Lorentz Jr

The tricky part is, what happens to the weights? What effect do they have on the belt when they go up and down? ... and D*A < 100,000 liters! 😆

What continent? Don't forget about survival though. That's important too. 😶 Assume that W is big enough for the weights on the left side of the belt to hang down, even at the bottom of the belt. The condition for buoyancy is that the weights on the left side hang down. That means [math]W > \rho g DA[/math], where [math]\rho[/math] is the density of water, [math]A[/math] is the cross-sectional area of each cup, and [math]D[/math] is the depth at the bottom of the belt.* The question is, what happens when a cup goes around the top or bottom of the belt? For simplicity, you can assume that something keeps each weight locked in place while it goes around a pulley, and the weight is unlocked when the cup is vertical again. So you don't need to worry about the cup's rotation while it's happening. Only the final result of it being turned upside-down. * (with possible adjustment(s) for atmospheric pressure, depending on what's inside the cup)

Air. Or a vacuum, if you like. Something light and compressible.

I can't give you strength, studiot. I can only help you understand. How about we forget about designs, studiot, because they're not really on topic, they're all subject to the same physics, and using big words like "Montgolfier" doesn't prove anything. That applies to any balloon. Small hole, no hole, whatever. Obviously the total internal force pushing down on the lower part of the balloon has to be greater than the internal force pushing up on the upper part, because the net force of the fabric on the hot air has to support the air's weight.

Of course, except I'm treating the high-pressure gas inside the balloon as part of the structure. A rigid object is a kind of structure, a gas-filled balloon is a kind of structure, the rim and spokes of a bicycle wheel are a kind of structure, the spars and stays on a sailboat are a kind of structure, and those funny combinations of hook-shaped thingies that somehow hang together are a kind of structure. The nature of the internal structure and the external forces acting on the structure are separate issues.

The entire surface of the balloon is supported from the inside by whatever the pressure is at the opening (or at least it doesn't rise fall so much with height), which is higher than the outside pressure at higher elevations. So no buckling, but don't try using a hot-air balloon upside-down. 😁

It acts on the air at the opening (obviously), and it acts on the fabric in the region surrounding the opening. This is possible because the hot air in the balloon maintains a combination of high pressure and low density. I would imagine that may be one reason the lower conical part of a typical balloon is so long: The air inside it helps to insulate the hot air in the upper part from the cooler air below.

The OP already told us what they wanted to know: whether the buoyant forces on pieces of wood and hot-air balloons are of the "same type" and where they "come from". Buoyancy comes from the force of a high-pressure area underneath an object, which is caused by the weight of the surrounding fluid, even if the object is a balloon. The only relevant difference between balloons and rigid objects is how the forces pushing them up from below are transmitted internally, and that's not what the OP asked about. Maybe they'll be interested in that, I don't know, but please introduce related topics like that as additional information instead of starting your comment with "Not quite", as though it's a correction.

Nothing! The cups on the left are "inflated" more, so the belt will rotate clockwise until one of the cups reaches a wheel. 😎 Now someone else has to finish the problem. 😋

Inadequate for what? The OP wants a beginner's introduction, not a PhD. This text is very impressive and authoritative, but I don't see where it adds anything helpful to the conversation. It repeats the basic facts several times, expresses things mathematically, and adds lots of details about specific gasses and the nature of the atmosphere. It doesn't even mention hot-air balloons. 🙄 The things that uniquely affect a hot-air balloon are: The hot air has to be treated as part of the balloon (or at least it can be treated that way as an approximation), even though there's an opening at the bottom. The balloon keeps reducing its own buoyancy by heating up the surrounding air and simultaneously cooling off. (This decreases the volume of the air inside the balloon. Some of the outside air enters the balloon, so the mass of the inside air is higher). Someone in the basket periodically increases the buoyancy by heating the air with a torch. (This increases the volume of the hot air. Some of the air exits the balloon, so the mass of the remaining air is lower.) Of course, the balloon will collapse and fall if the supply of heat fails for any reason.

Right. And in both cases the total downward force on the pencil is the pencil's weight minus the total weight of displaced fluids, including both air and water. The standard pressure analysis applies to any object once its size, shape, and mass have been established. An ordinary object's deformability only affects its shape and volume. In the case of a hot-air balloon, only its mass is affected (except to the extent that its fabric stretches), and the pressure analysis still applies to it. The definition is simple: It's just the total force of the fluid on the object due to the fluid's weight, minus the object's weight, whatever that might be once any unrestrained hot air inside the object has equilibrated with the ambient pressure at the opening. Complications involving the object's internal mechanical properties aren't part of the definition. True, but not exactly on topic, I think, and the final result is still determined by the pressure analysis (or the fluid-weight calculation, once you know that works).

