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26

No. The answer is clearly no. This building is 800 meter high. Some comparison: Skydivers are falling more kilometers in free fall. They experience absolutely no damage from the pressure increase. Scuba divers moving fast upwardly or downwardly also don't get any wounds, although 10 meter deep water has the same pressure as there is between the sea level ...


16

The reason is electron degeneracy pressure. The cores of giant planets are dense enough that the electrons in the gas occupy about $h^3$ of phase space each. The Pauli exclusion principle means that they cannot all occupy low energy/momentum states. This means that even at relatively cool temperatures the gas can still exert considerable pressure due to the ...


11

Although we don't have a quantum theory of gravity, we think we have some reliable knowledge about the properties of black holes from general relativity. One thing we think we know is the so-called "No-hair conjecture", which says that black holes can be described by just three numbers: mass, charge, and angular momentum (i.e. how much they are spinning). ...


8

Ok, trying my luck with a physics answer. Let's first look at the boundary conditions given in the movie, since we're particularly talking about that here. The water planet is said to have $130\%$ of earth's gravitational acceleration on the surface. So we have \begin{equation} g_W = 1.3 g_E \end{equation} This is a given and not to be violated. And in fact ...


7

Density is a 3-form, since you would write it as $$\omega:=\rho\text dx\wedge\text dy\wedge\text dz.$$ In special relativity it remains (the time component of) a 3-form. More specifically you have a current density $J$ of the form $$J = \rho\text dx\wedge\text dy\wedge\text dz + J_x \text dt\wedge\text dy\wedge\text dz+ J_y \text dx\wedge\text dt\wedge\text ...


6

It depends on how the quantity in question transforms. Almost always, densities in the form of "stuff per unit volume" and generally the "stuff" (like a charge) is a scalar (a number of things - number of elementary charges), but the volume it is contained in is observer dependent, owing to the Lorentz contraction. Therefore the density is ...


4

Basically, it has to do with the density of the material as a function of temperature. The density of iron increases as it cools, that is, solid iron is more 'packed tight' than when it is melted. This is understandable, since the kinetic energy of the iron atoms decreases as the temperature drops (ie: the average velocity of the atoms decreases), allowing ...


4

This is an instrument that measures fog density and has an experimental plot, figure 9 . Once you have the relative humidity at the fog appearance at a temperature and pressure , one can use known equations to get the density. This link gives a calculator.


4

You would be wise to somehow determine the exact fluid used by the original manufacturer. Consider that each of the floats has a fixed density, and has a temperature marked on its hanging tag. So you need a liquid which will have the correct, different density at each temperature marked on a tag. In short, the liquid you choose must match both the ...


4

There more sides to this scenario that you're considering. Firstly, if we are assuming that the temperature is the same at sea level and on the high mountains, then the speed of sound doesn't actually change, as a constant temperature will take care of the air pressure-density ratio. $$c = \sqrt{\kappa \frac{p}{\rho}} $$ Where $p$: static air pressure, ...


4

The trouble is that your table, or whatever object it is, will act as a waveguide. That's because the sound waves will (partially) reflect of the wood/air surface then travel back into the table and interfere with other waves. The result is going to be hideously complicated to calculate. As LuboŇ° says in a comment, if the thickness of the table is much less ...


4

It's true. Special equipment and a long time is required to mix helium and nitrogen. According to one study, a mixture of 2.7% He, 93.3% N at 800 p.s.i.g. required a special cradle to repeatedly upend the cylinder, and 20.5 hours to reach equilibrated gas, which then remained mixed: http://pubs.acs.org/doi/abs/10.1021/je60005a002. The helium repeatedly ...


4

It is commonly believed that the speed of sound at high densities is bounded from above by $c/\sqrt{3}$, where $c$ is the speed of light. Calculations of this quantity in many theories, ranging from QCD to systems with scale invariance, have all shown it to either stay below or exactly saturate the bound. See the introduction of this paper for a recent ...


3

Far away from a black hole, spacetime is curved only a little bit, and many different things could curve it like that out there. It's like if you had a dollar in your pocket, and it's been there for a long time, and you can't remember if you got it from your boss or from your friend. But a dollar is a dollar. So you could have a massive star, or a black ...


3

This is because the whole boat, along with the air in the boat, is lighter than the water it displaces. For example, if a small boat will take up 1 cubic meter of water, then it has to be heavier than the weight of 1 cubic meter of water. This is explained in this post by What If here. For the same reason that bowling balls float (because salt water the ...


