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Questions tagged [density]

Density is defined as the mass per unit volume of a substance.

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Invariant density of Harmonic oscillator

In general, dynamical systems described by a pure Hamiltonian can have an infinite number of invariant densities. In fact, each initial state determines exactly a closed path in phase-space and the ...
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Electron density in DFT (*ρ*(r)) and probability density (wave function squared)

Are the electron density in density functional theory, ρ(r), and probability density, defined as wave function squared, the same quantities?
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Density $\rho$ in the Friedmann equations

In the Friedmann equations: $$\ddot{a}=-\frac{4}{3}\pi G(\rho+\frac{3p}{c^2})$$ $$\dot a^2+Kc^2=\frac{8}{3}\pi G\rho a^2$$ I didn't understand if $\rho$ is the mass density deriving from $m_0$ (the ...
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$\rho(t)\gt or \lt \rho_{critical}(t)$ depends upon $k$ for expansion or contraction in cosmology?

From friedmann equation $$1=\frac{\rho(t)}{\rho_c(t)}-\frac{k}{a^2H^2},$$$$\dot a(t)=+-\sqrt\frac{k}{\frac{\rho(t)}{\rho_c(t)}-1}$$ for $k\gt0$,$$\rho(t)\gt\rho_c(t)$$ and for $k\lt0$,$$\rho(t)\lt\...
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where would the thrust be upwards or downwards [closed]

NOTE: I have assumed that the block is kept partly submerged in water and partly in kerosene like in the picture. I was reading about Archimedes principle from my book when I came across an a example ...
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58 views

Cause of change of tea volume during cooling

At work I often drink tea, and i usually fill my cup to the brim with boiling water. When I let it cool though, until it's ready to drink, the liquids surface has sunken by about a fingers width. To ...
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33 views

The Speed of Light and Its Medium's Density

When reviewing a refractive index chart there is a relationship to the density of the medium and the velocity of electromagnetic radiation through the medium. The lower the density the greater the ...
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88 views

Finding the expression for probability density (the Klein Gordon equation)

Source: Quantum Field Theory for the Gifted Amateur by Tom Lancaster, Stephen J. Blundell. I am struggling to understand the logical step from the outline of the 'proof' in the footnote, to the fact ...
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How does density affect gravity?

Say we have two masses, mass A and mass B. These two masses are identical in every dimension. The only difference is the density. Do they not curve the same amount of space-time, and if not, why?
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How can I calculate the density of Mars' atmosphere during dust storms?

I have been searching to try to estimate the air density of the atmosphere on Mars during a dust storm. I am trying to use this dynamic pressure equation to calculate the pressure on a theoretical ...
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What is the meaning of effective density in porous media? Is the density of air inside the pore space not same as density of free air?

I am trying to understand the physical meaning of using effective density in porous media. Is it a fictitious value? Can't I use the density of solid and fluid as it is while modeling porous media?
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By which physical mechanism does the continuity equation in fluid mechanics work?

The Navier-Stokes equations consist of the momentum equation and the continuity equation. Consider the incompressible versions for the purpose of this question. Continuity is always talked about as a ...
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How to find density of a wire when we know information of it in polar form

We know that the wire has the "path" in the shape of the polar graph $$r = \theta, \quad 0 \leq \theta \leq \pi/2 $$ and we know at point $(\theta,\theta)$ the density of the wire is $2\theta$. I ...
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Energy Density Calculation Formula?

What I wish to know is how does one calculate the energy density of materials such as silicon. I was told that a way of finding energy density is through the calculation of stress-Strain Curve. ...
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Are there physical properties that can be used to differentiate stainless steel from copper in a home environment? [closed]

So the backstory is that I purchased a reusable drinking straw that is copper coloured, but is advertised to be stainless steel. That got me thinking about whether I could be sure it was one or the ...
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66 views

How to calculate the normal force of a box in the bottom of a bucket of liquid? [closed]

I have been trying for some time now, and seem to be unable to come up with the correct answer. The setup for the problem is as follows: After finding a similar question and rechecking the buoyancy ...
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1answer
67 views

How much harder is a proton theoretically speaking than a diamond? [closed]

It's generally said that a diamond is the hardest substance known to man (apparently there are a few materials known to be harder). However, one ought to expect that a proton or neutron should be ...
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1answer
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How do fluids behave in space with regards to bouyancy and density?

