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In
science Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for ...
and
engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...
, the weight of an object is the
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...
acting on the object due to
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
. Some standard textbooks define weight as a
vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...
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 Reaction may refer to a process or to a response to an action, event, or exposure: Physics and chemistry *Chemical reaction *Nuclear reaction *Reaction (physics), as defined by Newton's third law *Chain reaction (disambiguation). Biology and me ...
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 In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on i ...
, the weight would be zero. In this sense of weight, terrestrial objects can be weightless: ignoring
air resistance In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding flu ...
, the famous apple falling from the tree, on its way to meet the ground near
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...
, would be weightless. The
unit of measurement A unit of measurement is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can ...
for weight is that of
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...
, which in the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(SI) is the
newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * ''Newton'' (film), a 2017 Indian film * 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 The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
. 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 The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...
according to which gravity is modeled as a consequence of the
curvature In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonic ...
of
spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
. 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 co-exist 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 Ancient Greek philosophy arose in the 6th century BC, marking the end of the Greek Dark Ages. Greek philosophy continued throughout the Hellenistic period and the period in which Greece and most Greek-inhabited lands were part of the Roman Empire ...
. These were typically viewed as inherent properties of objects.
Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...
described weight as the natural tendency of objects to seek their kin. To
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...
, 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 Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists ...
saw weight as a quality opposed to
buoyancy Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the p ...
, with the conflict between the two determining if an object sinks or floats. The first operational definition of weight was given by
Euclid Euclid (; grc-gre, Wikt:Εὐκλείδης, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Euclid's Elements, Elements'' trea ...
, 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. 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 Jean Buridan (; Latin: ''Johannes Buridanus''; – ) was an influential 14th-century French people, French Philosophy, philosopher. Buridan was a teacher in the Faculty (division)#Faculty of Art, faculty of arts at the University of Paris for hi ...
's impetus, a precursor to
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
. 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 Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
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 Aristotelean view of physics.


Newton

The introduction of
Newton's laws of motion Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in moti ...
and the development of
Newton's law of universal gravitation Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distanc ...
led to considerable further development of the concept of weight. Weight became fundamentally separate from
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
. Mass was identified as a fundamental property of objects connected to their
inertia Inertia is the idea that an object will continue its current motion until some force causes its speed or direction to change. The term is properly understood as shorthand for "the principle of inertia" as described by Newton in his first law ...
, 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 The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established i ...
(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 In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (suc ...
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 physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag). This is the steady gain in speed caused exclusively by the force of gravitational attraction. All bodies ...
. In 1901, the 3rd
General Conference on Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established i ...
(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 standard acceleration due to gravity (or standard acceleration of free fall), sometimes abbreviated as standard gravity, usually denoted by or , is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. ...
. The force whose magnitude is equal to ''mg'' newtons is also known as the m kilogram weight (which term is abbreviated to kg-wt)


Operational definition

In the operational definition, the weight of an object is the
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...
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. Also 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 In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on i ...
exerts little if any force on its support, a situation that is commonly referred to as
weightlessness Weightlessness is the complete or near-complete absence of the sensation of weight. It is also termed zero gravity, zero G-force, or zero-G. Weight is a measurement of the force on an object at rest in a relatively strong gravitational fi ...
. 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 The standard acceleration due to gravity (or standard acceleration of free fall), sometimes abbreviated as standard gravity, usually denoted by or , is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. ...
). 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 Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the p ...
, 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 A balloon is a flexible bag that can be inflated with a gas, such as helium, hydrogen, nitrous oxide, oxygen, and air. For special tasks, balloons can be filled with smoke, liquid water, granular media (e.g. sand, flour or rice), or light so ...
or an object floating in water might be said to have zero weight.


ISO definition

In the
ISO ISO is the most common abbreviation for the International Organization for Standardization. ISO or Iso may also refer to: Business and finance * Iso (supermarket), a chain of Danish supermarkets incorporated into the SuperBest chain in 2007 * Iso ...
International standard ISO 80000-4:2006, describing the basic physical quantities and units in mechanics as a part of the International standard
ISO/IEC 80000 ISO 80000 or IEC 80000 is an international standard introducing the International System of Quantities (ISQ). It was developed and promulgated jointly by the International Organization for Standardization (ISO) and the International Electrotech ...
, the definition of ''weight'' is given as: The definition is dependent on the chosen
frame of reference In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points― geometric points whose position is identified both mathema ...
. 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. A common example of this is the effect of
buoyancy Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the p ...
, when an object is immersed in a
fluid In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
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 Levitation (from Latin ''levitas'' "lightness") is the process by which an object is held aloft in a stable position, without mechanical support via any physical contact. Levitation is accomplished by providing an upward force that counteracts ...
and mechanical suspension. 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.