3

Your intuition is right: the density of the string goes down a little bit when you increase the tension. HOWEVER: the wave in a string is a transverse wave which depends on the tension and the mass per unit length. If you double the tension the mass per unit length goes down by a small amount (the string gets a bit "thinner" because it gets longer) . Both ...


3

This answer will not make me popular because it gets people up to speed fast on protecting themselves from thieves and levels the playing field for people who like to maintain their advantage over others. There are a few methods we use to determine if gold is bunk or real...Methods that test if your gold is hollow, filled, alloyed (and the alloy percentages ...


3

I'll use this answer to provide some information that's mostly orthogonal to what Phonon said. As Phonon pointed out, the speed of sound depends on temperature, not pressure. It's cold on the top of high mountains, so the speed of sound would tend to be lower. Some mechanisms for sound production have a frequency that depends on the speed of sound, and ...


3

As an experimental answer, for 12" latex balloons, I could lift about 5 grams (in addition to the balloon). It of course will depend on how full you fill the balloons.


3

There is no relationship between the density of a metal and its electrical resistivity. There is a big database of material properties called MatWeb which is recommend as a legitimate source of data by UCSD's and Stanford's library systems, Rose-Hulman, etc. I took data from around 60 different metals and graphed them: As you can see there is no ...


3

Assuming you are talking about exoplanets, I'll offer this. To obtain a density you need a mass and radius. Masses come via two methods - either measuring the radial velocity variations of the star it orbits (the bigger the RV variations, the bigger the planet mass), or so-called transit timing variations. This latter works in multiple "transiting planet" ...


3

If we take neutron star material at say a density of $\sim 10^{17}$ kg/m$^{3}$ the neutrons have an internal kinetic energy density of $3 \times 10^{32}$ J/m$^{3}$. So even in a teaspoonful (say 5ml), there is $1.5\times10^{27}$ J of kinetic energy (more than the Sun emits in a second, or a billion or so atom bombs) and this will be released instantaneously. ...


2

So I am guessing you have a a 2 dimensional density? say, kg/m^2? In this case, you will need to get the area of your box -> say it is 2m^2. The mass of the box is 2 * 0.5 = 1 kg. But the mass of your person is 80kg. So your new mass is 81kg. This means the new density will be 81/2 = 40.5kg/m^2. The item will only float if the item has a lower density ...


2

One should always specify whether one is talking about rest mass per unit rest frame volume, $\rho_0 = m_0/V_0$, rest mass per unit observer-frame volume, $D = m_0/(V_0/\gamma) = \gamma\rho_0$, or relativistic mass per unit observer-frame volume, $(\gamma m_0)/(V_0/\gamma) = \gamma^2\rho_0$.1 (I can't imagine the fourth case, relativistic mass per unit rest ...


2

Your parameter $E$ is the bulk modulus, and this is a measure of how compressible the medium is. Easily compressible media like gases have a low value of $E$ while almost incompressible fluids like water have a very high value for $E$. Actually we should really use the symbol $K$ rather than $E$, because $E$ is normally used for the Young's modulus. And ...


2

I don't see how this can be done, given the problem as-stated. What defines it as being 2 superimposed sounds, rather than just 1 sound, other than just an arbitrary definition? What stops me coming along and saying: "No, it's actually 4 superimposed sounds, or 27!"? If both sounds are coming from the same source then any shift in speed or frequency of each ...


2

The density of a black hole is the mass divided by volume: $$ \rho=\frac M V=\frac M{4/3\pi R^3}=\frac{3M}{4\pi}\left(\frac{c^2}{2GM}\right)^3=\frac{3c^6}{32\pi G^3 M^2}\approx1.9\times10^{19}\text{ kg}/\text{m}^3\left(\frac{M_\odot}M\right)^2 $$ This means that the average density of the black hole decreases as the mass increases! We can also solve for the ...


2

I'll write my comments here as a full answer, as suggested by Floris. I won't use the moment of inertia tensor: it's simpler from pure angular momentum of each point particle. We know that $$\vec{L} = (\vec{r} \times \dot{\vec{r}})\,m .$$ So, for a point particle, $$d\vec{L} = (\vec{r} \times \dot{\vec{r}})\, dm .$$ Noting that $\rho = \frac{dm}{dV}$, ...


2

It depends on the fluid. Consider, for example, an ideal gas at fixed temperature near the surface of the Earth. Does the density vary in such a column? Yes. Let's investigate as follows. Imagine that the column is in the $z$-direction and has cross-sectional area $A$. Let $z=0$ at the ground. Consider a small, vertical "piece" of the column between ...



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