Yes, that's right. And the pressure difference is caused by the weight of the surrounding fluid.

Yes, it's the same force. The net downward force on any object immersed in air or water, or any other fluid, is the difference between the weight of the object and the weight of the fluid that would otherwise fill up the volume that's currently occupied by the object. So it's a buoyant force (i.e. upward) if the object is less dense than the fluid. Generally speaking, the difference between the pressures at two points in a fluid that are separated by a height [math]h[/math] is equal to [math]\rho g h[/math], where [math]\rho[/math] is the fluid's density. It's just the weight of any column of fluid of height [math]h[/math] divided by the column's cross-sectional area.1 If you integrate that difference over a submerged object's horizontal cross section, calculating [math]h[/math] at each point from the vertical distance between the object's upper and lower surfaces above and below the point,2 you get the total weight of the displaced water, and the net upward force on the object is that force minus the object's weight. 1 For a tall object in a gas (e.g. air), you may have to take the gas's altitude-dependent density into account. 2 Of course, this assumes the surfaces aren't too convoluted, i.e. it assumes there's no fluid in the space between the upper and lower surfaces. If there are any holes in the sides of the object, you'll have to compensate for them in the same way, by calculating the volumes of water in them and subtracting their weights from the total.

From Fashion, Faith, and Fantasy in the New Physics of the Universe by Roger Penrose Chapter 2, section 2.12: Quantum Reality Hah! Penrose uses the word the same way. 😎

Yep. It doesn't make sense otherwise. From an efficiency standpoint, powers of 2 are better for computers (e.g. 8-bit bytes and 64-bit CPUs). And 12 would be more useful, because it can be divided up in more ways (i.e. into 2, 3, 4, or 6 parts).

Yes, much too far. Time travel isn't just physically impossible, it's logically impossible. Either something happened or it didn't. As much as I distrust the principle of relativity, I don't object to Einstein's geometric model of gravity nearly as much. The only thing about it that I have any really strong objection to is its allowance of time cycles.

Yes, I think all matter and radiation are made of waves. I don't believe in particles. I think they're artifacts of classical thinking.

Not much in the foundations that seems productive to me. I keep reading about tenure and grant money being monopolized by ideas like string theory and the Big Bang, and then about how there are both serious problems and promising alternatives to these theories, but they're suppressed by academic politics.

Well, we still don't have a warp drive. Physics has already stagnated for the last half century (because of relativity, IMO), but there's certainly plenty more out there to be discovered.

I see. I guess I should have figured that out. Maybe time for some coffee.

p is a proposition, not a number. If p is "Love is blind", then ~p -> p would mean "If love is not blind, then love is blind." That can't be true, because either love is blind or it's not blind. EDIT: Okay, this isn't technically a contradiction. It's considered true if p is true, and of course it's false if p is false. "~p ↔ p" would be a contradiction.

Yes, that's reasonable. I believe it would be an extension of Newton's original formulation for thin shells, but it's simple enough. You can think of any spherically symmetric planet as an onion, with lots of concentric shells. 🙂

It means you're analyzing the problem in the object's initial reference frame. It may simplify the math a bit. It's the object's kinetic energy at the end of the experiment. It's the object's kinetic energy at the beginning of the experiment. It may be zero, but it doesn't have to be. It's the difference between the final and the initial.

Trillions of neutrinos fly through every person's body every second. Electrons as solid particles have no currently observed size, and even quantum field theory models them as waves. And electrons occupy something like 99.9999999 percent of the volume of every atom. I believe macroscopic "solids" are waves that repel each other. Or maybe they're collections of "wavicles", or whatever you want to call wavelike quanta. It's very puzzling to me, because quantized wavelike entities seem like they would be very hard to implement. I think quantized field interactions might be easier to implement, because they're more localized. I have my own interpretation of QM. I call it the "Brownian motion" interpretation. It's not exactly based on motion, but it says the quantum uncertainty of (low-dimensional) particle behavior (that people obsess over so much in Bell's inequality) is ultimately derived from the (high-dimensional) structure and deterministic behavior of the vacuum at some very small scale. Larger than the Planck scale, smaller than whatever is the smallest scale of quarks or other forms of matter that has been detected.

Okay, that makes sense.