Shear Modulus of jiggling jello

[Bob Loblaw]

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!

 

[PhanthomJay]

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.

 

[Bob Loblaw]

Thanks! I guess I was seeing 'jiggling' as more lateral movement.

 

[jobu]

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?

 

[PhanthomJay]

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?

Your edited 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

 

[jobu]

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

 

[PhanthomJay]

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.