It seems pretty self-evident that less dense things float in more dense things. But why, really? What’s happening at the microscopic level to cause, say, a piece of cork to float in water?
Here was my thinking at first: take the somewhat different example of a helium balloon. The gravitational attraction between two objects (like the Earth and a particle of gas) depends on their masses, so we’d expect this attraction to be stronger for nitrogen or oxygen molecules than for the helium. Since air molecules get pulled toward the Earth with greater force than helium, collisions between air molecules and the balloon are ever so slightly more energetic toward the bottom of the balloon than at the top, and the balloon gets pushed up.
But this can’t quite be right – first of all, gravity is such a weak force that, when acting on something with a small mass (like a gas molecule), I’d think the effects of gravity would be swamped by the random collisions between the air and the balloon, which are way more energetic.
And besides, it’s the density that’s important, not just the mass of the molecules. Otherwise, in water, a cork would sink like a stone because its molecules are way heavier than water molecules.
I feel kinda dumb here. Everybody knows less dense things float, but I’m having a brain fart trying to come up with a mental image of what causes it. Maybe I woke up too early for deep thinking today…
The pressure at any location in a body of fluid is a function of altitude. So any object immersed in that fluid will have greater pressure on its bottom (pushing it up) than on its top (pushing it down). For an object with surfaces facing in directions other than down, you can identify the component of fluid pressure acting in a vertical direction, construct an integrand, and integrate over the entire surface of the object; the result would be the net buoyant force. If that force is less than the weight of the object, then the object will move upward.
And yet it’s not. When there are only a few gas molecule collisions at a time, those random influences do indeed overwhelm gravity, and we get Brownian motion, which can be observed on very small particles of dust/smoke. Increase the collision rate, and those random events begin to cancel each other out, and the overall influence of gravity is the only thing left uncancelled.
Gravity isn’t that weak of force – it’s certainly stronger than the random collisions of gas molecules keeping me up. The same force of gravity is acting on all those gas molecules – they’re not moving in completely random directions – gravity is a one-directional (on a local scale) force pulling them all down. Don’t think of it as a lone gas molecule being pulled down by gravity in a sea of randomly moving gas molecules – it’s a collection of randomly-moving gas molecules, all of which are being pulled down in the same direction while moving around.
As for what pushes a buoyant object up, like a balloon in a sea of gas – it’s the gradient of the pressure. Because of gravity the pressure is slightly greater at the bottom of the balloon than at the top, and this imbalance pushes the balloon up.
I know that may be hard to believe – if you have a hard time thinking of a randomn molecule being preferentially pulled in one direction by gravity, it’s even harder to think that the gravity causes a change i n pressure over such a middlin’ distance as the size of a balloon. true. Furthermore, it’s calculable. Figuring out the pressure difference and the buoyant force due to it on a perfectly spherical balloon* is a simple enough problem to give to Freshman mechanics students to solve by integration… You can do it more easily by imagining an impossible cubical balloon – the forces on the vertical walls cancel, and all you need worry about are the unbalanced forces on the horizontal top and bottom.
Of course, a real balloon won’t be spherical, but it’ll be close enough.
Ahhh, I see – you’re right, I’m surprised that difference in gravity over as small a range as the height of a balloon could make such a difference.
Based on the responses so far, would I be right in thinking that the bouyant force is proportional to the surface area of the object rather than the volume? And, by extension, it’s mass divided by surface area that’s important, rather than density?
In general not strictly proportional to the surface area, except in the case of that unrealistic cube. In the case of the spherical balloon the force varies not only with location along the balloon, but also in direction, with much of it cancelling out. So the force of buoyancy on a cube and on a balloon is not going to be proportional to the difference in their surface area.
On the other hand, the force is exerted on the surface of the object. It will scale will the surface area, so if you compare the forces on two different objects of the same shape but different size, I think the ratio of the forces will be in proportion to the ratio of their surface areas.
The fluid forces on the object are dependent on the orientation, altitude, AND area of the object’s surfaces.
Suppose you start with a spherical balloon, and you want to increase the buoyant force. You know that fluid pressure at the bottom is greater than at the top, so you add a large, flat horizontal flange at the bottom (imagine the sphere now sitting on a disc with negligible thickness and a diameter twice as the sphere, so negligible additional volume). You’ve increased the total downward-facing area for the fluid to push upwards, true, but now there’s also an upward-facing area on that flange that the fluid is pushing down on with pretty much the same force. The net change is zero.
Well shoot, now what? Let’s make that disk thicker, so that its top surface is at a higher altitude; then the fluid pressure on the top surface won’t be as great as the pressure on the bottom surface. That should result in a net increase in buoyancy, right? It will, sure, but you’ve just increased the volume of your object.