Will a fluid loose it's bouyancy in zero-gravity. What would happen if an object is immersed in a liquid in space (if the liquid is still very much together and not spilling as big bubbles or droplets)...
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why do fluids become less dense when heated?

I have been told that fluids expand and become less dense when heated, but i never been told why. So my question is why do fluids become less dense when heated? What is going on in a microscopic level ...
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What is the equation of state of foam, on a macroscopic scale?

Consider a large amount of soap foam (or any other substance producing foam), of mass density $\rho$ in a gravityless environment. What is the internal pressure $p$ of that foam, viewed as a fluid on ...
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1answer
32 views

Effect of temperature on specific weight

How much of an impact has a temperature difference when the specific weight of an object in water is measured, e.g. the weight of a mussel in seawater. Would the two scenarios yield the same specific ...
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Charge density of sea water

If sea water contains salt ions and some H+ and OH- ions, what are the charge density of a certain volume of sea water? And is there a way to calculate?
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33 views

Non-relativistic limit of the cosmological constant

Usually, when we apply the non-relativistic limit ($c \rightarrow \infty$) to relativistic equations, the cosmological constant $\Lambda \sim \mathrm{L}^{-2}$ is simply offhandedly neglected by ...
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3answers
564 views

BH singularity? Infinite density

How can the density of a region of space go from finite density to infinite when there are no numbers larger than any Aleph0 number but smaller than any Aleph1 number (no decimal point in front of it, ...
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1answer
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Why does the pressure change on uniformly mixing two liquids?

The two cylinders are connected the upper cylinder has a cross-section of A and the lower one has a cross-section of 2A (I've taken the cross-sections to be A and 2A as they are easier to work with ...
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Which weighs more in atmosphere, $1\,{\rm kg}$ of steel or $1\,{\rm kg}$ of feathers?

I'm having a discussion at the moment regarding the mass of $1\,{\rm kg}$ of feathers and $1\,{\rm kg}$ of steel. The person I'm arguing with states that $1\,{\rm kg}$ of feathers will be lighter ...
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1answer
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Does the amount/speed a balloon rises vary with the temperature of the gas inside, given a constant type and amount of gas?

I'm attempting to conduct an experiment with a balloon. I fill it up with some amount of helium. If I cool the balloon down (say with liquid nitrogen), the balloon's volume will decrease (because of ...
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5answers
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If gravity accelerates all objects the same, why does a ball in water sink? [closed]

I recently learned the law of universal gravitation: F = GmM / d². It dictates that all objects should fall at the same acceleration. But how is density explained ...
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Scaling of mass density

Let distances scale as $L'=kL$, $k$ is the scaling factor. Then spherical volume will scale as $V'=k^3 V$. Say, the sphere is filled with mass with constant density. If we scale the model with ...
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Why the body is drowning in the swamp?

Is it correct explanation why does the body sink? Swamp is not a liquid, but particle suspension, that's why Archimedes principle not working and upward buoyant force not applied to the body.
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By how much does space-time curvature modify the density of an object?

Let's imagine a transparent object with a density $\rho_0$ [$kg/m^3$] (A sphere of glass as example). Now I send through this object a long flat impulse of electromagnetic plane wave with frequency $\...
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Do the weights of two liquids not add when mixed?

I was given an interesting dilemma today. A co-worker saw me adding a liquid (Diisopropyl ethylamine AKA DIPEA) to a flask filled with another liquid (Tetrahydrofuran AKA THF). I needed to weigh out ...
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Silly question about Schwarzschild Black holes and scientific communication

Well, in scientific communication literature often we encounter the following phrase about black holes: A Black Hole is a body that have infinite curvature and infinite density So, with basic GR ...
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How can the Friedman Equation produce negative pressure or density?

