# Tag Info

163

Needing any excuse to break away from the work I was doing, I immediately assumed the task of answering this question. Yes, ants can walk on mercury with no trouble at all. I bet it was even kind of fun, but this little punk just split as soon as possible. I got a video, but had to settle for a screenshot for this post.

134

Of course, by common sense, if you put together two objects with masses $m_1$ and $m_2$, and nothing comes out, then you end up with mass $m_1 + m_2$. Weights are a little more complicated because of buoyant forces. All objects on Earth continuously experience a buoyant force from the volume of the air they displace. This doesn't matter as long as volume ...

87

When put in water, an objects sinks to the point where the volume of water it displaces has the same weight as the object. Archimedes was the one who discovered this. When you put lead in water, the weight of the lead is much greater than that of the same volume of water. Hence it sinks to the bottom. As ice only weighs about 90% of its volume of water, 90% ...

86

When submerged, the coin displaces as much water as it has volume (logical). When floating on the box, the coin displaces as much water as corresponds to its weight. As metal has a higher density than water, it means that the coin in the box displaces more water than when the coin is submerged.

82

Sound doesn't go through walls? Please tell my neighbor. In electromagnetism, a medium has a property called an "impedance" which is related to the index of refraction and the speed of waves in the medium. At an interface between two media, the relative impedances determine how much of an incoming wave is transmitted or reflected, so that the entire power ...

79

Density relates to the mass per unit volume. If your molecules are heavier but take up more space, the net result could be more or less mass per unit volume. When you look at a typical hydrocarbon, it has a lot of carbon and hydrogen. Now atom for atom, oxygen is heavier than carbon (ignoring isotopic abundance, roughly a 16:12 ratio). So if the molecules ...

76

Because water molecules are small and pack tightly together, causing water to have a greater density than petrol.

62

Whether or not a small animal/insect can walk on a liquid is determined much more by surface tension than by density. To see why this is consider a dense liquid without any surface tension. You would float in it very well, but if you tried to walk on it you would step right through the surface and fall over, sinking until you were sufficiently submerged to ...

51

I like to answer by reinterpreting your question: if you expect the ice to be completely atop the water because ice is less dense than water (as indicated in your left image), then you would also expect the ice to be completely below air because ice is more dense than air (in order for this to be true, think pushing your ice cube down into the water so that ...

50

Under special relativity nothing can be incompressible: consider any object of nonzero size and finite mass in its rest frame; when you apply a force to it on one side it will start moving. If it were completely incompressible, the other end would start moving simultaneously. Since the ends are spatially separated, there is a frame in which the other end ...

47

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 ...

47

The phrase black hole tends to be used without specifying exactly what it means, and defining exactly what you mean is important to answer your question. The archetypal black hole is a mathematical object discovered by Karl Schwarzschild in 1915 - the Schwarzschild metric. The curious thing about this object is that it contains no matter. Techically it is a ...

44

Take advantage of the large difference in thermal conductivity between copper and stainless steel (approximately $400$ and $16$ $\mathrm{Wm^{-1}K^{-1}}$ respectively). If you put one end of a metal rod into contact with something held at a constant high or low temperature $T_C$, you would expect the other end to asymptotically approach that temperature like: ...

42

As you suggest, long before you got that large gravitation would become dominant. One of the early what ifs is about what you get if you take a mole (ie $6\times 10^{23}$) of moles (small animals) which results in something a little larger than the Moon, and the answer is not very pretty (at least not for the moles). This is indeed why stars happen: if you ...

40

Wikipedia gives a pretty much straightforward answer. In an ideal gas, the speed of sound depends only on the temperature: $$v = \sqrt{\frac{\gamma \cdot k \cdot T}{m}}$$ So it neither decreases, nor increases with altitude, but just follows air temperature as can be seen in this graph:

37

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 $2.85 \times 10^{10}\ \mathrm{Pa}$ and the density is $13534\ \mathrm{kg/m^3}$, so the equation gives $v = 1451\ \mathrm{m/s}$. The speed of sound in solids is given by: $$v = \sqrt{\frac{K + ... 34 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 ... 34 In quantum field theory, an elementary particle doesn't have one precise location and size in space. The quantum of an electron field in free space has different extent compared to the electron around a hydrogen atom, for example (i.e. it's harder to bounce an electron off a free electron than off a hydrogen atom). While in one very real way, an electron's ... 32 @knzhou supplied a good answer. I’m going to offer a couple of other interpretations. The first has nothing to do with the fact that you’re mixing liquids—it’s just that there are difficulties in determining mass precisely by measuring weight. As already pointed out, there is the buoyancy of the air—that produces a mass error of about -0.0013 g/l at sea ... 32 Why not density? At least for a quick check and as for the title question. You are dealing with about < 8 and 9 g per cubic cm, respectively for steel and copper. Not overly laborious and especially non destructive at all. To measure the volume you can submerge the object in the narrow container of your kitchen. If isn't graduated you just mark the ... 30 I think the real question you're asking here is: why do less-dense fluids completely stay above more dense fluids, whereas less-dense solids partly sink? If the ice covered the same area as the water below, then it would sit completely on top of the water. That's the case in a completely ice-covered pond.But because the ice does have a non-negligible weight,... 28 The object would actually float exactly the same for both values of g. Let V be the volume of the body, d its relative density, and V' be the volume inside water. Then for equilibrium of the body, V \cdot d \cdot g=V' \cdot 1 \cdot g So, V'/V is independent of acceleration due to gravity. 27 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}. This is calculated by multiplying the number density of the neutrons n_n by, 3p_{f}^2/10m_n, the average KE per fermion in a non-relativistically degenerate gas and where p_f =(3/8\pi)hn_n^{... 26 Because of its high density. This meant that, for given masses of spheres, the centres of a fixed sphere and its neighbouring moving sphere could be closer to each other (than if a less dense material had been used). So the force between the spheres would be greater. The force was small and hard to measure, so any increase in the force would have been ... 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: ... 23 The buoyant force* depends on the volume of the object (or at least the volume of the object submerged in the fluid) and the density of the fluid that object is in, not necessarily/directly on the density of the object. Indeed, you will usually see the buoyant force written as$$F_B=\rho_{\text{fluid}}V_{\text{sub}}g=w_{\text{disp}}$$which just shows that ... 22 Let's look at this another way: you're just moving from one fluid to another. Sounds harmless, right? By specification of the problem, we're at terminal velocity when we hit the water. The force of drag (in both mediums) is roughly:$$ F_D\, =\, \tfrac12\, \rho\, v^2\, C_D\, A = \rho \left( \frac{1}{2} v^2 C_D A \right)  You can imagine that ...

22

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 ...

22

The coin is denser than water. When placed on the box, it will displace it's weight in water, which is more volume than the coin. When placed directly in the water it will sink to the bottom and displace only it's own volume in water, which will be less because it's denser. Another way to think about it is to have a platform below the box open to the water ...

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 ...

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