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In physics, buoyancy is an upward force on an object immersed in a fluid (i.e. a liquid or a gas),

enabling it to float or at least to appear lighter.

Buoyancy is important for many vehicles such as boats, ships, balloons, and airships.

Forces and equilibrium:

The buoyancy provides an upward force on the object. According to Newton's first law of motion,

if the upward forces (including the buoyancy) balance the downward forces (including the weight)

he object will either remain at rest or remain in motion at a constant rate. Otherwise, it will accelerate upwards or downwards.

If such an object's compressibility is less than that of the surrounding fluid, it is in stable equilibrium and will, indeed,

remain at rest, but if its compressibility is greater, its equilibrium is unstable, and it will rise and expand on the slightest upward perturbation,

or fall and compress on the slightest downward perturbation.

For an object to float, it must be able to displace enough water equal to its weight.

When you walk into the water at a swimming pool or at the seaside, do you feel lighter or heavier?

If you walk deep enough(up to your chin), your feet tend to come off the ground and you start to float.

This is because the water is exerting on you a force called buoyancy.

Archimedes's principle:

It was the ancient Greek, Archimedes of Syracuse, who first discovered the law of buoyancy, sometimes called Archimedes's principle:

The story of Archimedes discovering buoyancy while sitting in his bathtub is described in Book 9 of De architectura by Vitruvius.

Typically, the weight of the displaced fluid is directly proportional to the volume of the displaced fluid

(specifically if the surrounding fluid is of uniform density).

Thus, among objects with equal masses, the one with greater volume has greater buoyancy.

Suppose a rock's weight is measured as 10 Newtons when suspended by a string in a vacuum.

Suppose that when the rock is lowered by the string into water, it displaces water of weight 3 Newtons.

The force it then exerts on the string from which it hangs will be 10 Newtons minus the 3 Newtons of buoyant force: 10 − 3 = 7 Newtons.

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Density:

If the weight of an object is less than the weight of the fluid the object would displace if it was fully submerged,

then the object is less dense than the fluid and it floats at a level so it displaces the same weight of fluid as the weight of the object.

If the object has exactly the same density as the liquid, then it will stay still, neither sinking nor floating upwards, just as the liquid nearby stays still.

An object made of a material of higher density than the fluid, for example a metal object in water,

can still float if it has a suitable shape (e.g. a hollow which is open upwards or downwards)

that keeps a large enough volume of air below the surface level of the fluid.

In that case, for the average density mentioned above, the air is included also,

which may reduce this density to less than that of the fluid.

Acceleration:

Although Archimedes's principle gives the force on a buoyant object,

this does not allow the direct determination of the acceleration of the object in the usual way using Newton's second law.

This is because as well as accelerating the object, the fluid also has to be dynamically displaced- resulting in drag.

While Archimedes's principle is hydrostatic force, it must be taken into account, even in hydrodynamical situations.

A simple case would be that of a submerged sphere that is twice as dense as water starting at rest and as it first starts to fall through the water.

Initially ignoring drag, a first approximation might be to include the force of gravity and subtract the force of buoyancy

and then apply Newton's equation F = ma.

The next step would be to attempt to take into account the drag forces due to viscosity,

which is a form of dynamic friction. Next is the inertial forces of the water that has to get pushed out of the way as the sphere passes through the water:

the inertial component of drag. One might use the drag equation.

The velocity would increase and the force of drag will increase until the object reached terminal velocity,

where turbulence might also be a consideration.

Still, the hydrostatic force of buoyancy operating on the submerged or floating object must be taken into account.