relationship between density and elastisity

soandos

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

Astronuc

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...nts_(data_page) - need to verify data.

http://en.wikipedia.org/wiki/List_of...nts_by_density

soandos

to answer your questions in order:

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

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...d/souspe2.html

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

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

soandos

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

Andy Resnick

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.

soandos

i am not asking about anything special, just the norm.
is this clearer:
what amount of force is needed on the poles to extend the major axis by a given amount?

rcgldr

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)?

granpa

is a neutron star a solid or a liquid?

does it even matter?

soandos

solid, i do not know

mordechai9

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.

soandos

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

mordechai9

Yes; such formulas exist. See book listed above.

soandos

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.

mordechai9

Library...

soandos

none of the ones in nassau county have it