# What atomic forces are acting to resist me pushing an air filled bottle underwater?

Yes air is less dense than water but how does the bottle know to rise or indeed to move? It's not electromagnetism I think. Does this have a relation to gravitational forces? Is it to do with the number of protons in the molecules of the different substances?

• Google for "Buoyancy." – Solomon Slow May 15 '18 at 21:40
• It is electromagnetism – Bobak Hashemi May 15 '18 at 21:54

The microscopic explanation for the macroscopic phenomenon of pressure is that momentum is transferred by electromagnetic forces from individual fluid particles (in this case, water molecules) to anything they approach closely enough, including other water molecules or the molecules of plastic that make up the bottle. The momentum transferred by a single water molecule to the bottle during an interaction depends on the details of that interaction, but you don't have to resolve those details to say something about the total amount of force--for that you only need a statistical description of the sum total of all the interactions, which is what pressure is.

So, why is the force exerted on the bottom of the bottle by all these collisions greater than that exerted on the top? Because of gravity and the mass of the overlying water, the water molecules further from the surface are packed slightly more closely together on average than the ones closer to the surface. Their mutual repulsion is therefore greater on average--this repulsive electromagnetic force grows very quickly as water molecules move closer together. The water molecules closest to the bottle are squeezed a bit closer to it where the pressure is greater (deeper below the surface), transmitting the higher average intermolecular repulsive forces there to the surface of the bottle.

• Yes this is convincing but its the air that makes the body of the bottle less dense and hence rise. What is the force that would make an air filled bottle rise but a lead filled bottle sink? Imagine: I'm filled with lead and you, water are less dense therefore I must sink. I'm thinking in the International Space Station a bottle filled with air would not move up or down in a body of water. – Greg Martin May 15 '18 at 21:59
• Gravity between the bottle/contents and the earth. For air, the total gravitational force is less than the pressure force. For lead, it’s greater. – Ben51 May 15 '18 at 22:02
• I'll accept that for the moment as I don't have the background to analyse the gravitational or the pressure forces. It's elegant. – Greg Martin May 15 '18 at 22:06
• One remark: momentum is transferred as a result of Pauli exclusion, not by electromagnetic forces. – my2cts May 15 '18 at 22:34
• @ben51 please answer my newest question on physics. – Nobody recognizeable May 19 '18 at 2:30

Archimedes figured this one out around 250 BC. If you push an empty bottle underwater you have to raise the surface of the water by the same volume. This is the counterforce that you feel.

• You haven't really explained what the force is. Why does the fact that the water level rises mean a force must be applied? – Aaron Stevens May 15 '18 at 21:47
• Ah yes, I forgot to state that water is heavy because of gravity ! – my2cts May 15 '18 at 21:50
• So the answer of Archimedes gets -2. :) – my2cts May 15 '18 at 22:36
• I think your answer, though obvious, is on point and others may have read too much into this question. – V.F. May 15 '18 at 23:34
• I think that OP asks "how" on a more detailed level, while this answer is more "why" on a higher level. – Alex May 16 '18 at 14:45