Weight

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Weight is a name for the reactive half of a repulsive force exerted on a body with a particular mass, by contact with, or support from, another body (e.g. the Earth, and specifically the Earth's surface). The force between the bodies prevents them from entering free-fall, which they would otherwise do, due to gravity.[1]. This repulsive force, which acts equally between gravitating objects whose natural motion has been stopped or slowed it, is called "weight." Weight is not directly caused by the "force of gravity," for whenever gravity operates alone and unopposed, there is no force that corresponds to weight. Weight is rather a name for any mechanical forces (or other types of forces) that oppose the natural free-fall motion of objects caused by gravity, when gravity acts alone.

Sometimes weight is defined in operational terms of the weighing process, as the force exerted by an object upon its support against gravity.[2]. This is equivalent to the above definition. Strictly speaking, a weighing scale measures the force exerted by an object on its support, which is defined as the weight. For example, standing at rest on a weighing scale on Earth, a person's weight equals the person's mass multiplied by the gravitational acceleration produced by the Earth. However, the direction of weight is downwards, whereas the acceleration from the force of the support is upwards. On the surface of the Moon, an object's weight is approximately one sixth of the weight at rest on Earth, as the gravitational force exerted by the Moon is much smaller than that of Earth.

In a free falling elevator, a scale indicates a zero weight, as no net force is exerted by the body on the support; the person experiences weightlessness. Similarly, and for similar reasons, in a space craft in orbit around the Earth, the weight is also zero, as orbital motion also represents a type of free fall in which the only force acting, is that of gravity.

The weight of an object when supported against gravity, often denoted W, is often defined as the "gravitational force" exerted on it, but this is the same as the opposite of the force that supports it (the real cause of weight). The object's weight is thus the product of the mass m of the object and the local gravitational acceleration g:[3] W = m g. In the International System of Units (SI), the unit of measurement for weight is that of force, the newton.

On the surface of the Earth, the acceleration due to gravity is approximately constant; this means that the magnitude of an object's weight on the surface of the Earth is proportional to its mass. In situations other than that of a constant position on the Earth, so long as the acceleration does not change, the force it exerts against support in any accelerated frame is proportional to its mass, also. In everyday practical use, therefore, including commercial use, the term weight is commonly used to mean mass.[4]

In technical terms which also cover accelerating frames and scales (such as the case of an an elevator which is accelerating upward or downward, but is not in free-fall), the weight is given by:

\vec{W} = - m \vec{g} Where the vector-g is the g-force.

The g-force is the proper acceleration which causes the object to deviate from a free-fall or inertial trajectory. A non-gravitational mechanical accelerating force must provide this proper acceleration, since gravitation does not cause proper acceleration (this is the basic reason that an object free-falling in a gravity field feels no weight, and is weightless). An example of a force that produces proper acceleration would be the mechanical force exerted by a scale, or the floor of an elevator. The reaction force resulting from the inertia of the mass, that resists the mechanical accelerating force, must be equal to the mechanical accelerating force, but acting in the opposite direction, according to Newton's third law of motion. This reaction force (with direction denoted by the minus sign) is what is defined by the ISO as "weight." The ISO standard ISO 80000-4 (2006) defines weight as follows:

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