# Does gravity cause Archimedes' principle and how?

Why do lighter objects float and denser sink? I understand this from the perspective that if the object can displace the equal mass of water it will float, but I wonder from the perspective of gravity! How does gravity cause Archimedes' principle? It must be gravity, right, because in space Archimedes' principle doesn't work!

The ultimate question I need to answer is how all this force interplay causes density stratification. For example, how does gravity cause Earth to have a density gradient: the densest elements in the core, and the lightest in the crust?

Here's what I got from the comments so far. I though it should be a good starting point if someone wants to write an answer. It also can be totally wrong.

There is a pressure gradient inside a body of liquid along the depth gradient. It is caused by the fact that the distance between two objects is squared and inversely proportional to the gravitational pull (see the image below). The deeper water thus is attracted to the Earth stronger, and where there is a pressure difference, there is a force, the buoyant force in this case.

However, now I have even more questions than I used to:

1. If there is a pressure gradient, why there's no flow in water along the depth gradient?
2. What mechanism (or what part of the gravity equation) makes denser objects sink despite the buoyant force? Is it the mass? What about Galileo's experiment then? Doesn't it show that the effect of mass is negligible?

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If a heavy thing sinks, what must happen to a "lighter" (less dense" thing underneath it? – Carl Witthoft Apr 13 '14 at 12:14
Maybe you should read up on Archimedes principle en.wikipedia.org/wiki/Archimedes%27_principle . It explains how in liquids dense material goes to the bottom. Stratification happened mainly in the magma phase of the earth. – anna v Apr 13 '14 at 12:14
Archimedes' principle doesn't explain the FORCE that causes this phenomenon. Sure, it's called Archimedes' force, but really? It's not an answer. It must be gravity because in space a golf ball won't float on water, and air bubbles in a Coke won't go up! Do you get the point I'm trying to make? I'm asking about the fundamental force that causes Archimedes' principle and how it does it? – Th334 Apr 14 '14 at 8:40
The gravitational force on one's foot is stronger than on his head, and this is explained by the inverse square law. In water, bottom layer has more force (more pressure) than on top. The force due to this pressure difference is the buoyant force. So, if gravity isn't there, there won't be a pressure difference to begin with. – Renae Lider Apr 14 '14 at 9:20
@user3058846, so it's r in G*m1*m2/r^2 that causes the gravitational force to be stronger the closer you get to the Earth's core, right? I see. Could you please develop the idea further? How exactly does this pressure difference causes buoyant force and eventually density stratification? It'd be great if you could post it as an answer, because apparently nobody else seems to understand what I'm asking here, yet :) – Th334 Apr 15 '14 at 4:43

The deeper you are under water the higher pressure. This is because the deeper you are the more water is above you. And water is pushing downwards due to gravity, thus more water above you means more push and hence more pressure.

Please note that deep under water the pressure is not caused by higher gravity. The gravity at depth is in fact lower than on the surface. The only cause of water pressure is the weight of the water above.

Objects under water occupy certain space and they have certain non-zero height. There is a pressure difference between the top and the bottom part of the object. This is causing a difference in the pressure force pushing on the object from above and from below: the force from below is bigger because of the weight of the water above. The difference is enough to overcome the weight of the object, if the object is less dense than water. In other words, if the object weights less than water of the same volume.

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How does gravity cause Archimede's principle?

Well the Archimede's principle says that the buoyancy force $F_g$ of an object of volume $V$ dipped in a liquid with density $\rho_f$ equals to:

$$F_g=\rho_f Vg$$

Now if the weight of the body is stronger than the buoyancy force then the object will fall deep in the water, if the weight is equal the object will be immersed and will float if the weight is less than the buoyancy force.

Now we can set the equations and the inequalities: $$mg=\rho_f Vg\quad mg>\rho_fVg\quad mg<\rho_f Vg$$ BUT we know that $\rho=\frac{m}{V}$ and so $m=V\rho$ $$V\rho g=\rho_f Vg\quad V\rho g>\rho_fVg\quad V\rho g<\rho_f Vg$$ $$\rho=\rho_f \quad \rho >\rho_f \quad \rho <\rho_f$$ that are the condition for floatation ONLY IF the object immersed in the liquid "has" weight.

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1. If there is a pressure gradient, why there's no flow in water along the depth gradient?

There is actually a flow. The exchange of water between the upper and lower parts of a lake, for instance, is just slow.

1. What mechanism (or what part of the gravity equation) makes denser objects sink despite the buoyant force? Is it the mass? What about Galileo's experiment then? Doesn't it show that the effect of mass is negligible?

The Galileo's experiment shows that the velocity of the falling objects is the same. However the force ($F=mg$) the falling objects exert depends on their mass (and therefore density). Simply throw a 0,1 kg ball and a 10 kg ball out of your window and see the marks they left on your lawn.

That's why denser objects sink deeper: the pressure (force/area) they exert is greater.

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I would add that the flow of water in a lake is caused by other things, not by the hydrostatic pressure gradient. The pressure at depth does not force the water to flow upwards, because it is the weight of the upper layers of water that keeps the lower layers under pressure. – mpv Jun 3 '14 at 19:46
Sure, the brownian motion does its job in mixing fluids. And in a real life lake there are certainly additional factors. – bright magus Jun 3 '14 at 19:51