield strength and plastic deformation.

I hope this helps and good luck with your assignment! Keep up the curiosity and enthusiasm for science.