Editing Weight (section)

==Definitions==
{{Excessive examples|date=October 2023}}
Several definitions exist for ''weight'', not all of which are equivalent.<ref name="Gat"/><ref name="King">{{cite journal
|title=Weight and weightlessness
|author=Allen L. King
|journal=[[American Journal of Physics]] |volume=30 |page=387 |date=1963 |issue=5
|doi=10.1119/1.1942032
|bibcode = 1962AmJPh..30..387K }}</ref><ref name="French">{{cite journal |title=On weightlessness |author=A. P. French |journal=[[American Journal of Physics]] |volume=63 |pages=105–106 |date=1995 |issue=2 |doi=10.1119/1.17990|bibcode = 1995AmJPh..63..105F }}</ref><ref name="Galili-Lehavi">{{cite journal |last1=Galili |first1=I. |last2=Lehavi |first2=Y. |date=2003 |title=The importance of weightlessness and tides in teaching gravitation |journal=[[American Journal of Physics]] |volume=71 |issue=11 |pages=1127–1135 |url=http://sites.huji.ac.il/science/stc/staff_h/Igal/Research%20Articles/Weight-AJP.pdf |doi=10.1119/1.1607336|bibcode = 2003AmJPh..71.1127G }}</ref>

===Gravitational definition===
The most common definition of weight found in introductory physics textbooks defines weight as the force exerted on a body by gravity.<ref name="Morrison"/><ref name="Galili-Lehavi"/> This is often expressed in the formula {{nowrap|1=''W'' = ''mg''}}, 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'':
{{blockquote|The word ''weight'' denotes a quantity of the same nature{{#tag:ref
 |The phrase "quantity of the same nature" is a literal translation of the [[French (language)|French]] phrase ''grandeur de la même nature''. Although this is an authorized translation, VIM 3 of the [[International Bureau of Weights and Measures]] recommends translating ''grandeurs de même nature'' as ''quantities of the same kind''.<ref>{{cite book
 |author=Working Group 2 of the Joint Committee for Guides in Metrology (JCGM/WG 2)
 |title=International vocabulary of metrology – Basic and general concepts and associated terms (VIM) – Vocabulaire international de métrologie – Concepts fondamentaux et généraux et termes associés (VIM)
 |url=http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2008.pdf
 |date=2008 |edition=3rd |type=JCGM 200:2008 |publisher=[[BIPM]]
 |at=Note 3 to Section 1.2
 |language=en, fr
}}</ref>|group=Note
}} as a ''force'': the weight of a body is the product of its mass and the acceleration due to gravity.
|Resolution 2 of the 3rd General Conference on Weights and Measures<ref name="3rdCGPM"/><ref name="NIST330">{{Cite book |editor1=David B. Newell |editor2=Eite Tiesinga |title=The International System of Units (SI) |url=https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.330-2019.pdf |publisher=[[National Institute of Standards and Technology|NIST]] |location=Gaithersburg, MD |date=2019|edition=NIST Special publication 330, 2019 |page=46 }}</ref>}}
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:
{{blockquote|The weight ''W'' of a body is equal to the magnitude ''F<sub>g</sub>'' of the gravitational force on the body.<ref name="Halliday 2007 95">{{cite book |title=Fundamentals of Physics |volume=1 |first1=David |last1=Halliday |first2=Robert |last2=Resnick |first3=Jearl |last3=Walker |publisher= Wiley |date=2007 |edition=8th |page=95 |isbn= 978-0-470-04473-5}}</ref>}}

The gravitational acceleration varies from place to place. Sometimes, it is simply taken to have a [[standard gravity|standard value]] of {{nowrap|9.80665 m/s<sup>2</sup>}}, which gives the [[standard weight]].<ref name="3rdCGPM">{{cite web
 |url=http://www.bipm.org/en/CGPM/db/3/2/
 |title=Resolution of the 3rd meeting of the CGPM (1901)
 |publisher=BIPM
}}</ref>

The force whose magnitude is equal to ''mg'' newtons is also known as the '''m kilogram weight''' (which term is abbreviated to '''kg-wt''')<ref>Chester, W. Mechanics. George Allen & Unwin. London. 1979. {{ISBN|0-04-510059-4}}. Section 3.2 at page 83.</ref>

===Operational definition===
{{multiple image
| align             = right
| direction         = horizontal
| header            = Measuring weight versus mass
| image1            = Weegschaal-1.jpg
| width1            = 125
| image2            = Bascula_9.jpg
| width2            = 220
| footer            = Left: A [[Weighing scale|spring scale]] measures weight, by seeing how much the object pushes on a spring (inside the device). On the Moon, an object would give a lower reading. Right: A [[weighing scale|balance scale]] indirectly measures mass,<!-- It compares weights. It has the secondary effect of comparing masses because weight is proportional to mass. --> by comparing an object to references. On the Moon, an object would give the same reading, because the object and references would ''both'' become lighter.
}}
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'''.<ref name="King"/> 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.{{Citation needed|date=May 2010}} However, this raises the issue of defining "at rest" (usually being at rest with respect to the Earth is implied by using [[standard gravity]]).{{Citation needed|date=May 2010}} 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 [[International Organization for Standardization|ISO]] International standard ISO 80000-4:2006,<ref>ISO 80000-4:2006, Quantities and units - Part 4: Mechanics</ref> 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:
{{blockquote|
'''Definition'''
:<math>F_g = m g \, </math>,
:where ''m'' is mass and ''g'' is local acceleration of free fall.

'''Remarks'''
*When the reference frame is Earth, this quantity comprises not only the local gravitational force, but also the local centrifugal force due to the rotation of the Earth, a force which varies with latitude.
*The effect of atmospheric buoyancy is excluded in the weight.
*In common parlance, the name "weight" continues to be used where "mass" is meant, but this practice is deprecated.
|ISO 80000-4 (2006)}}

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.<ref name="French"/> 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 ===
{{Main|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.<ref>{{cite journal
 |author = Galili, Igal
 |title = Weight and gravity: teachers' ambiguity and students' confusion about the concepts
 |journal = International Journal of Science Education
 |volume = 15
 |number = 2
 |pages = 149–162
 |date = 1993
 |doi = 10.1080/0950069930150204
|bibcode = 1993IJSEd..15..149G }}</ref> 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.<ref>{{cite book
 |title=Principles of mechanics and biomechanics
 |author=Bell, F.
 |isbn=978-0-7487-3332-3
 |url=https://books.google.com/books?id=bPcPnZQ36KwC&pg=PA174
 |pages=174–176
 |date=1998
 |publisher=Stanley Thornes Ltd
}}</ref> The apparent weight may be similarly affected by [[Levitation (physics)|levitation]] and mechanical suspension.