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weight, measure of the force of gravity on a body (see gravitation). Since the weights of different bodies at the same location are proportional to their masses, weight is often used as a measure of mass. However, the two are not the same; mass is a measure of the amount of matter present in a body and thus has the same value at different locations, and weight varies depending upon the location of the body in the earth's gravitational field (or the gravitational field of some other astronomical body). A given body will have the same mass on the earth and on the moon, but its weight on the moon will be only about 16% of the weight as measured on the earth. The distinction between weight and mass is further confused by the use of the same units to measure both—the pound, the gram, or the kilogram. One pound of weight, or force, is the force necessary at a given location to accelerate a one-pound mass at a rate equal to the acceleration of gravity at that location (about 32 ft per sec per sec). Similar relationships hold between the gram of force and the gram of mass and between the kilogram of force and the kilogram of mass.

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

In the physical sciences, weight is a measurement of the gravitational force acting on an object. Near the surface of the Earth, the acceleration due to gravity is approximately constant; this means that an object's weight is roughly proportional to its mass.

In commerce and in many other applications, weight means the same as mass as that term is used in physics. In modern scientific usage, however, weight and mass are fundamentally different quantities: mass is an intrinsic property of matter, whereas weight is a force that results from the action of gravity on matter: it measures how strongly gravity pulls on that matter.

However, the recognition of this difference is, historically, a relatively recent development and in many everyday situations the word "weight" continues to be used when "mass" is meant. For example, we say that an object "weighs one kilogram", even though the kilogram is a unit of mass.

The distinction between mass and weight is unimportant for many practical purposes because the strength of gravity is very simliar everywhere on the surface of the Earth. In such a constant gravitational field, the gravitational force exerted on an object (its weight) is directly proportional to its mass. So, if object A weighs, say, 10 times as much as object B, then object A's mass is 10 times that of object B. This means that an object's mass can be measured indirectly by its weight (for conversion formulas see below). For example, when we buy a bag of sugar we can measure its weight (how hard it presses down on the scales) and be sure that this will give a good indication of the quantity that we are actually interested in, which is the mass of sugar in the bag.

Nevertheless, the Earth's gravitational field 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. To eliminate this variation, when the weight of objects is used in commerce, the value given is what they would weigh at a nominal standard gravitational acceleration of 9.80665 m/s^{2} (approx. 32.174 ft/s^{2}) Spring scales, which measure local weight, must be calibrated at the location at which they will be used to show this standard weight, to be legal for commerce.

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

The difference between mass and force may be important when:

- objects are compared in different gravitational fields, such as away from the Earth's surface. For example, on the surface of the Moon, gravity 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 is only one-sixth of what the object would experience on Earth.
- locating the center of gravity of an object (although if the gravitation field is uniform, the center of gravity will coincide with the center of mass).
- an object is submersed in a fluid (for instance, a brick weighs less when placed in water, and helium balloon in the atmosphere appears to have negative weight).

Systems of units of weight (force) and mass have a tangled history, partly because the distinction was not properly understood when many of the units first came into use.

The gravitational force exerted on an object is proportional to the mass of the object, so it is reasonable to think of the strength of gravity as measured in terms of force per unit mass, that is, newtons per kilogram (N/kg). However, the unit N/kg resolves to m/s²; (metres per second per second), which is the SI unit of acceleration, and in practice gravitational strength is usually quoted as an acceleration.

In United States customary units, the pound can be either a unit of force or a unit of mass. Related units used in some distinct, separate subsystems of units include the poundal and the slug. The poundal is defined as the force necessary to accelerate an object of one-pound *mass at 1 ft/s², and is equivalent to about 1/32 of a pound-force. The slug is defined as the amount of mass that accelerates at 1 ft/s² when one pound-force is exerted on it, and is equivalent to about 32 pounds (mass).*

*The kilogram-force is a non-SI unit of force, defined as the force exerted by a one kilogram mass in standard Earth gravity (equal to 9.80665 newtons exactly). The dyne is the cgs unit of force and is not a part of SI, while weights measured in the cgs unit of mass, the gram, remain a part of SI.
*

For a body supported in a stationary position, the normal force balances the earth's gravitational force, and so apparent weight has the same magnitude as actual weight. (Technically, things are slightly more complicated. For example, an object immersed in water weighs less, according to a spring scale, than the same object in air; this is due to buoyancy, which opposes the weight force and therefore generates a smaller normal. These and other factors are explained further under apparent weight.)

If there is no contact with any surface to provide such an opposing force then there is no sensation of weight (no apparent weight). This happens in free-fall, as experienced by sky-divers (until they approach terminal velocity) and astronauts in orbit, who feel "weightlessness" even though their bodies are still subject to the force of gravity: they're just no longer resisting it. The experience of having no apparent weight is also known as microgravity.

A degree of reduction of apparent weight occurs, for example, in elevators. In an elevator, a spring scale will register a decrease in a person's (apparent) weight as the elevator starts to accelerate downwards. This is because the opposing force of the elevator's floor decreases as it accelerates away underneath one's feet.

A balance on the other hand, compares the weight of an unknown object in one scale pan to the weight of standard masses in the other, using a lever mechanism - a lever-balance. The standard masses are often referred to, non-technically, as *"weights" . Since any variations in gravity will act equally on the unknown and the known weights, a lever-balance will indicate the same value at any location on Earth. Therefore, balance "weights" are usually calibrated and marked in mass units, so the lever-balance measures mass by comparing the earth's attraction on the unknown object and standard masses in the scale pans. In the absence of a gravitational field, away from planetary bodies, (e.g. space), a lever-balance would not work. Some balances can be marked in weight units, but since the weights are calibrated at the factory for standard gravity, the balance will measure standard weight, i.e. what the object would weigh at standard gravity, not the actual local force of gravity on the object.*

*If the actual force of gravity on the object is needed, this can be calculated by multiplying the mass measured by the balance by the acceleration due to gravity – either standard gravity (for everyday work) or the precise local gravity (for precision work). Tables of the gravitational acceleration at different locations can be found on the web.*

*Gross weight is a term that generally is found in commerce or trade applications, and refers to the total weight of a product and its packaging. Conversely, net weight refers to the weight of the product alone, discounting the weight of its container or packaging.
*

*The table below shows comparative gravitational accelerations at the surface of the Sun, the Earth's moon, each of the planets in the solar system, and Pluto. The “surface” is taken to mean the cloud tops of the gas giants (Jupiter, Saturn, Uranus and Neptune). For the Sun, the surface is taken to mean the photosphere. The values in the table have not been de-rated for the centrifugal effect of planet rotation (and cloud-top wind speeds for the gas giants) and therefore, generally speaking, are similar to the actual gravity that would be experienced near the poles.*

Body | Multiple of Earth gravity | m/s² |
---|---|---|

Sun | 27.90 | 274.1 |

Mercury | 0.3770 | 3.703 |

Venus | 0.9032 | 8.872 |

Earth | 1 (by definition) | 9.8226 |

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 |

Pluto | 0.0621 | 0.610 |

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Last updated on Friday October 10, 2008 at 01:55:54 PDT (GMT -0700)

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Last updated on Friday October 10, 2008 at 01:55:54 PDT (GMT -0700)

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