In science and engineering, the weight of an object is a quantity associated with the gravitational force exerted on the object by other objects in its environment, although there is some variation and debate as to the exact definition.
Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. Others define weight as a scalar quantity, the magnitude of the gravitational force. Yet others define it as the magnitude of the reaction force exerted on a body by mechanisms that counteract the effects of gravity: the weight is the quantity that is measured by, for example, a spring scale. Thus, in a state of free fall, the weight would be zero. In this sense of weight, terrestrial objects can be weightless: so if one ignores air resistance, one could say the legendary apple falling from the tree, on its way to meet the ground near Isaac Newton, was weightless.
The unit of measurement for weight is that of force, which in the International System of Units (SI) is the newton. For example, an object with a mass of one kilogram has a weight of about 9.8 newtons on the surface of the Earth, and about one-sixth as much on the Moon. Although weight and mass are scientifically distinct quantities, the terms are often confused with each other in everyday use (e.g. comparing and converting force weight in pounds to mass in kilograms and vice versa).The National Standard of Canada, CAN/CSA-Z234.1-89 Canadian Metric Practice Guide, January 1989: 5.7.3 Considerable confusion exists in the use of the term "weight". In commercial and everyday use, the term "weight" nearly always means mass. In science and technology "weight" has primarily meant a force due to gravity. In scientific and technical work, the term "weight" should be replaced by the term "mass" or "force", depending on the application. 5.7.4 The use of the verb "to weigh" meaning "to determine the mass of", e.g., "I weighed this object and determined its mass to be 5kg," is correct.
Further complications in elucidating the various concepts of weight have to do with the theory of relativity according to which gravity is modeled as a consequence of the curvature of spacetime. In the teaching community, a considerable debate has existed for over half a century on how to define weight for their students. The current situation is that a multiple set of concepts coexist and find use in their various contexts.
History Discussion of the concepts of heaviness (weight) and lightness (levity) date back to the ancient Greek philosophers. These were typically viewed as inherent properties of objects. Plato described weight as the natural tendency of objects to seek their kin. To Aristotle, weight and levity represented the tendency to restore the natural order of the basic elements: air, earth, fire and water. He ascribed absolute weight to earth and absolute levity to fire. Archimedes saw weight as a quality opposed to buoyancy, with the conflict between the two determining if an object sinks or floats. The first operational definition of weight was given by Euclid, who defined weight as: "the heaviness or lightness of one thing, compared to another, as measured by a balance." Operational balances (rather than definitions) had, however, been around much longer.http://www.averyweigh-tronix.com/museum accessed 29 March 2013.
According to Aristotle, weight was the direct cause of the falling motion of an object, the speed of the falling object was supposed to be directly proportionate to the weight of the object. As medieval scholars discovered that in practice the speed of a falling object increased with time, this prompted a change to the concept of weight to maintain this cause-effect relationship. Weight was split into a "still weight" or , which remained constant, and the actual gravity or , which changed as the object fell. The concept of was eventually replaced by Jean Buridan's impetus, a precursor to momentum.
The rise of the Copernican view of the world led to the resurgence of the Platonic idea that like objects attract but in the context of heavenly bodies. In the 17th century, Galileo made significant advances in the concept of weight. He proposed a way to measure the difference between the weight of a moving object and an object at rest. Ultimately, he concluded weight was proportionate to the amount of matter of an object, not the speed of motion as supposed by the Aristotelian view of physics.
Newton The introduction of Newton's laws of motion and the development of Newton's law of universal gravitation led to considerable further development of the concept of weight. Weight became fundamentally separate from mass. Mass was identified as a fundamental property of objects connected to their inertia, while weight became identified with the force of gravity on an object and therefore dependent on the context of the object. In particular, Newton considered weight to be relative to another object causing the gravitational pull, e.g. the weight of the Earth towards the Sun.
Newton considered time and space to be absolute. This allowed him to consider concepts as true position and true velocity. Newton also recognized that weight as measured by the action of weighing was affected by environmental factors such as buoyancy. He considered this a false weight induced by imperfect measurement conditions, for which he introduced the term apparent weight as compared to the true weight defined by gravity.
