# Weight

File:Weeghaak.JPG
A spring scale measures the weight of an object

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. The words "weight" and "mass" are therefore often used interchangeably, even though they do not describe the same concept.

## Weight and mass

In modern usage in the field of mechanics, 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.

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 strictly speaking "mass" is meant. For example, we say that an object "weighs one kilogram", even though the kilogram is actually a unit of mass. This common usage is due to the displacement of earlier force-based measurement systems by the more scientific mass-based SI system. This transition has led to the common and even legal intertwining of "weight" and "mass."

The distinction between mass and weight is unimportant for many practical purposes because, to a reasonable approximation, the strength of gravity is the same 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, slight variations in the Earth's gravitational field do exist (see Earth's gravity), and these must be taken into account in high precision weight measurements.

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", rather than the preferred "atomic mass" etc.

The difference between mass and force becomes obvious 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 downwards force due to gravity is only one-sixth of what the object would experience on Earth.
• masses are considered in the context of a lever, such as a cantilever structure.

## Units of weight (force)

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.

### SI units

In most modern scientific work, physical quantities are measured in SI units. The SI unit of mass is the kilogram. The SI unit of force (and hence weight) is the newton (N) – which can also be expressed in SI base units as kg·m/s² (kilograms times meters per second squared).

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 about 9.8 newtons).

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.

### The pound and related units

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 a one-pound object 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 a pound of force is exerted on it, and is equivalent to about 32 pounds (mass).

### Conversion between weight (force) and mass

To convert between weight (force) and mass we use Newton's second law, F = ma (force = mass × acceleration). Here, F is the force due to gravity (i.e. the weight force), m is the mass of the object in question, and a is the acceleration due to gravity, on Earth approximately 9.8 m/s² or 32 ft/s²). In this context the same equation is often written as W = mg, with W standing for weight, and g for the acceleration due to gravity.

## Sensation of weight

The weight force that we actually sense is not the downward force of gravity, but the normal force (an upward contact force) exerted by the surface we stand on, which opposes gravity and prevents us falling to the center of the Earth. This normal force, called the apparent weight, is the one that is measured by a spring scale.

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 "weightless" 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.

## Measuring weight

Main article: Weighing scale

Weight is commonly measured using one of two methods. A spring scale or hydraulic or pneumatic scale measures weight force (strictly apparent weight force) directly. If the intention is to measure mass rather than weight, then this force must be converted to mass. As explained above, this calculation depends on the strength of gravity. Household and other low precision scales that are calibrated in units of mass (such as kilograms) assume roughly that standard gravity will apply. However, although nearly constant, the apparent or actual strength of gravity does in fact vary very slightly in different places on the earth (see standard gravity, physical geodesy, gravity anomaly and gravity). This means that same object (the same mass) will exert a slightly different weight force in different places. High precision spring scales intended to measure mass must therefore be calibrated specifically according their location on earth.

Mass may also be measured with a balance, which compares the item in question to others of known mass. This comparison remains valid whatever the local strength of gravity. If weight force, rather than mass, is required, then this can be calculated by multiplying mass by the acceleration due to gravity – either standard gravity (for everyday work) or the precise local gravity (for precision work).

Gross weight is a term that generally is found in commerce or trade applications, and refers to the gross or total weight of a product and its packaging. Conversely, net weight refers to the intrinsic weight of the product itself, discounting the weight of packaging or other materials.

## Relative weights on the Earth, other planets and the Moon

The following is a list of the weights of a mass on the surface of some of the bodies in the solar system, relative to its weight on Earth:

 Mercury 0.378 Venus 0.907 Earth 1 Moon 0.165 Mars 0.377 Jupiter 2.364 Saturn 0.91 Uranus 0.889 Neptune 1.125 