Calculating Potential Energy Stored in Compressed Abductin

In summary: The value for x should indeed be 0.001 m as rsk stated. The potential energy, calculated using the given formula, is 0.167 N*m.In summary, A scallop uses an elastic material called abductin to force open its shell. The elastic modulus of abductin is 2.0 x 106 N/m2 and when compressed by 1.0 mm, it stores a potential energy of 0.167 N*m. This can be calculated using the formula U = \frac{F \Delta L}{2}, where \Delta L is the length of compression, and finding the force F using the relation \Delta L = \frac{F L }{EA}. The cross-sectional area
  • #1
needhelp83
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0
A scallop forces open its shell with an elastic material called abductin, whose elastic modulus is about 2.0 x 106 N/m2. If this piece of abductin is 3.0 mm thick and has a cross-sectional area of .5 cm2, how much potential energy does it store when compressed 1.0 mm?

I have no idea how to solve for the potential energy when compressed. How would i do this?
 
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  • #2
http://dictionary.laborlawtalk.com/prev_wiki/images/math/f264a029703a35c1bd6a9b835613e7b1.png

Does this help?
 
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  • #3
The potential energy due to compression equals [tex]U = \frac{F \Delta L}{2}[/tex], where [tex]\Delta L[/tex] is the length of compression. You only have to find the force F now from the relation [tex]\Delta L = \frac{F L }{EA}[/tex]. If I understood the problem right, 'thick' does represent some kind of length here, so it equals L (?).

Edit: basically, this is the same what rsk wrote, if [tex]\lambda[/tex] is the module of elasticity E, and E the potential energy U. :smile:
 
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  • #4
How about this...

displacement=3-1 mm=2 mm

E=(lamda)Ax^2/2l
E=(2000000 n/m^2)(0.005 m)(0.002 m)^2 / 2(0.003 m)= 6.67

This is a shot! Does anybody else agree?
 
  • #5
needhelp83 said:
How about this...
E=(2000000 n/m^2)(0.005 m)(0.002 m)^2 / 2(0.003 m)= 6.67

5cm^2 is 0.0005 m^2 I think. Also why do you have 0.002 for x? Isn't it 0.001?
 
  • #6
I was thinking the displacement was the uncompressed abductin- the compressed abductin
 
  • #7
needhelp83 said:
I was thinking the displacement was the uncompressed abductin- the compressed abductin

The displacement x states the amount of compression. Correct your numbers (as rsk suggested), and this should work just fine.
 
  • #8
Ahh.. okay

E=(2000000 n/m^2)(0.0005 m^2)(0.001 m)^2 / 2(0.003 m)= 0.167 N*m

Here we go
 
  • #9
The cross sectional area is 0.5 cm^2 and not 5 cm^2 (according to the text of the problem). So, 0.5 cm^2 = 0.00005 m^2.
 

Related to Calculating Potential Energy Stored in Compressed Abductin

1. What is potential energy?

Potential energy is the energy that an object possesses due to its position or state. It is the stored energy that can be converted into other forms of energy.

2. How does a crab have potential energy?

A crab has potential energy because it has the ability to do work due to its position or state. For example, a crab sitting on a rock has potential energy because it can potentially release its energy by jumping off the rock.

3. What factors affect the potential energy of a crab?

The potential energy of a crab is affected by its mass, height, and the force of gravity acting on it. A heavier crab sitting at a greater height will have more potential energy than a lighter crab at a lower height.

4. How is the potential energy of a crab calculated?

The potential energy of a crab can be calculated using the formula PE = mgh, where m is the mass of the crab, g is the acceleration due to gravity, and h is the height of the crab.

5. Can a crab's potential energy be converted into other forms of energy?

Yes, a crab's potential energy can be converted into other forms of energy. For example, when a crab jumps off a rock, its potential energy is converted into kinetic energy, which is the energy of motion.

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