Mass

In modern scientific usage, weight and
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
are fundamentally different quantities: mass is an
intrinsic In science and engineering, an intrinsic property is a property of a specified subject that exists itself or within the subject. An extrinsic property is not essential or inherent to the subject that is being characterized. For example, mass ...
property of
matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic partic ...
, whereas weight is a ''force'' that results from the action of
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
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. The distinction between mass and weight is unimportant for many practical purposes because the strength of gravity does not vary too much on the surface of the Earth. In a uniform gravitational field, the gravitational force exerted on an object (its weight) is
directly proportional In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant ...
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 In science and engineering, the weight of an object is the force acting on the object due to gravity. Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. Others define weight as a scalar quan ...
(using a
weighing scale A scale or balance is a device used to measure weight or mass. These are also known as mass scales, weight scales, mass balances, and weight balances. The traditional scale consists of two plates or bowls suspended at equal distances from a ...
) is an entirely acceptable way of measuring mass. Similarly, a
balance Balance or balancing may refer to: Common meanings * Balance (ability) in biomechanics * Balance (accounting) * Balance or weighing scale * Balance as in equality or equilibrium Arts and entertainment Film * ''Balance'' (1983 film), a Bulgarian ...
measures mass indirectly by comparing the weight of the measured item to that of an object(s) of known mass. Since the measured item and the comparison mass are in virtually the same location, so experiencing the same
gravitational field In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenome ...
, the effect of varying gravity does not affect the comparison or the resulting measurement. The Earth's
gravitational field In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenome ...
is not uniform but can vary by as much as 0.5% at different locations on Earth (see
Earth's gravity The gravity of Earth, denoted by , is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation). It is a vector quantity ...
). 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 scale A spring scale, spring balance or newton meter is a type of mechanical force gauge or weighing scale. It consists of a spring fixed at one end with a hook to attach an object at the other. It works in accordance with Hooke's Law, which states th ...
s, 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. The historical use of "weight" for "mass" also persists in some scientific terminology – for example, the
chemical A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., wi ...
terms "atomic weight", "molecular weight", and "formula weight", can still be found rather than the preferred "
atomic mass The atomic mass (''m''a or ''m'') is the mass of an atom. Although the SI unit of mass is the kilogram (symbol: kg), atomic mass is often expressed in the non-SI unit dalton (symbol: Da) – equivalently, unified atomic mass unit (u). 1&nbs ...
", etc. In a different gravitational field, for example, on the surface of the
Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
, 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 man of mass 180 pounds weighs only about 30
pounds-force The pound of force or pound-force (symbol: lbf, sometimes lbf,) is a unit of force used in some systems of measurement, including English Engineering units and the foot–pound–second system. Pound-force should not be confused with pound-ma ...
when visiting the Moon.


SI units

In most modern scientific work, physical quantities are measured in SI units. The SI unit of weight is the same as that of force: the
newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * ''Newton'' (film), a 2017 Indian film * Newton ( ...
(N) – a derived unit which can also be expressed in
SI base unit The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which all ...
s as kg⋅m/s2 (kilograms times metres per second squared). In commercial and everyday use, the term "weight" is usually used to mean mass, and the verb "to weigh" means "to determine the mass of" or "to have a mass of". Used in this sense, the proper SI unit is the
kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially ...
(kg). As of 20 May 2019, the kilogram, which is essential to evaluate the weight of an object, has been redefined in terms of Planck's constant. The new definition does not affect the actual amount of the material but increases the measurement's quality and decreases the uncertainty associated with it. Prior to using Planck's constant, a physical object was used as a standard. The object, located in a vault in Sèvres, France, has fluctuated by approximately 50 micrograms of its mass since it was first introduced in 1889. Consequently, the following must be true. Mass, which should be the same whether on earth or the moon for example, is only valid on earth since it needs to be referenced. Also, comparing a weight measurement to a standard that changes with time cannot be used as a reference without citing the actual value of it at the time and moment it was used as such. Therefore, to redefine the kilogram all National Metrology Institutes (NMIs) involved determined the new value of Planck's constant by evaluating a mass which was calibrated against the IPK.Ehtesham, B., John, T., Yadav, S., Singh, H. K., Mandal, G., & Singh, N. (2020). Journey of Kilogram from Physical Constant to Universal Physical Constant (h) via Artefact: A Brief Review. MAPAN - Journal of Metrology Society of India, 1-9 To this extent one kilogram is equal to h/(6.62607015×10^(-34) ) m^(-2) s which equals 1 m^(-2) s. A kilogram has remained the same quantity it was before the redefinition. But as of May 2019, the weights measured and recorded can be traced back and used as comparison for current and future work.


