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Mass

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Replica of the national prototype kilogram standard no. K20 kept by the US government National Institute of Standards and Technology (NIST).

Mass is a fundamental property of matter and a key property of any object.

Conservation of mass

Until the twentieth century, scientists regarded as settled the following Law of Conservation of Mass:

Matter can neither be created nor destroyed.

In any physical interaction or chemical reaction, that law still holds: the total mass of all products of any reaction must be equal to the total mass of any reactants with which that reaction began. Likewise, in any collision or explosion, the mass of all objects after the event must be equal to the mass of all objects before the event.

However, with the advent of nuclear physics, that law no longer holds. But the related concept of the Law of Conservation of Mass-Energy does hold. It states:

While mass and energy might transform one into the other, mass-energy can neither be created nor destroyed.

This implies that the total quantity of mass-energy in the universe must remain constant, and has implications for Einsteinian general relativity and cosmology.

Note that the law of Conservation of Mass firmly refutes certain non-Biblical cosmologies, especially the ones that require that the Universe came into existence out of nothingness.

Kinematics and Dynamics

Mass is an important factor in two concepts related to motion: momentum and force.

For any object in motion, the relation between momentum p, mass m, and speed v is:

\,\!p=mv

Any object subject to a force will accelerate in the direction of that force. The simple Newtonian equation is:

\,\!F=ma

Moreover, the kinetic energy that any object possesses is proportional to its mass:

E={{\frac  {1}{2}}}mv^{2}

Gravitation

Sir Isaac Newton determined the following Law of Gravitation:

Every particle in the universe attracts every other particle with a force inversely proportional to the square of the distance between their centers and directly proportional to the product of their masses.

Or, in mathematical terms,

F={\frac  {GMm}{R^{2}}}

Until Newton, most observers held mass to be the same as weight, which is actually the force of gravity acting on any object within the gravitational field of another. But while mass and weight are proportional, they are not identical. Weight changes with altitude, even on earth, though the change is usually negligible. More to the point, an object will have different weights in the gravitational fields of different celestial bodies, but its mass will remain the same.

Relativity

Albert Einstein predicted, and subsequent experiments have shown, that the mass of an object is not constant. Instead, mass increases with speed and also increases with either acceleration or with position in a gravity well. This latter relation enabled Einstein to solve a problem with the precession of the orbit of the planet Mercury, which, alone among the eight planets, draws close enough to the Sun to be subject to a second-order relativistic effect. Indeed, an object having any proper mass would become infinitely heavy as the speed of that object approached the speed of light.