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Yes, a ship can float in a tub. The second link you provided (to this blog post) is wrong. @sammy gerbil wrote a good answerwrote a good answer explaining why it's possible, so I will reply to the points made in the incorrect blog post one by one.

Yes, a ship can float in a tub. The second link you provided (to this blog post) is wrong. @sammy gerbil wrote a good answer explaining why it's possible, so I will reply to the points made in the incorrect blog post one by one.

Yes, a ship can float in a tub. The second link you provided (to this blog post) is wrong. @sammy gerbil wrote a good answer explaining why it's possible, so I will reply to the points made in the incorrect blog post one by one.

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Yes, a ship can float in a tub. The second link you provided (to this blog post) is wrong. @sammy gerbil wrote a good answer explaining why it's possible, so I will reply to the points made in the incorrect blog post one by one.

They ignore Archimedes' assumption that the body of water has enough water and enough unused volume to combine together to balance the weight of the immersed body.

It's unclear what "unused" water and volume are, or what it means for them to "combine"; this argument is too poorly-specified to be rebutted.

A floating ship is hydraulically balanced against the mass of the top layer of water that the ship has displaced upward in the body of water on which the ship floats. A ship can only float if the body of water can contain that top layer of water and that water has a mass equal to that of the ship.

What is a "top layer" of water? How thick is this "top layer" supposed to be? The claims here are again too vague to be meaningful.

Another way to think about it is to ask whether the battleship in the empty bathtub could be floated simply by pouring in the water to fill the bathtub around it. Battleship floaters claim this would work with an arbitrarily small amount of water. But there is no free lunch -- you can't do the enormous work of lifting a massive ship merely by balancing it against a small mass of water.

So-called "battleship floaters" are correct. A very small mass can absolutely raise a very large mass; for example this happen when you use a lever for mechanical advantage (like playing see-saw with one adult and one child). The battleship, though huge, will only rise a very tiny amount whereas the water will fall a much longer distance when you pour it in.

Let us suppose the battleship has mass $m$ and the volume submerged in water is $v$. Its cross-sectional area at the water line is $a$. This means the average depth of the bottom of the battleship (averaged over unit of cross-sectional area) is $v/a$.

The ship sits in a tank with cross-sectional area $A$ at the water line. Then if the ship were to rise an infinitesimal height $\mathrm{d}h$, its gravitational energy would increase by $m g \mathrm{d}h$. Imagining the water were stationary, the ship would leave an empty volume behind it of $a \mathrm{d} h$. Allowing the water to flow from the surface into the empty volume left behind by the ship, the water's gravitational potential energy would decrease by $\rho a \mathrm{d}h g f$ as it flowed in, with $f$ the mean distance the water falls, but the water simply falls to where the bottom of the ship was, an average fall of $v/a$. So the drop in energy of the water is $\rho g v \mathrm{d}h$. If we are to have equilibrium, we need the energy gained by the ship to equal the energy lost by the water, or $m g \mathrm{d}h = \rho g v \mathrm{d}h$, or

$$ m = \rho v$$

that is the volume of the ship under the water line, times the density of water, must be equal to the mass of the ship. However, nowhere did our calculation involve $A$, the cross-sectional area of the tub or $V$, the volume of water. These things are simply not relevant to the calculation and can be made very small. There is no problem with conservation of energy in floating a battleship. In fact, demanding energy be conserved gives us Archimedes' principle and demonstrates that a small volume of water can float the ship.

Some floaters point to canal locks (e.g. the Miraflores in Panama) that can float a ship with just a foot of clearance on the sides (and allegedly the bottom). However, they ignore the clearance at the front and back. After a ship enters a canal lock, you can bet that there is a new top layer of water (relative to the prior water level) whose mass is equal to that of the ship.

I don't know the details of canal locks in practice, but there is no such requirement in theory and the author does not justify their claim.

Floaters tell naive skeptics that when an object is floated in a full tub, the system doesn't remember that some water overflowed when the object was added, and that it floats just as well when it is taken out and then added back to the tub -- which now will not overflow at all. However, what the floaters don't notice is that the no-overflow system has just enough room at the top to hold the mass of water that balances the object.

This is false. Here is a short video I made that shows a cup with more water floating inside a cup with less water.

https://youtu.be/mVSDKQY7WeI

The cup with more water can float in the cup with less water with no trouble.

Some floaters point out that large machines like telescopes are often "afloat" on a thin film of oil. However, these lubricants are kept pressurized in a sealed system, and the pool of oil is not open to the atmosphere. It's a safe bet that such a telescope cannot be levitated (i.e. lifted) by a thin film of oil unless there is some balancing mass of oil (or some other way of pressurizing the oil).

Again I wouldn't know the details of actual telescopes, but there's no reason this couldn't work and the author fails to justify his claims.

So yes, the battleship can float, and the page you found claiming it cannot was simply mistaken.