Potential Energy Stored by Elastic

In summary, the elastic potential energy stored by a piece of elastic can be approximated by the following equation: kx2
  • #1
Mikoden
1
0
Hi.

I'm trying to calculate the amount of P.E. stored by a piece of elastic. I've been looking for formulas but all i can find is how to calculate gravitational potential energy and spring potential energy. The piece of elastic is to be streched by about 1-2cm (from an original 30cm length) along the horizontal, and then twisted alot.

Any links to sites talking about this sort of problem would be handy, as well as any help that can be posted here. I'm after a formula of some sort to theoretically calculate the energy that is going to be stored, so that i have theory to back up my assumptions.

Thanks,
 
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  • #2
Basically, an elastic is just a spring. The force necessary to stretch a spring (or elastic) a distance x is kx (k is a constant depending on the particular spring (or elastic)) and the work done (therefore potential energy stored) is (1/2)kx2.
 
  • #3
If you are interested in learning some of the basics of general elasticity theory,
"Continuum Mechanics" in the Schaum's Outline's series might be a good start.
 
  • #4
The structural moduli will allow you to translate the strains (Young's for stretch and shear? for twist) into required forces. If you integrate these from some relaxed state up to the deformation you specify, then they should give you the work required to cause the deformation. If the order of the deformations has no influence on the work calculated (for which I am suspicious of the twisting), then you can interpret this as an increase in the potential energy.

I think the spring potential energy will only give you a first order approximation. If your strains are a significant fraction of original length, then I suspect that you will incur significant (at least) second order corrections.
 
  • #5
Just adding to turin's comment:
For the type of deformations you're talking about, I suspect that the
"small deformations theory" used widely would be invalid, and that stress-strain relationships should utilize the fully nonlinear tensor of relative displacements
 

1. What is potential energy stored by elastic?

Potential energy stored by elastic is the energy that is stored in an elastic material when it is stretched or compressed. This energy is potentially released when the material returns to its original shape.

2. How is potential energy stored by elastic calculated?

The formula for calculating potential energy stored by elastic is PE = 1/2kx^2, where PE is the potential energy, k is the spring constant, and x is the displacement of the material.

3. What is the relationship between potential energy stored by elastic and the material's elasticity?

The potential energy stored by elastic is directly proportional to the material's elasticity. This means that the more elastic the material is, the more potential energy it can store when stretched or compressed.

4. How does the shape of an elastic material affect its potential energy storage?

The shape of an elastic material can affect its potential energy storage by changing the amount of displacement when stretched or compressed. Materials with a larger surface area will typically have a greater potential energy storage capacity.

5. What are some real-life examples of potential energy stored by elastic?

Some examples of potential energy stored by elastic include a stretched rubber band, a compressed spring, and a bow and arrow. These objects all have elastic materials that store potential energy when stretched or compressed.

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