trọng lượng kí hiệu là gì

This page is about the physical concept. In law, commerce, and in colloquial usage weight may also refer vĩ đại mass. For other uses see Weight (disambiguation).

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A spring scale measures the weight of an object.

Common symbols

SI unitnewton (N)

Other units

pound-force (lbf)
In SI base unitskg⋅m⋅s−2

Derivations from
other quantities


In science and engineering, the weight of an object is the force acting on the object due vĩ đại acceleration or gravity.[1][2][3]

Some standard textbooks[4] define weight as a vector quantity, the gravitational force acting on the object. Others[5][6] define weight as a scalar quantity, the magnitude of the gravitational force. Yet others[7] define it as the magnitude of the reaction force exerted on a body toàn thân 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 miễn phí fall, the weight would be zero. In this sense of weight, terrestrial objects can be weightless: ví if one ignores air resistance, one could say the legendary táo Apple falling from the tree, on its way vĩ đại 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 vĩ đại mass in kilograms and vice versa).[8]

Further complications in elucidating the various concepts of weight have vĩ đại tự with the theory of relativity according vĩ đại 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 vĩ đại define weight for their students. The current situation is that a multiple phối of concepts co-exist and find use in their various contexts.[2]


Ancient Greek official bronze weights dating from around the 6th century BC, exhibited in the Ancient Agora Museum in Athens, housed in the Stoa of Attalus.
Weighing grain, from the Babur-namah[9]

Discussion of the concepts of heaviness (weight) and lightness (levity) date back vĩ đại the ancient Greek philosophers. These were typically viewed as inherent properties of objects. Plato described weight as the natural tendency of objects vĩ đại seek their kin. To Aristotle, weight and levity represented the tendency vĩ đại restore the natural order of the basic elements: air, earth, fire and water. He ascribed absolute weight vĩ đại earth and absolute levity vĩ đại fire. Archimedes saw weight as a quality opposed vĩ đại 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 vĩ đại another, as measured by a balance."[2] Operational balances (rather than vãn definitions) had, however, been around much longer.[10]

According vĩ đại Aristotle, weight was the direct cause of the falling motion of an object, the tốc độ of the falling object was supposed vĩ đại be directly proportionate vĩ đại the weight of the object. As medieval scholars discovered that in practice the tốc độ of a falling object increased with time, this prompted a change vĩ đại the concept of weight vĩ đại maintain this cause-effect relationship. Weight was split into a "still weight" or pondus, which remained constant, and the actual gravity or gravitas, which changed as the object fell. The concept of gravitas was eventually replaced by Jean Buridan's impetus, a precursor vĩ đại momentum.[2]

The rise of the Copernican view of the world led vĩ đại the resurgence of the Platonic idea that lượt thích 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 vĩ đại measure the difference between the weight of a moving object and an object at rest. Ultimately, he concluded weight was proportionate vĩ đại the amount of matter of an object, not the tốc độ of motion as supposed by the Aristotelean view of physics.[2]


The introduction of Newton's laws of motion and the development of Newton's law of universal gravitation led vĩ đại considerable further development of the concept of weight. Weight became fundamentally separate from mass. Mass was identified as a fundamental property of objects connected vĩ đại 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 vĩ đại be relative vĩ đại another object causing the gravitational pull, e.g. the weight of the Earth towards the Sun.[2]

Newton considered time and space vĩ đại be absolute. This allowed him vĩ đại consider concepts as true position and true velocity.[clarification needed] 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 vĩ đại the true weight defined by gravity.[2]

Although Newtonian physics made a clear distinction between weight and mass, the term weight continued vĩ đại be commonly used when people meant mass. This led the 3rd General Conference on Weights and Measures (CGPM) of 1901 vĩ đại officially declare "The word weight denotes a quantity of the same nature as a force: the weight of a body toàn thân is the product of its mass and the acceleration due vĩ đại gravity", thus distinguishing it from mass for official usage.


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 vĩ đại an ambiguity as vĩ đại 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, vĩ đại considerable debate in the teaching community as how vĩ đại define weight for their students, choosing between a nominal definition of weight as the force due vĩ đại gravity or an operational definition defined by the act of weighing.[2]


This top-fuel dragster can accelerate from zero vĩ đại 160 kilometres per hour (99 mph) in 0.86 seconds. This is a horizontal acceleration of 5.3 g. Combined with the vertical g-force in the stationary case the Pythagorean theorem yields a g-force of 5.4 g. It is this g-force that causes the driver's weight if one uses the operational definition. If one uses the gravitational definition, the driver's weight is unchanged by the motion of the xế hộp.

