Challenge question for physicists

[gunslingor]

Okay, I have been wondering this for a long time. The question concerns buoyancy of objects in water.

Question:
Imagine you have a balloon filled with air. Imagine the balloon has virtually zero mass, but actually has a virtually infinite hardness. You could replace the balloon with a force field or sorts, like star trek. So, will the hypothetical balloon float? The arrangement in itself would have less mass than water; so by this reasoning it will float. But it has infinite hardness and therefore cannot bend in the expected way (if you were to hold a real balloon by the filling point underwater, it would stretch out as you go deeper and deeper). So the water can have no direct or indirect interaction with the mass inside the balloon. So will the balloon float? If not, has as hardness been accounted for in buoyancy calculations?

 

[Doc Al]

I don't understand the issue. Why wouldn't it float? The calculation of buoyant force does not require any "bending" of the object.

 

[Gokul43201]

Hardness, or interaction with the contents of the balloon are not relevant.

1. The pressure exerted on the top surface of the balloon is smaller than the pressure exerted on the bottom surface (because the top surface is at a smaller depth where the water pressure is smaller). This difference in pressures depends only on the density of water and the geometry of the balloon, and it gives rise to an upward buoyant force.

2. If this upward force exceeds the downward gravitational force on the balloon (determined by the mass of air in it), the balloon will float.

So the water does not need to interact with the insides of the balloon, only gravity does. And gravity doesn't care about the hardness of the balloon shell.

As a practical example, consider a submarine - essentially a steel balloon that is capable of floating.

 

[gunslingor]

Hardness, or interaction with the contents of the balloon are not relevant.

1. The pressure exerted on the top surface of the balloon is smaller than the pressure exerted on the bottom surface (because the top surface is at a smaller depth where the water pressure is smaller). This difference in pressures depends only on the density of water and the geometry of the balloon, and it gives rise to an upward buoyant force.

2. If this upward force exceeds the downward gravitational force on the balloon (determined by the mass of air in it), the balloon will float.

So the water does not need to interact with the insides of the balloon, only gravity does. And gravity doesn't care about the hardness of the balloon shell.

As a practical example, consider a submarine - essentially a steel balloon that is capable of floating.

Dah, I think I'm an idiot, lol. You explain it very well, which braught back a lot of examples from physics I had forgotten. For some reason, I think I had made the assumption that gravity couldn't interact with the balloon mass internal; I assumed that the waters interaction with gravity was the only effect.