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To see if you have understood it right, think about the following question. Take a pencil 20 cm long and 0.5 cm thick. Compare the buoyancy in these two cases: 1) you push it under water while holding it vertically, 2) you push it under water while holding it horizontally. In the case 1, the pressure difference between the water underneath and above the pencil is greater than in the case 2. Is the buoyant force different in these two cases?

No. For instance, in science we demand reproducible observations. That is a collective requirement the science community as a whole has adopted, in an attempt to achieve objectivity. That has not been arrived at subjectively.

No my decision is final in all cases.

Yes to everything BTW, you did much better than ChatGPT. When I've asked ChatGPT the same question, its response was this:

Not sure ..........because if the out side pressure was grater the balloon would not hold its shape ? and deflate ?

The graph you posted only goes out to 3 microns, so no, it didn’t show the peak at 15 microns (or the ones near 10 microns) When you said “As you can see at normal temperatures nearly all the absorbable IR energy is of way too long a wavelength.” it’s because you weren’t showing the right ones. But there isn’t much light there. There’s a lot more light emitted from the earth out at 10-15 microns. The absorption peaks there aren’t quite as tall (but not 2-3 orders of magnitude), but they are a lot wider. Were you looking at the ~1.5 micron features? Your statements make a lot more sense for that, but that’s not the absorption that’s important.

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).

Can you read minds from long distances ? Because i was thinking about the very same question in my mind today * not with pencil but with a wooden bar And i thought no .....the buoyant forces must be the same in both cases right ? In the vertical mode the pressure difference is way higher but the area that the pressure is applied to is less In the horizontal mode its vise versa meaning pressure difference is lower but area of that the pressure app,lies to is more

Good question. +1 Think carefully about your definition of bouyancy force.

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

Thank you very much Mr Lorents Reading your post i understood that the Buoyant force is actually originated by the pressure difference between the fluid underneath & above the object Have i understood it right ?

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.