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32

The speed of sound in a liquid is given by: $$ v = \sqrt{\frac{K}{\rho}} $$ where $K$ is the bulk modulus and $\rho$ is the density. The bulk modulus of mercury is $2.85 \times 10^{10}$ Pa and the density is $13534$ kg/m$^3$, so the equation gives $v = 1451$ m/sec. The speed of sound in solids is given by: $$ v = \sqrt{\frac{K + \tfrac{4}{3}G}{\rho}} $$ ...


31

When you would enter the water, you need to "get the water out of the way". Say you need to get 50 liters of water out of the way. In a very short time you need to move this water by a few centimeters. That means the water needs to be accelerated in this short time first, and accelerating 50 kg of matter with your own body in this very short time will deform ...


25

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 ...


23

It's not the falling that's fatal, it's the deceleration at the end that kills you. Something like water or concrete does this on a sub-meter distance (which requires extremely high forces). On the other hand a gas is much less dense, so it cannot decelerate a falling object nearly as quick. Sometimes inflatable cushions are used as safety nets (think: ...


21

If gas A and gas B are of different density, then the situation sketched is not in equilibrium: the water level on the side of the light gas will be higher. There, the containers are moving down, and you have to push your containers through this net difference in level. You do need to put in energy here, which is probably the piece that you are trying to ...


16

Squeezing the bottle does decrease its volume. Rather than a bottle, it may be more helpful to think of a full toothpaste tube; the mechanics will be the same. If you squeeze the middle of the tube, the middle will collapse, the back will expand, and the front will expand and squirt out some toothpaste. Treating the toothpaste in the tube (or the water in ...


16

The density does increase with depth, but only to a tiny extent. At the bottom of the deepest ocean the density is only increased by about 5% so the change can be ignored in most situations. If you're dealing with these sorts of depths you also need to take temperature into account because the water temperature changes with depth and the density also ...


16

If something is infinitely dense, must it not also be infinitely massive? Nope. The singularity is a point where volume goes to zero, not where mass goes to infinity. It is a point with zero volume, but which still holds mass, due to the extreme stretching of space by gravity. The density is $\frac{mass}{volume}$, so we say that in the limit ...


14

Well, it can't (float), since a Black Hole is not a solid object that has any kind of surface. When someone says that a super massive black hole has less density than water, one probably means that since the density goes like $\frac{M}{R^3}$ where M is the mass and R is the typical size of the object, then for a black hole the typical size is the ...


13

You have hit on the major explanation of the unusual thermal stability of surface-frozen lakes. The deep earth is temperature stable, since the surface seasonal fluctuations can't penetrate the heat by diffusion more than some meters into the deep ground. So the deep ground is at a temperature which is stable all year. Advection only raises heat to the ...


13

Gaseous hydrogen and helium are lighter than air. Hydrogen, helium and air are close approximations to ideal gases, and for an ideal gas the volume of one mole of gas is about 22.4 litres. That means the density of an ideal gas is proportional to its molecular weight, so hydrogen ($M_w = 2$) and helium ($M_w = 4$) are lighter than air (average $M_w = 28.8$). ...


12

The ocean surface is not as hard as the ground but if you drop from a plane, you would hit it with such a high velocity that the pressure would most likely kill you or cause very serious damage. Considering air resistance, the terminal velocity of a human, right before reaching the water, would be at most some $150\text{ m/s}$. If you weigh $70\text{ kg}$, ...


12

Consider jumping into a swimming pool. Do a barrel-roll (sorry I mean cannon ball, that just kind of slipped out). It's fun, you enter the water nicely and make a huge splash, probably soaking your sister in the process (that'll learn her). Now do a belly flop. Not as fun. You displace exactly the same amount of water in the same time, but this time there is ...


11

Let's look at this another way: you're just moving from one fluid to another. Sounds harmless, right? By specification of the problem, we're at terminal velocity when we hit the water. The force of drag (in both mediums) is roughly: $$ F_D\, =\, \tfrac12\, \rho\, v^2\, C_D\, A = \rho \left( \frac{1}{2} v^2 C_D A \right) $$ You can imagine that ...


