Relationship between gravity and density

Question

So I have recently found that flat earthers believe gravity is not real and everything goes down because of densities, obviously, if this were true things would float up as our air is not very dense, but ill move on. These are a few questions I have that I cant find online because everywhere I look is talking about specific gravity which say wether or not somehting floats is completely based on density.

Is the reason an anvil floats on mercury purely due to it being so much less dense?

How does gravity affect this and what role does it play?

If we use the flat earths idea that it is only about dnesity then would the entire anvil sit ontop?

Why is a large portion of the anvil underwater?

Even if something is only, say, 0.01% less dense would it float?

I know theres a lot of qustions but this seemingly simple topic has me quite cofused. Maybe im overthinking it. If someone could explain the math and physics behind this, maybe even a force diagram of some kind to help me visualize it, to help me understand this I would really appreciate it!

Answer 1

An object placed on the surface of a liquid will sink in the liquid until the weight of the volume of liquid that it displaces is equal to the object's own weight (this is Archimedes' principle). If the average density of the object is greater than the density of the liquid then it never displaces its own weight of liquid even when totally submerged and it will sink completely. So:

1. Whether an object sinks or floats in a liquid is completely determined by whether it is more dense or less dense than the liquid.
2. The height at which an object floats is determined by how much less dense it is than the liquid. An object with a low density will not need to displace much liquid. An object with a density that is just less than the density of the liquid will be almost completely submerged before it displaces sufficient liquid.
3. Gravity has proportionally the same effect on the weight of the object and the weight of the displaced liquid. So an object will sink or float (and, if it floats, it will float at exactly the same level) regardless of gravity (as long as there is some non-zero value of gravity).

Answer 2

Things would not float up if "everything goes down because of densities". I think the link you're missing is this: Density is a property of an object, and gravity is a force on an object. Things float or sink because of a force, whose magnitude depends on a property the objects have. Larger density means gravity will affect an object more strongly. In a way, gravity would have no effect on an object if it has no density. And on the other hand, if there were no gravity, objects would not move/sink/float no matter what their densities are, because there would be no force present.

I would like emphasize that there would be no phenomenon of buoyancy (objects positioning themselves based on their density) without gravity. The gravitational force is what drives the "vertical" sorting of non-miscible fluids and objects in fluids.

Answer 3

"How does gravity affect this and what role does it play?"

Wikipedia on Buoyancy teaches us:

"Buoyancy (...), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid."

From both sentences taken together it cannot easily be infered that gravity as the counterforce of buoyancy thus is it's prerequiste, as the second sentence introduces "pressure" as a result of the "weight" of the water above.

However, understood correctly, Wikipedia tells us that gravity is a prerequisite for buoyancy, and in wording of the question, nothing goes down because of densities.

"Weight" of the "object" (boats) means gravitational force, the mass of the object; direction is down. There is no upthrust without downthrust. If there is no gravity (space capsule) there is no buoyancy, no direction up.

Introducing "pressure" and depth seems to contradict textbooks as buoyancy is defined, as the first answer correctly states, as the

"weight of the volume of liquid that it displaces". Pressure and depth does not relate to this.

Personal remark: Pressure of the water might indeed underlie buoyancy and be its reason. However, as pressure according to Wikipedia is derived from the "weight" of the water that would be another argument, the second one, for gravity being the source of buoyancy and its prerequisite.

Last remark: Do not think of the column being up above "The boat".

Further reading I recommend is Lewis C. Epstein, Thinking physics, that got the situation on its cover.