| A boat stays afloat because its weight is
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| | slightest downward perturbation.
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| equal to that of the water it displaces.
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| | The depth of a submarine tends to be
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| The material of the boat itself may be
| |
| | unstable. A submarine is more
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| heavier than water (per volume!), but it
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| | compressible than the surrounding water.
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| forms only the outer layer. Inside it is
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| | As depth increases, the resulting
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| air, which is negligible in weight. But
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| | pressure causes the submarine's volume to
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| it does add to the volume. The central
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| | decrease more than the volume of the
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| term here is density, which is mass
| |
| | surrounding water decreases. Buoyancy
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| ('weight') per volume. One has to divide
| |
| | depends upon the object's volume and the
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| the mass of the boat (plus contents) as a
| |
| | weight of the displaced fluid. Volume has
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| whole by the volume below the waterline.
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| | decreased so the the weight displaced has
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| If the boat floats than that is equal to
| |
| | decreased which means a decrease in
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| the density of water (1 kg/l). One could
| |
| | buoyancy and the submarine tends to sink
|
| say that to the water it is as if there
| |
| | further. A rising submarine expands more
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| is water there because the average
| |
| | than the surrounding water, the submarine
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| density is the same. If one adds weight
| |
| | tends to rise further.
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| to the boat, the volume below the
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| | The height of a balloon tends to be
|
| waterline will have to increase too, to
| |
| | stable. As a balloon rises it will tend
|
| keep the mass/weight balance equal, so
| |
| | to increase in volume with reducing
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| the boat sinks a little to compensate.
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| | atmospheric pressure. But the balloon's
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| In physics, buoyancy is the upward force
| |
| | cargo will not expand. The average
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| on an object arising from the
| |
| | density of the balloon decreases less,
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| displacement of the fluid (i.e., a liquid
| |
| | therefore, than that of the surrounding
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| or a gas) in which it is fully or
| |
| | air. The balloon's buoyancy reduces
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| partially immersed. This force enables
| |
| | because the weight of the displaced air
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| the object to float or to at least to
| |
| | is reduced. A rising balloon tends to
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| appear lighter. Buoyancy is important for
| |
| | stop rising. Similarly a sinking balloon
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| many vehicles such as boats, ships,
| |
| | tends to stop sinking.
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| balloons, and airships.
| |
| | Archimedes' principle
|
| Explanation
| |
| | It was the ancient Greek, Archimedes of
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| The downward force on the top surface of
| |
| | Syracuse, who first discovered the law of
|
| an immersed object in a fluid is smaller
| |
| | buoyancy, sometimes called Archimedes's
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| than the butt upward force on the bottom
| |
| | principle:
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| surface, because pressure increases with
| |
| | The buoyant force is equal to the weight
|
| depth. The vector sum of the forces is
| |
| | of the displaced fluid.
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| thus vertically upward. The buoyancy
| |
| | The story of Archimedes discovering
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| force disappears if the fluid is not
| |
| | buoyancy while sitting in his bathtub is
|
| allowed to flow under the bottom of the
| |
| | described in Book 9 of De architectura by
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| object, for example if the object's
| |
| | Vitruvius.
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| bottom is fully in contact with the
| |
| | The weight of the displaced fluid is
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| bottom of the container.
| |
| | directly proportional to the volume of
|
| Forces and equilibrium
| |
| | the displaced fluid (specifically if the
|
| Buoyancy provides an upward force on the
| |
| | surrounding fluid is of uniform density).
|
| object. The magnitude of this force is
| |
| | Thus, among objects with equal masses,
|
| equal to the weight of the displaced
| |
| | the one with greater volume has greater
|
| fluid. (Displacement is the term used for
| |
| | buoyancy.
|
| the weight of the displaced fluid and,
| |
| | Suppose a rock's weight is measured as 10
|
| thus, is an equivalent term to buoyancy.)
| |
| | newtons when suspended by a string in a
|
| The buoyancy of an object depends,
| |
| | vacuum. Suppose that when the rock is
|
| therefore, only upon two factors: the
| |
| | lowered by the string into water, it
|
| object's volume, and the density of the
| |
| | displaces water of weight 3 newtons. The
|
| surrounding fluid. The greater the
| |
| | force it then exerts on the string from
|
| object's volume and surrounding density,
| |
| | which it hangs will be 10 newtons minus
|
| the higher the buoyancy.
| |
| | the 3 newtons of buoyant force: 10 - 3 =
|
| If the buoyancy of an (unrestrained and
| |
| | 7 newtons.
|
| unpowered) object exceeds its weight, it
| |
| | The density of the immersed object
|
| will tend to rise. And an object whose
| |
| | relative to the density of the fluid is
|
| weight exceeds its buoyancy will tend to
| |
| | easily calculated without measuring any
|
| sink.
| |
| | volumes:
|
| The atmosphere's density depends upon
| |
| | Density
|
| altitude. As an airship rises in the
| |
| | If the weight of an object is less than
|
| atmosphere, therefore, its buoyancy
| |
| | the weight of the fluid the object would
|
| reduces as the density of the surrounding
| |
| | displace if it was fully submerged, then
|
| air reduces. The density of water is
| |
| | the object has an average density less
|
| essentially constant: As a submarine
| |
| | than the fluid and has a buoyancy greater
|
| expels water from its buoyancy tanks (by
| |
| | than its weight. If the fluid has a
|
| pumping them full of air) it rises
| |
| | surface, such as water in a lake or the
|
| because its buoyancy stays the same
| |
| | sea, the object will float at a level so
|
| (because volume of water it displaces
| |
| | it displaces the same weight of fluid as
|
| stays the same) while its weight is
| |
| | the weight of the object. If the object
|
| decreased.
| |
| | is immersed in the fluid, such as a
|
| As a floating object rises or falls the
| |
| | submerged submarine or a balloon in the
|
| forces external to it change and, as all
| |
| | air, it will tend to rise.
|
| objects are compressible to some extent
| |
| | If the object has exactly the same
|
| or another, so will the object's volume.
| |
| | density as the liquid, then it's buoyancy
|
| Buoyancy depends on volume and so an
| |
| | equals its weight. It will tend neither
|
| object's buoyancy reduces if it is
| |
| | to sink nor float.
|
| compressed and increases if it expands.
| |
| | An object with a higher average density
|
| If an object's compressibility is less
| |
| | than the fluid has less buoyancy than
|
| than that of the surrounding fluid, it is
| |
| | weight and it will sink.
|
| in stable equilibrium and will, indeed,
| |
| | A ship floats because although it is made
|
| remain at rest, but if its
| |
| | of steel which is more dense than water,
|
| compressibility is greater, its
| |
| | it encloses a volume of air and the
|
| equilibrium is unstable, and it will rise
| |
| | resulting shape has an average density
|
| and expand on the slightest upward
| |
| | less than that of water.
|
| perturbation, or fall and compress on the
| |
| |
|