10

The surface area of the bottle is conserved, but the volume is not. Squeezing the bottle deforms it into a shape whose volume to surface area ratio is lower than it was previously. As an example consider a bottle whose cross-section is initially a circle. The volume of the bottle will be $V_0=\pi r^2h$ where $h$ is the height of the bottle, and the ...


10

Send an ultrasonic pulse through the gold bar and analyse the returning wave. This technique is actually used to detect impurities in gold bars. To quote this article: Where the wave encounters a region of material with different physical properties – particularly the density and elastic constants – to the rest of the metal, the beam is affected in a ...


10

It's actually a surprisingly straightforward differential equation. If you assume that the acceleration due to gravity $g$ doesn't change with altitude (a good approximation if the atmosphere is thin compared to the radius of the earth), Bernoulli's relation tells you the change in the pressure $P$ with height $h$: $$ \frac{dP}{dh} = -\rho g$$ Meanwhile the ...


9

The observation that old windows are sometimes found to be thicker at the bottom than at the top is often offered as supporting evidence for the view that glass flows over a timescale of centuries. The assumption being that the glass was once uniform, but has flowed to its new shape, which is a property of liquid. However, this assumption is incorrect; ...


8

The answer is No and the reason is the equivalence principle which says that there exist natural units in which the gravitational mass (the mass $m$ in $F=GMm/r^2$) is equal to the inertial mass (the mass $m$ in $F=ma$) for all objects in the Universe. This is equivalent to the statement that all objects, regardless of their composition, density, and other ...


8

The reason that the density is so high is because the pressures are so immense. If we somehow teleported a teaspoonful of neutron star material to earth, it would very rapidly inflate because the pressures aren't high enough to crush it into its dense form. This would effectively be an enormous explosion. It is difficult to describe what it would inflate ...


8

Due to the crystal structure of the solid phase of water, the molecules arrange themselves in a rigid, ordered fashion and end up being, on average, farther apart from each other (than they are in the liquid phase), and thus less dense. Less dense things float because of buoyancy.


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

"The speed of sound is variable and depends on the properties of the substance through which the wave is traveling. In solids, the speed of transverse (or shear) waves depend on the shear deformation under shear stress (called the shear modulus), and the density of the medium. Longitudinal (or compression) waves in solids depend on the same two factors with ...


7

I don't think that this question is still fully resolved, water is a fascinating molecule! But here are some thoughts. Clearly, if ice is lighter than liquid water it is because it doesn't pack as well. Its an example of how a random-ish packing can be more efficient than an ordered packing of a "weirdly" shaped molecule. Imagine throwing LEGOs into a box, ...


7

I'm not a physicist. So I am treading very carefully attempting to answer a question here... :) A physical example that may help explain this is rock skipping. When you skip a rock, it will 'bounce' off of the water when at high speeds. Eventually it slows enough to no longer bounce but 'sink' into the water. Picture your body doing the same thing. Your ...


7

1/3) As Newton pointed out way back in the Principia, the gravitational attraction due to a spherically symmetric mass distribution is, assuming you are outside of it, the same as if all the mass were at a point at the center. Thus the gravitational acceleration at the surface of a sphere is determined solely by the total mass $M$ and the radius $R$. What is ...


7

Here is a table I made for you listing the elements with a density higher than 10 g/cm$^3$ and their approximate price per kg: I couldn't find any prices for Einsteinium or Actinium and some of the other prices might come from poor sources, but take it as a rough guide. Now you only have to figure out how much you need and your budgetetary constraints, ...


6

Black holes are really hard to get a density. Basically, they are so dense that there is no known mechanism for providing sufficient outward force to counterbalance the inward pull of gravity, so they will collapse into an infinitesimally small size. Of course, that doesn't seem likely, it seems likely there is something that will keep the volume from being ...


6

One way to discuss the maximum density of a gas is to look at its phase diagram. In a PT phase diagram, we will obviously seek a point on the boundary of the gas region where the temperature is low and the pressure is high. For at least the Oxygen and Nitrogen phase diagrams, it looks like the critical point would be a good candidate for these maximum gas ...


6

The article's preprint Mayer H. C., Krechetnikov R. "Walking with coffee: why does it spill?," Phys. Rev. E 85, 046117 (2012). is available from the UCSB site. From a glance of the article the phenomenon is not specific only to coffee. The authors make use of the next formula: The natural frequencies of oscillations of a frictionless, ...



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