Several definitions exist for weight, not all of which are equivalent.[3][11][12][13]

Gravitational definition[edit]

The most common definition of weight found in introductory physics textbooks defines weight as the force exerted on a body toàn thân by gravity.[1][13] This is often expressed in the formula 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:

The word weight denotes a quantity of the same nature[Note 1] as a force: the weight of a body toàn thân is the product of its mass and the acceleration due vĩ đại gravity.

— Resolution 2 of the 3rd General Conference on Weights and Measures[15][16]

This resolution defines weight as a vector, since force is a vector quantity. However, some textbooks also take weight vĩ đại be a scalar by defining:

The weight W of a body toàn thân is equal vĩ đại the magnitude Fg of the gravitational force on the body toàn thân.[17]

The gravitational acceleration varies from place vĩ đại place. Sometimes, it is simply taken vĩ đại have a standard value of 9.80665 m/s2, which gives the standard weight.[15]

The force whose magnitude is equal vĩ đại mg newtons is also known as the m kilogram weight (which term is abbreviated vĩ đại kg-wt)[18]

Left: A 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 balance scale indirectly measures mass, by comparing an object vĩ đại references. On the Moon, an object would give the same reading, because the object and references would both become lighter.

Operational definition[edit]

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.[11] Since W is the downward force on the body toàn thân by the centre of earth and there is no acceleration in the body toàn thân, there exists an opposite and equal force by the tư vấn on the body toàn thân. Also it is equal vĩ đại the force exerted by the body toàn thân on its tư vấn 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 miễn phí fall exerts little if any force on its tư vấn, a situation that is commonly referred vĩ đại as weightlessness. However, being in miễn phí fall does not affect the weight according vĩ đại the gravitational definition. Therefore, the operational definition is sometimes refined by requiring that the object be at rest.[citation needed] However, this raises the issue of defining "at rest" (usually being at rest with respect vĩ đại the Earth is implied by using standard gravity).[citation needed] 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 vĩ đại have zero weight.

ISO definition[edit]

In the ISO International standard ISO 80000-4:2006,[19] 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:


where m is mass and g is local acceleration of miễn phí fall.


  • When the reference frame is Earth, this quantity comprises not only the local gravitational force, but also the local centrifugal force due vĩ đại 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 vĩ đại 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.[12] If the specified frame is the surface of the Earth, the weight according vĩ đại the ISO and gravitational definitions differ only by the centrifugal effects due vĩ đại the rotation of the Earth.

Apparent weight[edit]

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 vĩ đại as the apparent weight of the object. 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.[20] The apparent weight may be similarly affected by levitation and mechanical suspension. When the gravitational definition of weight is used, the operational weight measured by an accelerating scale is often also referred vĩ đại as the apparent weight.[21]


An object with mass m resting on a surface and the corresponding miễn phí body toàn thân diagram of just the object showing the forces acting on it. The magnitude of force that the table is pushing upward on the object (the N vector) is equal vĩ đại the downward force of the object's weight (shown here as mg, as weight is equal vĩ đại the object's mass multiplied with the acceleration due vĩ đại gravity): because these forces are equal, the object is in a state of equilibrium (all the forces and moments acting on it sum vĩ đại zero).

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.[8][22] 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 vĩ đại its mass. For example, object A weighs 10 times as much as object B, ví therefore the mass of object A is 10 times greater than vãn that of object B. This means that an object's mass can be measured indirectly by its weight, and ví, for everyday purposes, weighing (using a weighing scale) is an entirely acceptable way of measuring mass. Similarly, a balance measures mass indirectly by comparing the weight of the measured item vĩ đại that of an object(s) of known mass. Since the measured item and the comparison mass are in virtually the same location, ví experiencing the same gravitational field, the effect of varying gravity does not affect the comparison or the resulting measurement.

