# Floating a cruise ship in a bucket of water

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In all cases, the buoyancy force is still there...
An eloquent analysis and explanation!

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There is a buoyancy force on the ball, that is counteracted by the force in the string tying it down to the floor.
I have a bucket full of water. Is there a buoyancy force on the bottom of the bucket? How about the upper half thickness of the bottom? Your argument holds no water. 🐡
If there is a seal it is part of the bucket.

italicus
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In all cases, the buoyancy force is still there. It does not suddenly disappear when you replace the rope with a weld, or with a vacuum.
I disagree with this statement. With a flat bottom to the boat and a water-tight seal, the buoyancy force is gone and replaced by a force from the bottom. Meanwhile air pressure forces are normally transferred as well to the buoyancy force, (i.e. the same air pressure that acts above also acts from underneath), but those also disappear with the water-tight seal, and then the air pressure only acts from above to pin the boat to the bottom, along with water pressure from above that also adds to the air pressure.

Fundamentally, the buoyant force arises because the water pressure increases with depth. If the water pressure is unable to reach the underside of the boat which has vertical sides, the buoyant force is gone. There can still be forces from above that haven't disappeared, and they will act to pin the boat to the bottom.

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hutchphd
italicus
I wasn't, I was speaking of objects that are lighter than water, that are held to the floor through a water-tight seal. Although it does not matter for the principle. Your rubber ball example shows exactly what I was pointing out. There is a buoyancy force on the ball, that is counteracted by the force in the string tying it down to the floor. The same is true for an object that is held to the floor with a water tight seal. There is the same buoyancy force on the object, that is counteracted by a force from the floor. The same is true for an object that is welded to the floor. There is the same buoyancy force on the object, that is counteracted by the force through the weld.
In all cases, the buoyancy force is still there, it does not matter whether there is water under the object. It does not suddenly disappear when you replace the rope with a weld, or with a vacuum.
No, Rene! You are making the mistake that Haruspex pointed out in a recent reply. What do you know about hydrostatics? Look at the following drawing.

There is a pool , with a vertical wall on the left, and an inclined wall on the right. The reason for the inclined right wall is only the make it clear that the (relative) pressure , on horizontal planes, is the same. So, in points A (left) and B ( right) we have the same pressure because the depth under the free surface is the same : h_A = H_B . The diagram on the left is known as “pressure diagram” , and shows the linear increase of pressure with depth.
An important issue to understand is that pressure is NOT a vector quantity , but a scalar. But this would be too long and difficult to explain for me, because I have some problems with English, which isn’t my mother tongue. So let me go on.
Consider the ball , kept tied to the bottom by a rope. The buoyant force acting on the ball is due to vertical components of all elementary forces acting on elementary surfaces of the ball, which are to be "summed up” (to be mathematically correct: integrated) all over the surface. You will easily understand that the pressure at point U is less than the one at point V , which is vertically under U at a distance of 2R (R being the radius of the ball) . So you have a difference of pressure , which increases with depth, as already said. The length of the rope has no importance, it can be as short as a single chain link, connected by a hook to a fixed half-ring bolted to the bottom. There is still buoyancy here, because the geometry hasn’t changed, and the water is still “pushing up” the ball.

Now, consider a cubic box made of steel , 5 mm thickness of each wall and 1 square meter of each face. When put free into water, it floats, because it is lighter than an equal volume of water; its mean density, mass/volume, is less than that of water . Push it until it reaches the bottom of the pool, and weld it all around the base perimeter ( suppose the pool too is made of steel) . After having welded it this way , no pressure acts beneath , because no water is there. The pressure acts on the four vertical walls and the horizontal upper surface.
No buoyant force acts on the cube.
Of course, the water level of the pool has increased , but this means only an increase of max pressure at the bottom, as well as at any surface of objects in fixed position in the pool.

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I disagree with this statement. With a flat bottom to the boat and a water-tight seal, the buoyancy force is gone and replaced by a force from the bottom.
Agree. Further, the force between a flat boat bottom and a flat surface against which it tightly mates is indeterminate. It can take on a range of values depending on the other forces on the boat. One can pull strongly upward on the boat while the pressure from the water above resists motion. Or one can push strongly downward on the boat while the normal force from the ground below resists motion.

Since the force is variable, it immediately follows that no formula such as ##F=\rho g V## that does not vary can plausibly capture the net force on the boat from water plus tank bottom.

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Now, consider a cubic box made of steel , 5 mm thickness of each wall and 1 square meter of each face. When put free into water, it floats, because it is lighter than an equal volume of water; its mean density, mass/volume, is less than that of water . Push it until it reaches the bottom of the pool, and weld it all around the base perimeter ( suppose the pool too is made of steel) . After having welded it this way , no pressure acts beneath , because no water is there. The pressure acts on the four vertical walls and the horizontal upper surface.
No buoyant force acts on the cube.
Of course, the water level of the pool has increased , but this means only an increase of max pressure at the bottom, as well as at any surface of objects in fixed position in the pool.
I tried this with several flat bottom containers with straight sides including a cube but I could not sense the buoyancy force diminish as the object was pushed against the bottom and the water squeezed out. Next, I put a weak seal (toothpaste) around the base of the cube resting on the bottom to keep it dry underneath before putting water in the tank. It held for about ten seconds till the water worked its way underneath. This may be a very small scale experimental confirmation of the original thesis of floating on a very thin layer of water.

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Nice use of materials (the toothpaste is perfect...first it seals, then it doesn't).

Are we done here?