Formula for potential energy store din a strained solid?

In summary, the formula for finding potential energy stored in a strained solid is E = (λAx^2) / (2L), where E is the elastic potential energy, λ is the modulus of elasticity, A is the cross-sectional area, x is the displacement, and L is the natural length. By using this formula, the potential energy stored in the scallop's abductin material can be calculated.
  • #1
formula for potential energy stored in a strained solid??

I was wondering of there was some formula for finding the potential energy stored in a strained/stressed solid. I have this problem:

A scallop forces open its shell with a material called abductin, the elastic modulus of which is about 2.20×106 N/m2. If this piece of abductin is 2.88 mm thick and has a cross-sectional area of 0.515 cm2, how much potential energy does it store when compressed 1.19 mm?

Unfortunately my prof. didnt mention a damned thing about potential energy, so i was wondering if someone could help me out with this... oh yeah and it's not in our book either...
 
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  • #2
[tex] F = \lambda \frac {Ax}{L} = T [/tex]

F = force, [tex] \lambda [/tex]= modulus of elasticity, A = cross sectional area x = displacement L = natural length T = tension

[tex] E = \int F dx = \lambda \frac {Ax^2}{2L} [/tex]

E = elastic potential energy
 
  • #3
Wow thanks a bunch. However I'm still not getting the correct answer...

I'm calculating this:


2.20x10^6 * (0.0000515 *(0.00119^2) / 0.00288*2) = 23.4075J which is incorrect.

I got it... turned out to be some weird computational error. Anyway, thanks again !
 
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1. What is potential energy?

Potential energy is the energy an object possesses due to its position or configuration. It is the energy that is stored within an object and has the potential to do work in the future.

2. How is potential energy stored in a strained solid?

When a solid is strained or deformed, the molecules within the solid are stretched or compressed, resulting in a change in their potential energy. This change in potential energy is stored within the solid and can be released when the solid returns to its original shape.

3. What is the formula for calculating potential energy stored in a strained solid?

The formula for potential energy stored in a strained solid is PE = 1/2kx^2, where PE is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position.

4. How does the spring constant affect the potential energy stored in a strained solid?

The higher the spring constant, the stiffer the solid is and the more potential energy it can store when strained. This means that objects with a higher spring constant will require more force to be deformed, and they will have a greater potential energy when they are strained.

5. Can the potential energy stored in a strained solid be converted into other forms of energy?

Yes, the potential energy stored in a strained solid can be converted into other forms of energy. For example, when a spring is released, the potential energy stored in the strained solid is converted into kinetic energy, causing the spring to bounce back to its original shape.

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