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        riddles >> general problem-solving / chatting / whatever >> what's the new density?
        
(Message started by: Marissa on May 2^nd, 2008, 1:15pm)

Title: what's the new density?
Post by Marissa on May 2^nd, 2008, 1:15pm

Suppose you have a long cylinder has internal and external radius, R1 and R2 respectively. It is made of an elastic material with density p.

The cylinder is then loaded such that the internal and external pressures are maintained at P. What is the new density of the deformed cylinder material?

And, suppose that hollow cylinder contains a gas at an internal pressure of P. The external pressure (outside the cylinder) is also maintained at P.

What is the maximum stress occuring in the cylinder material?

Title: Re: what's the new density?
Post by temporary on May 11^th, 2008, 9:52am

Pressurizing it changes not its density, it is still the same material with the same mass and density. The density is still p.

Title: Re: what's the new density?
Post by BenVitale on May 11^th, 2008, 12:32pm

In high school, I was told that solids (and liquids) don't compress; as opposed to a gas. But, later, when i took college physics, i learnt that solids do compress by a very small amount. This small amount is described as "bulk modulus."

Title: Re: what's the new density?
Post by Sir Col on May 11^th, 2008, 1:01pm

@temporary: Density is defined as mass/volume. Change the volume of an object with fixed mass and guess what happens to its density? Admittedly the ideal gas law doesn't apply to solids, but solids under pressure will compress.

on 05/11/08 at 12:32:30, BenVitale wrote:

In high school, I was told that solids (and liquids) don't compress...

That's why sponges make particularly good steps. ;)

Title: Re: what's the new density?
Post by temporary on May 11^th, 2008, 3:48pm

If the object is compressed with pressure and it changes the volume, it changes the mass also. The material is the same, so is the density. I'm not saying there is no compression, I'm saying compression isn't relevant.

Title: Re: what's the new density?
Post by ThudanBlunder on May 11^th, 2008, 4:22pm

on 05/11/08 at 15:48:09, temporary wrote:

If the object is compressed with pressure and it changes the volume, it changes the mass also.

Is the mass destroyed? ;D

Title: Re: what's the new density?
Post by mikedagr8 on May 12^th, 2008, 3:12am

on 05/11/08 at 16:22:26, ThudanBlunder wrote:

Is the mass destroyed? ;D

Only the maths :P

Title: Re: what's the new density?
Post by BenVitale on May 12^th, 2008, 8:23am

on 05/02/08 at 13:15:35, Marissa wrote:

......
And, suppose that hollow cylinder contains a gas at an internal pressure of P. The external pressure (outside the cylinder) is also maintained at P.

What is the maximum stress occuring in the cylinder material?

The maximum stress is constant and isotropic stress -- which is called pressure -- achieved everywhere, is equal to P

Title: Re: what's the new density?
Post by JiNbOtAk on May 13^th, 2008, 8:52pm

on 05/11/08 at 15:48:09, temporary wrote:

If the object is compressed with pressure and it changes the volume, it changes the mass also.

What ?? :o

I think you mean specific density, otherwise referred to as relative density. This remains constant, as long as the reference density is the same.