Pound and other non-SI units

In
United States customary units United States customary units form a system of measurement units commonly used in the United States and U.S. territories since being standardized and adopted in 1832. The United States customary system (USCS or USC) developed from English 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 The poundal (symbol: pdl) is a unit of force, introduced in 1877, that is part of the Absolute English system of units, which itself is a coherent subsystem of the foot–pound–second system. :1\,\text = 1\,\text\text/\text^2 The poundal is def ...
and the
slug Slug, or land slug, is a common name for any apparently shell-less terrestrial gastropod mollusc. The word ''slug'' is also often used as part of the common name of any gastropod mollusc that has no shell, a very reduced shell, or only a smal ...
. The poundal is defined as the force necessary to accelerate an object of one-pound ''mass'' at 1ft/s2, and is equivalent to about 1/32.2 of a pound-''force''. The slug is defined as the amount of mass that accelerates at 1ft/s2 when one pound-force is exerted on it, and is equivalent to about 32.2 pounds (mass). The
kilogram-force The kilogram-force (kgf or kgF), or kilopond (kp, from la, pondus, lit=weight), is a non-standard gravitational metric unit of force. It does not comply with the International System of Units (SI) and is deprecated for most uses. The kilogram-f ...
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 The dyne (symbol: dyn; ) is a derived unit of force specified in the centimetre–gram–second (CGS) system of units, a predecessor of the modern SI. History The name dyne was first proposed as a CGS unit of force in 1873 by a Committee of ...
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.


Sensation

The sensation of weight is caused by the force exerted by fluids in the
vestibular system The vestibular system, in vertebrates, is a sensory system that creates the sense of balance and spatial orientation for the purpose of coordinating movement with balance. Together with the cochlea, a part of the auditory system, it constitutes ...
, a three-dimensional set of tubes in the inner
ear An ear is the organ that enables hearing and, in mammals, body balance using the vestibular system. In mammals, the ear is usually described as having three parts—the outer ear, the middle ear and the inner ear. The outer ear consists of ...
. It is actually the sensation of
g-force The gravitational force equivalent, or, more commonly, g-force, is a measurement of the type of force per unit mass – typically acceleration – that causes a perception of weight, with a g-force of 1 g (not gram in mass measure ...
, regardless of whether this is due to being stationary in the presence of gravity, or, if the person is in motion, the result of any other forces acting on the body such as in the case of acceleration or deceleration of a lift, or centrifugal forces when turning sharply.


Measuring

Weight is commonly measured using one of two methods. A
spring scale A spring scale, spring balance or newton meter is a type of mechanical force gauge or weighing scale. It consists of a spring fixed at one end with a hook to attach an object at the other. It works in accordance with Hooke's Law, which states th ...
or hydraulic or pneumatic scale measures local weight, the local
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...
of
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
on the object (strictly ''apparent'' weight force). Since the local force of gravity can vary by up to 0.5% at different locations, spring scales will measure slightly different weights for the same object (the same mass) at different locations. To standardize weights, scales are always calibrated to read the weight an object would have at a nominal
standard gravity The standard acceleration due to gravity (or standard acceleration of free fall), sometimes abbreviated as standard gravity, usually denoted by or , is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. ...
of 9.80665m/s2 (approx. 32.174ft/s2). However, this calibration is done at the factory. When the scale is moved to another location on Earth, the force of gravity will be different, causing a slight error. So to be highly accurate and legal for commerce,
spring scale A spring scale, spring balance or newton meter is a type of mechanical force gauge or weighing scale. It consists of a spring fixed at one end with a hook to attach an object at the other. It works in accordance with Hooke's Law, which states th ...
s must be re-calibrated at the location at which they will be used. A ''
balance Balance or balancing may refer to: Common meanings * Balance (ability) in biomechanics * Balance (accounting) * Balance or weighing scale * Balance as in equality or equilibrium Arts and entertainment Film * ''Balance'' (1983 film), a Bulgarian ...
'' 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 A lever is a simple machine consisting of a beam or rigid rod pivoted at a fixed hinge, or ''fulcrum''. A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, load and effort, the lever is div ...
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 Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
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, but on the Moon, for example, it would give the same reading as on Earth. Some balances are 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 is generally 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; and
tare weight Tare weight , sometimes called unladen weight, is the weight of an empty vehicle or container. By subtracting tare weight from gross weight ( laden weight), one can determine the weight of the goods carried or contained (the net weight). Etymol ...
is the weight of the packaging alone.


Relative weights on the Earth and other celestial bodies

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. The “surface” is taken to mean the cloud tops of the
gas giants A gas giant is a giant planet composed mainly of hydrogen and helium. Gas giants are also called failed stars because they contain the same basic elements as a star. Jupiter and Saturn are the gas giants of the Solar System. The term "gas giant ...
(Jupiter, Saturn, Uranus and Neptune). For the Sun, the surface is taken to mean the
photosphere The photosphere is a star's outer shell from which light is radiated. The term itself is derived from Ancient Greek roots, φῶς, φωτός/''phos, photos'' meaning "light" and σφαῖρα/''sphaira'' meaning "sphere", in reference to it ...
. 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.


See also

* *
Tare weight Tare weight , sometimes called unladen weight, is the weight of an empty vehicle or container. By subtracting tare weight from gross weight ( laden weight), one can determine the weight of the goods carried or contained (the net weight). Etymol ...
* the English unit


Notes


References

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