Although Newtonian physics made a clear distinction between weight and mass, the term weight continued to be commonly used when people meant mass. This led the 3rd General Conference on Weights and Measures (CGPM) of 1901 to officially declare "The word weight denotes a quantity of the same nature as a force: the weight of a body is the product of its mass and the acceleration due to gravity", thus distinguishing it from mass for official usage.
Relativity In the 20th century, the Newtonian concepts of absolute time and space were challenged by relativity. Einstein's equivalence principle put all observers, moving or accelerating, on the same footing. This led to an ambiguity as to what exactly is meant by the force of gravity and weight. A scale in an accelerating elevator cannot be distinguished from a scale in a gravitational field. Gravitational force and weight thereby became essentially frame-dependent quantities. This prompted the abandonment of the concept as superfluous in the fundamental sciences such as physics and chemistry. Nonetheless, the concept remained important in the teaching of physics. The ambiguities introduced by relativity led, starting in the 1960s, to considerable debate in the teaching community as how to define weight for their students, choosing between a nominal definition of weight as the force due to gravity or an operational definition defined by the act of weighing.
Definitions
Several definitions exist for weight, not all of which are equivalent.
Gravitational definition The most common definition of weight found in introductory physics textbooks defines weight as the force exerted on a body by gravity. This is often expressed in the formula , where W is the weight, m the mass of the object, and g gravitational acceleration.
In 1901, the 3rd General Conference on Weights and Measures (CGPM) established this as their official definition of weight:
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 have a standard value of , which gives the standard weight.
The force whose magnitude is equal to mg newtons is also known as the m kilogram weight (which term is abbreviated to kg-wt)Chester, W. Mechanics. George Allen & Unwin. London. 1979. . Section 3.2 at page 83.
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. Since W is the downward force on the body by the centre of Earth and there is no acceleration in the body, there exists an opposite and equal force by the support on the body. It is equal to the force exerted by the body on its support because action and reaction have same numerical value and opposite direction. This can make a considerable difference, depending on the details; for example, an object in free fall exerts little if any force on its support, a situation that is commonly referred to as weightlessness. However, being in free fall does not affect the weight according to the gravitational definition. Therefore, the operational definition is sometimes refined by requiring that the object be at rest. However, this raises the issue of defining "at rest" (usually being at rest with respect to the Earth is implied by using standard gravity). In the operational definition, the weight of an object at rest on the surface of the Earth is lessened by the effect of the centrifugal force from the Earth's rotation.
The operational definition, as usually given, does not explicitly exclude the effects of buoyancy, which reduces the measured weight of an object when it is immersed in a fluid such as air or water. As a result, a floating balloon or an object floating in water might be said to have zero weight.
ISO definition In the ISO International standard ISO 80000-4:2006,ISO 80000-4:2006, Quantities and units - Part 4: Mechanics describing the basic physical quantities and units in mechanics as a part of the International standard ISO/IEC 80000, the definition of weight is given as:
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. If the specified frame is the surface of the Earth, the weight according to the ISO and gravitational definitions differ only by the centrifugal effects due to the rotation of the Earth.
Apparent weight
In many real world situations the act of weighing may produce a result that differs from the ideal value provided by the definition used. This is usually referred to as the apparent weight of the object. For instance, when the gravitational definition of weight is used, the operational weight measured by an accelerating scale is often also referred to as the apparent weight. A common example of this is the effect of buoyancy, when an object is immersed in a fluid the displacement of the fluid will cause an upward force on the object, making it appear lighter when weighed on a scale. The apparent weight may be similarly affected by levitation and mechanical suspension.
Mass
In modern scientific usage, 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 the force of gravity pulls on that matter. However, in most practical everyday situations the word "weight" is used when, strictly, "mass" is meant. For example, most people would say that an object "weighs one kilogram", even though the kilogram is a unit of mass.