Shear Modulus of jiggling jello

AI Thread Summary
The discussion centers on the shear modulus of lime and orange jello, with the lime jello jiggling faster, leading to confusion about their shear modulus. It is clarified that lime jello has a higher shear modulus due to its greater stiffness, despite the higher x displacement seeming to suggest otherwise. The relationship between the shear modulus and the spring constant (k) is explored, concluding that k can be expressed as k = G*A/L, where A is the cross-sectional area. The conversation also touches on the nature of jello's motion and its implications for calculating shear properties. Overall, the participants clarify misconceptions about the relationship between jiggling motion and material stiffness.
Bob Loblaw
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Homework Statement



A student bumps into a tray of jello. The lime jello is jiggling side to side faster than the orange jello. Both jellos have the same spatial dimensions. Which statement is true?

Answer: Lime jello has a higher shear modulus than orange jello



Homework Equations


Shear modulus: (F/A)/(X displacement/initial length)
Hook's Law: angular frequency=sqrt(k/M)


The Attempt at a Solution



The only difference between the jello is the lime jello jiggles more and this has a higher x displacement. this increases the denominator and makes the shear modulus seem *smaller* to me. Then upon looking at Hook's law, I see that higher angular frequency must be due to a higher K since M in both jellos are equal. Stiffer spring means higher shear modulus, right? How can I reconcile these seemingly contradictory statements!
 
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Bob Loblaw said:

Homework Statement



A student bumps into a tray of jello. The lime jello is jiggling side to side faster than the orange jello. Both jellos have the same spatial dimensions. Which statement is true?

Answer: Lime jello has a higher shear modulus than orange jello



Homework Equations


Shear modulus: (F/A)/(X displacement/initial length)
Hook's Law: angular frequency=sqrt(k/M)


The Attempt at a Solution



The only difference between the jello is the lime jello jiggles more and this has a higher x displacement. this increases the denominator and makes the shear modulus seem *smaller* to me.
the lime jello does not displace more...it is given that the lime jello jiggles faster.
Then upon looking at Hook's law, I see that higher angular frequency must be due to a higher K since M in both jellos are equal. Stiffer spring means higher shear modulus, right?
yes, correct
How can I reconcile these seemingly contradictory statements!
They do not contradict.
 
Thanks! I guess I was seeing 'jiggling' as more lateral movement.
 
Sorry to bump up an old homework problem, but I was wondering what k is in terms of the shear modulus in a problem like this. If you could assume the Jello here is a cube of elastic material, and that the jello's motion was planar, would this be the relation between k and shear modulus (G):

k = G*J/L

where L is the height of the cube and J is the polar moment of inertia of the cube?
Thanks!

Edit: Actually, I guess it would be k = G*A/L where A is the cross sectional area of the jello as seen from the top. I think it would be A instead of J because the jello isn't rotating around an axis. Is that right?
 
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jobu said:
Sorry to bump up an old homework problem, but I was wondering what k is in terms of the shear modulus in a problem like this. If you could assume the Jello here is a cube of elastic material, and that the jello's motion was planar, would this be the relation between k and shear modulus (G):

k = G*J/L

where L is the height of the cube and J is the polar moment of inertia of the cube?
Thanks!

Edit: Actually, I guess it would be k = G*A/L where A is the cross sectional area of the jello as seen from the top. I think it would be A instead of J because the jello isn't rotating around an axis. Is that right?[/color]
Your edited[/color] remarks are correct. The constant k would be a measure of the stiffness of the material in shear, where k = F/Δx, and Δx is the transverse displacement of the cube in the direction of the shear force F. See

http://en.wikipedia.org/wiki/Shear_modulus
 
Thanks for the reply, Jay! Is there an expiration date on thanks? Something like "Best if thanked within 2 weeks of answer"? If so, sorry for the staleness :-D
 
jobu said:
Thanks for the reply, Jay! Is there an expiration date on thanks? Something like "Best if thanked within 2 weeks of answer"? If so, sorry for the staleness :-D
Thank you's are accepted anytime. You're welcome.:smile:
 
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