Buoyancy

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 to become lighter. If the buoyancy exceeds the weight, then the object floats; if the weight exceeds the buoyancy, the object sinks. If the buoyancy equals the weight, the body has neutral buoyancy and may remain at its level. If its 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, expanding, on the slightest upward perturbation, but fall, compressing on the slightest downward perturbation. It was the ancient Greek, Archimedes of Syracuse, who first discovered the law of buoyancy, sometimes called Archimedes' principle:
 The buoyant force is equal to the weight of the displaced fluid.
Suppose a rock's weight is measured at 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 whose weight is 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.
Buoyancy is the underlying principle of many vehicles such as boats, ships, balloons, and airships.
Density
If the weight of an object is less than that of the fluid that the object would displace if it was fully submerged, then the object is less dense than the fluid and it floats at such a level that the weight of the object is equal to the weight of the displaced fluid. If the object weighs more than that of the fluid that the object would displace if it was fully submerged, then the object is more dense than the fluid and the object sinks.
An object of a material of higher density than the fluid, e.g. a metal object in water, can still float if it has a suitable shape 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 and energy
Although Archimedes' principle gives the force on a buoyant object, this does not determine the related acceleration of the object in the usual way over Newton's first law. This is for two reasons: Not only has the mass of the object to be accelerated but also the mass of the displaced fluid. One can compare the situation to a scale, where the weight on one side is given by the object, and the weight on the other side by the displaced fluid element. Depending on which of the two is heavier, one side of the scale will drop and the other rise, but since both sides are rigidly connected, both masses have to be accelerated together at the same rate (albeit in opposite directions). The second reason is that viscosity dissipates energy, so that, even taking into account the kinetic and potential energies of the object and the fluid (but ignoring heat energy), energy is lost to viscosity, a form of friction.
It is obvious that without taking the displaced fluid element into account, energy would not be conserved during the buoyant motion of an object as it would gain both potential and kinetic energy when rising in the fluid.