Weight

measures the weight of an object]] 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. . 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.

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:

$\backslash vec\{W\}\; =\; -\; m\; \backslash vec\{g\}$ 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: }}

When the accelerating force is provided by a simple support on the surface of the Earth, then the mechanical force from the support provides the proper acceleration equal to $\backslash vec\{g\}$ and thus the weight of the object against the support is $-\; m\; \backslash vec\{g\}$.

Definitions

Several definitions exist for weight, not all of which are equivalent.

The main differences in these definitions are:

whether the definition is based on the standard gravity of the Earth, or is based on any other proper acceleration, for example, Moon's gravity for an object on the moon;

whether the quantity is determined directly and is thus weighing-instrument-dependent (see apparent weight), or is determined indirectly, from other measurements of mass and acceleration;

whether the quantity is a vector or a scalar.

Gravitational definition

One of the most common definitions of weight found in introductory physics textbooks defines weight as the force exerted on a body by gravity.}} This resolution defines weight as a vector, since force is a vector quantity. However, some textbooks also take weight to be a scalar by defining: }}

The gravitational acceleration varies from place to place. Sometimes, it is simply taken to a have a standard value of , which gives the standard weight.

Operational definition

In the operational definition, the weight of an object is the force measured by the operation of weighing it, which is the force it exerts on its support. }} This definition allows use of the formula W = m g, with g interpreted as the local acceleration of free fall in the specified frame. The definition is dependent on the chosen frame of reference. When the chosen frame is co-moving with the object in question then this definition precisely agrees with the operational definition. For example, most people would say that an object "weighs one kilogram", even though the kilogram is a unit of mass.

The scientific distinction between mass and weight is unimportant for many practical purposes because the strength of gravity is almost constant everywhere on the surface of the Earth. In a constant gravitational field, the gravitational force exerted on an object (its weight) is directly proportional to its mass. For example, object A weighs 10 times as much as object B, so therefore the mass of object A is 10 times greater than that of object B. This means that an object's mass can be measured indirectly by its weight, and so, for everyday purposes, weighing (using a weighing scale) is an entirely acceptable way of measuring mass. Conversely, a balance actually measures mass, not weight (in the scientific sense), but the quantity thus determined is still called "weight" in everyday use.

The Earth's gravitational field is not actually constant but can vary by as much as 0.5% at different locations on Earth (see Earth's gravity). These variations alter the relationship between weight and mass, and must be taken into account in high precision weight measurements that are intended to indirectly measure mass. Spring scales, which measure local weight, must be calibrated at the location at which the objects will be used to show this standard weight, to be legal for commerce.

This table shows the variation of acceleration due to gravity (and hence the variation of weight) at various locations on the Earth's surface.

{| class="wikitable" border="1" |- ! Location ! Latitude ! m/s² |- | Equator | 0° | 9.7803 |- | Sydney | 33° 52´S | 9.7968 |- | Aberdeen | 57° 9´N | 9.8168 |- |- | North Pole | 90° N | 9.8322 |- |}

The historic use of "weight" for "mass" also persists in some scientific terminology – for example, the chemical terms "atomic weight", "molecular weight", and "formula weight", can still be found rather than the preferred "atomic mass" etc.

In a different gravitational field, for example, on the surface of the Moon, an object can have a significantly different weight than on Earth. The gravity on the surface of the Moon is only about one-sixth as strong as on the surface of the Earth. A one-kilogram mass is still a one-kilogram mass (as mass is an intrinsic property of the object) but the downward force due to gravity, and therefore its weight, is only one-sixth of what the object would have on Earth. So a 180-pound man on Earth weighs only about 30 pounds when visiting the Moon.

Units

SI units

In most modern scientific work, physical quantities are measured in SI units. The SI unit of force (and hence weight in the mechanics sense) is the same as that of force: the newton (N) – a derived unit which can also be expressed in SI base units as kg·m/s² (kilograms times meters per second squared). |- | Moon | 0.1655 | 1.625 |- | Mars | 0.3895 | 3.728 |- | Jupiter | 2.640 | 25.93 |- | Saturn | 1.139 | 11.19 |- | Uranus | 0.917 | 9.01 |- | Neptune | 1.148 | 11.28 |- |}

See also

body mass

body mass index

obesity

overweight

Notes

References

Category:Commerce Category:Mass Category:Force Category:Physiology