As I understand it, the Friendman Equation provides the driving mechanism for Inflation.$$\frac{\ddot a}{a}=-\frac{4\pi G}{3}\left(\rho+\frac{3p}{c^2}\right)$$If $\rho$ or p is negative enough, you ...
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Relation between Young's modulus and density?

Can I calculate Young's modulus from density? Is there any mathematical relation between Young's modulus and density?
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Why are the volumes above and below the center of mass of a uniform cone not the same?

So today in my physics class we derived the center of mass of a uniform cone, and it all made sense, but near the end of class a student asked, "If you were to split an object into two parts with ...
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Density of Sea Water [duplicate]

Understandably, there is a clear-cut difference between liquids and gasses. Gasses being more compressible, liquids less so. If you bring a volume of air sealed in a container from sea level to 10k ...
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2answers
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Neutral buoyancy for cylinder/bladder in water

A 25 liter flexible plastic bladder consists of three parts: an air chamber located on top of the bladder, a large middle water chamber, and a lower weighted area that serves as a counterbalance and ...
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1answer
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Milky Way Density

It seems to be a simple question, but I wasn't really able to find an appropriate answer: How dense is the Milky Way? I am certain that there are reliable statistic, maybe even new ones from the GAIA ...
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1answer
134 views

Black Hole Surface Area-Mass Equation

Lets suppose we have a BH with mass $M$ and surface area $A$. From the Schwarzschild raidus we can say that the Area of the BH is proportional to its mass $$A=4\pi r^2=\frac {16 \pi G^2M^2} {c^4}$$ ...
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2answers
107 views

Dark matter density calculation

I find that the general dark matter density of the Milky Way is $$6.87 \times 10^9 \: \rm GeV/m^3$$ or $$1.225 \times 10^{-17} \: \rm kg/m^3$$ (by taking the size of the Milky Way and dividing it to ...
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1answer
143 views

Fractional change of density

I'm asked to prove that the fractional change of density of a fluid ($\frac{\Delta\rho}{\rho_0}$) is so that $$\frac{\Delta\rho}{\rho_0}=-\beta\,\Delta{T},$$ where $\beta$ is the volumetric ...
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59 views

How do you explain the “weight” of helium?

If weight is measured as M * g (mass x gravity), then how does the "weight" of a massive helium filled balloon negative? Let's say you have a 63,000 m^3 helium balloon. The mass of the helium is ...
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1answer
84 views

Continuity equation in the Lagrangian flow picture approach

In deriving continuity equations using Lagrangian. We consider the element of fluid which occupied a rectangular parallelopiped having its centre at the point $(a,b,c)$ and its edges $\delta a$ , $\...
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1answer
74 views

Movement of a helium filled vs lower-density-gas filled balloon inside an accelerated car

It's well known that a helium balloon inside of a car moves forward when the car accelerates, and backward when it slows down. What would happen, though, if a lower density gas was used instead of ...
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1answer
33 views

Where is mass density information of a Black Hole?

Have read that all the information of a black hole is contained on the Event Horizon. Does that include mass density of interior as a function of position? The shape of an event horizon depends on the ...
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Wood in water and buoyant force

Wood doesn't sink in water because its density is less than water density. So $ΣF=0$. But what is the force that counterbalances the gravitational force if the wood does not sink in water so that ...
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1answer
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Gravity and objects in substances

This is probably a matter of terminology and me not finding it due to the lack of it. An apple falls from a tree on the ground due to gravity. Yet, if it falls into a water pit it floats on top of ...
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2answers
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Derivation of pressure gradient stellar equation [duplicate]

I am trying to understand how to derive the following formula: $\frac{dP(r)}{dr}=-\frac{GM(r_<)\rho(r)}{r^2}$ The notes are as follow: Consider a star with COM and a shell: $P_1 - P_2 = -{\...
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1answer
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Non-invariance of density extrema with re-parameterization

Consider a density function $f(x)$, in one dimension for simplicity. Assume that it has an extremum at $x^*$, so that $f'(x^*) = 0$. If I make a change of variables via $x = x(\xi)$, then I must ...