It seems the characterisation of the "lowest energy" state of an iceberg is not correct for all objects For instance, if the iceberg is a long thin cylinder, it is obvious to anyone with experience of floating objects, that it will float with its axis horisontal - whereas a vertical alignment gives a lower center of gravity.
Also, once again it seems the extra credit question is easier than the main puzzle.
Also (Zaq, delete if too spoilery), I think the extra credit is harder. But *proving* that the extra credit is harder is harder than the extra credit itself. Unless I'm completely wrong.
This obviously will be different for differently-shaped objects, but "lowest COM" is probably the most stable position for bulky objects. My only experience with attempting to float (approximately) a long, thin cylinder (myself, 20 years ago when I was "thin") shows that the vertical position was definitely easier to maintain--but it that due to me being ~99% submerged? Now I'm really curious where the cutoff would be and why.
If the cylinder is so bulky that the surface tension of the water is negligible, such as an iceberg, its cutoff is half the density of the water.
If the density of the cylinder is less than that, the center of mass is above the water surface and tends downward, closer to the water surface, and the cylinder floats horizontally; otherwise, the center of mass tends away from the water surface and the cylinder maintains a vertical attitude. If you are in very salty water or have got enough fat on you now, you can float horizontally.
That's a surprising conclusion; what about Brownian motion forces and the like? This would imply a cylindrical iceberg really would float vertically. Now I want to carve a small ice cylinder and try to float it.
With nonuniform density, the center of mass could be as much as 0.9⋅√3 below the surface, though such a cube would surely be crushed by water pressure.
It seems the characterisation of the "lowest energy" state of an iceberg is not correct for all objects For instance, if the iceberg is a long thin cylinder, it is obvious to anyone with experience of floating objects, that it will float with its axis horisontal - whereas a vertical alignment gives a lower center of gravity.
Also, once again it seems the extra credit question is easier than the main puzzle.
Thanks. Not intended as a physics puzzle, and made a point of avoiding discussions of stability. I removed "lowest energy," since that was misleading.
Also (Zaq, delete if too spoilery), I think the extra credit is harder. But *proving* that the extra credit is harder is harder than the extra credit itself. Unless I'm completely wrong.
This obviously will be different for differently-shaped objects, but "lowest COM" is probably the most stable position for bulky objects. My only experience with attempting to float (approximately) a long, thin cylinder (myself, 20 years ago when I was "thin") shows that the vertical position was definitely easier to maintain--but it that due to me being ~99% submerged? Now I'm really curious where the cutoff would be and why.
If the cylinder is so bulky that the surface tension of the water is negligible, such as an iceberg, its cutoff is half the density of the water.
If the density of the cylinder is less than that, the center of mass is above the water surface and tends downward, closer to the water surface, and the cylinder floats horizontally; otherwise, the center of mass tends away from the water surface and the cylinder maintains a vertical attitude. If you are in very salty water or have got enough fat on you now, you can float horizontally.
That's a surprising conclusion; what about Brownian motion forces and the like? This would imply a cylindrical iceberg really would float vertically. Now I want to carve a small ice cylinder and try to float it.
I am sorry, but I am not familiar with Brownian motion forces.
A very small ice cylinder might float horizontally, pulled to the surface by surface tension, although I don't know the threshold.
A borderline cylinder might be able to float both vertically and horizontally as local optima.
I would like to see the results of your experiment.
With nonuniform density, the center of mass could be as much as 0.9⋅√3 below the surface, though such a cube would surely be crushed by water pressure.