# Relationship between density and elastisity

## Main Question or Discussion Point

what is the relationship between these two things for a given material?

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Astronuc
Staff Emeritus
what is the relationship between these two things for a given material?
Is this a homework assignment?

What properties of an element determine density? Is this mass density or atomic density?

What properties of an element determine the elastic (Young's) modulus?

Try to plot the elastic modulus as a function of the density for the corresponding element.

http://www.webelements.com/periodicity/youngs_modulus/
http://www.webelements.com/periodicity/density/

For a specific element, e.g. Fe - http://www.webelements.com/iron/physics.html

http://en.wikipedia.org/wiki/Elastic_properties_of_the_elements_(data_page [Broken]) - need to verify data.

http://en.wikipedia.org/wiki/List_of_elements_by_density

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1) no, it is a question to help explain another post of mine
2) i am not really sure if there is a difference here as the object in question is neuron star, with a density approaching that of an atomic nucleus
3) the material is roughly a constant, assume it is a mix of the lighter elements

i can see the young modulus and density at the point that it becomes a solid, but i do not see a way to relate the two

Astronuc
Staff Emeritus
Well, if the matter in question is a neutron star, then relating elasticity and density of atoms will not hold since the interactions of nucleons are fundamentally different than atoms. Is the question one of the 'acoustic' behavior?

The speed of sound is related to the bulk modulus and density. The more massive the particle - or more dense - the more resistance there is to the propagation of waves, which are basically a transfer of momentum/pressure through the medium.

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html

http://hyperphysics.phy-astr.gsu.edu/hbase/tables/soundv.html

http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html

no. it is related to how easily the minor axis would shrink if it was spinning.

Andy Resnick
what is the relationship between these two things for a given material?
I am unaware of any phenomenological relationship between the two. For nearly any solid material you provide me, I can provide a fluid with the same (or nearly so) density, and yet is not elastic at all.

For all but the most simple materials, there is currently no model to predict macroscopic material properties from microscopic properties.

is this clearer:
what amount of force is needed on the poles to extend the major axis by a given amount?

rcgldr
Homework Helper
How would the density be varied? Via temperature or by having voids (in a vacuum so air wouldn't fill the voids)? Via varius shapes (is a spring more elastic than a solid cylinder)?

is a neutron star a solid or a liquid?

does it even matter?

solid, i do not know

Um I can't remember the exact expression at the moment, but this is a pretty basic kind of question from solid mechanics; I suggest the book "Mechanics of Materials" by Gere. However, as Astronuc was trying to tell you, this question is quite dependent on material composition. The book by Gere mainly talks about metallic substances, at typical temperatures and densities. Once you start talking about colloidal substances (gels), high-temperature, high-pressure applications (e.g., subsurface rock mechanics), and especially, something like a neutron star, I'm not sure how much classical mechanics really applies.

thank you. are there any formulea that i can use though that have temperature and density as variables?

Yes; such formulas exist. See book listed above.

if you have a copy of the book can you please give me the formula?
it seems kind of silly to pay \$92 for a book that i just need a page out of.

Library...

none of the ones in nassau county have it