Archimedes figured this out a long time ago. You can deliberately add surfaces to your object pointing in particular directions to increase net force, and you will always end up being forced to add surfaces pointing in other directions that either cancel out your desired change, or add volume to your object in direct proportion to the change in buoyancy.
The upshot of all of this is that surface area ends up being irrelevant: you can calculate the buoyant force on your object as a product the volume of fluid it displaces and the density of that fluid.
I asked this very question of a group of physicists years ago. We ended up dividing the problem into two problems: 1) a closed space, like a balloon, and 2) gases with different densities.
#1 is easy - the difference in the densities around the balloon causes the balloon to rise or the air or water around the balloon to be pulled under the balloon by gravity. It isn’t hard to calculate the pressure at the top of the balloon and the pressure at the bottom and you see that the balloon has to go up if the pressure difference is greater than the weight. Doesn’t really matter what shape the thing has.
#2 is a little tricker - why does a section of hot air rise? Why doesn’t it break apart and disperse? If you imagine the air molecules as little balls bouncing around it is easy to see that the fastest moving balls will tend to rise or the slower balls will tend to settle under the faster balls. For something like your breath, the differences in pressure between the outside air and inside the bubble of breath-air are surprisingly larger than we imagine and the air will rise like a balloon faster than it can disperse.
I can’t remember all the details but this came about from me asking how altitudes are measured - which led to questions about air pressure.
In layman’s terms then, doesn’t this amount to saying that things float because the fluid they’re floating in is acted upon by gravity in such a way as to squeeze them up and out, like toothpaste from a tube - and that they are not sufficiently acted upon by gravity to be able to push back?
Sounds good to me. When we think of things rising I think we imagine light, ethereal things. In reality the air is pressing down with a lot of force and a slightly less dense thing, like a helium balloon, gets squirted upward by that force. It doesn’t get horribly deformed in the process because the pressure is all around the balloon, all the time.
That’s the way I’ve always thought of it. It isn’t so much that less dense things float, but that more dense things sink, leaving nowhere else for the less dense objects to go but up.
But of course one could ask, “Isn’t there more force acting on a kilogram of helium in a giant balloon than on a milliliter of mercury? Why doesn’t the mercury float?” That’s when you have to get into pressure and volume, rather than mass and gravitational force.
It isn’t the difference in gravity, it is the difference in pressure. If you have ever dived to the deep end of a swimming pool, you know that the gradient in pressure is quite large.
Here’s another way of looking at it - having the cork floating in the water is simply the lowest energy state, so it’s the preferable one.
By that, I mean things will come to rest at the lowest point they can, as that’s the point of lowest potential energy.
Imagine a bucket half-full of water, with a cork in it. If the cork is right at the bottom of the bucket, it is displacing the water so the water level is higher than it would otherwise be. The amount of water it has displaced is equal in **volume ** to the volume of the cork, but it **weighs ** a lot more than the cork, because water is denser. Let’s assume for the sake of argument that water is 5 times denser than cork.
So in this set-up, a mass of water 5 times greater than the cork is raised above its normal level.
Instead, what happens is that the cork floats with only one-fifth of its volume below the surface. Now the water is lower than it would be with the cork at the bottom, while the relatively light cork is higher. Clearly this set-up has lower potential energy.
In other words, having the densest stuff lower down and the less dense stuff higher up is energetically favourable.
Take a beaker of water and a piece of cork. Start with just the water in the beaker. It has some volume.
Now insert the cork into the beaker. In order to submerge the cork, it has to push water out of the way. How much water? The same size amount of water - the volume. The cork replaces its volume in the space where the water should be, so the water is moved up.
Water has a higher density, which is mass divided by volume. m/V
But the cork replaces exactly the same volume of water, so if the two volumes are equal, the difference between them is the difference in mass, which can be measured with weight. So the same volume of water is heavier than the volume of cork.
Now take that water and put it on one side of a balance (in a container that is part of the balance and doesn’t contribute to the weight), and put the cork on the other side of the balance. What happens? The water goes down and the cork goes up - the water pushes the cork up.
That is exactly what’s happening in the beaker. The water pushes the cork up, until the volume displaced by the cork matches the weight of the whole cork. That’s why ice floats mostly submerged - it is closer to the weight of water than the cork.
Gas in a balloon has a barrier, so it acts like a solid object - the balloon. Except pressure differential affects the volume of the balloon through stretching, so that affects the amount of displacement.
If there is no barrier, then two fluids have to deal with mixing. However, mixing can be a slow process - slower than the process of buoyancy (what we are discussing).
First, thanks for having such a conversation. I have a solution. It requires vibration instead of particles. It works with the standard model. It explains the effect; density, magnetism, electricity and temperature have on baryonic motion.