The Earth's gravitational field is not uniform but can vary by as much as 0.5%[23] at different locations on Earth (see Earth's gravity). These variations alter the relationship between weight and mass, and must be taken into trương mục in high-precision weight measurements that are intended vĩ đại indirectly measure mass. Spring scales, which measure local weight, must be calibrated at the location at which the objects will be used vĩ đại show this standard weight, vĩ đại be legal for commerce.[citation needed]

This table shows the variation of acceleration due vĩ đại gravity (and hence the variation of weight) at various locations on the Earth's surface.[24]

Location Latitude m/s2 Absolute difference from equator Percentage difference from equator
Equator 9.7803 0.0000 0%
Sydney 33°52′ S 9.7968 0.0165 0.17%
Aberdeen 57°9′ N 9.8168 0.0365 0.37%
North Pole 90° N 9.8322 0.0519 0.53%

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

In a different gravitational field, for example, on the surface of the Moon, an object can have a significantly different weight than vãn 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 vĩ đại 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 when visiting the Moon.

SI units[edit]

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 (N) – a derived unit which can also be expressed in SI base units as kg⋅m/s2 (kilograms times metres per second squared).[22]

In commercial and everyday use, the term "weight" is usually used vĩ đại 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 (kg).[22]

Pound and other non-SI units[edit]

In United States customary units, the pound can be either a unit of force or a unit of mass.[25] Related units used in some distinct, separate subsystems of units include the poundal and the slug. The poundal is defined as the force necessary vĩ đại accelerate an object of one-pound mass at 1 ft/s2, and is equivalent vĩ đại about 1/32.2 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 vĩ đại about 32.2 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 vĩ đại 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.


The sensation of weight is caused by the force exerted by fluids in the vestibular system, a three-dimensional phối of tubes in the inner ear.[dubious – discuss] It is actually the sensation of g-force, regardless of whether this is due vĩ đại being stationary in the presence of gravity, or, if the person is in motion, the result of any other forces acting on the body toàn thân such as in the case of acceleration or deceleration of a lift, or centrifugal forces when turning sharply.


A weighbridge, used for weighing trucks

Weight is commonly measured using one of two methods. A spring scale or hydraulic or pneumatic scale measures local weight, the local force of gravity on the object (strictly apparent weight force). Since the local force of gravity can vary by up vĩ đại 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 vĩ đại read the weight an object would have at a nominal standard gravity of 9.80665 m/s2 (approx. 32.174 ft/s2). However, this calibration is done at the factory. When the scale is moved vĩ đại another location on Earth, the force of gravity will be different, causing a slight error. So vĩ đại be highly accurate and legal for commerce, spring scales must be re-calibrated at the location at which they will be used.

A balance on the other hand, compares the weight of an unknown object in one scale pan vĩ đại the weight of standard masses in the other, using a lever mechanism – a lever-balance. The standard masses are often referred vĩ đại, 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, ví 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 vĩ đại 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 trang web.

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

Relative weights on the Earth and other celestial bodies[edit]

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 vĩ đại mean the cloud tops of the gas giants (Jupiter, Saturn, Uranus and Neptune). For the Sun, the surface is taken vĩ đại 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 vĩ đại the actual gravity that would be experienced near the poles.

Xem thêm: trần tình lệnh

Body Multiple of
Earth gravity
Surface gravity
Sun 27.90 274.1
Mercury 0.3770 3.703
Venus 0.9032 8.872
Earth 1 (by definition) 9.8226[26]
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

See also[edit]

  • Human body toàn thân weight – Person's mass or weight
  • Tare weight
  • weight – Unit of weight the English unit
  • Weight (object)


  1. ^ The phrase "quantity of the same nature" is a literal translation of the 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.[14]


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  2. ^ a b c d e f g h Igal Galili (2001). "Weight versus gravitational force: historical and educational perspectives". International Journal of Science Education. 23 (10): 1073. Bibcode:2001IJSEd..23.1073G. doi:10.1080/09500690110038585. S2CID 11110675.
  3. ^ a b Gat, Uri (1988). "The weight of mass and the mess of weight". In Richard Alan Strehlow (ed.). Standardization of Technical Terminology: Principles and Practice – second volume. ASTM International. pp. 45–48. ISBN 978-0-8031-1183-7.
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  8. ^ a b 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 vĩ đại 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 vĩ đại be 5 kg," is correct.
  9. ^ Sur Das (1590s). "Weighing Grain". Baburnama.
  10. ^ Archived 2013-02-28 at the Wayback Machine accessed 29 March 2013.
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  12. ^ a b A. P.. French (1995). "On weightlessness". American Journal of Physics. 63 (2): 105–106. Bibcode:1995AmJPh..63..105F. doi:10.1119/1.17990.
  13. ^ a b Galili, I.; Lehavi, Y. (2003). "The importance of weightlessness and tides in teaching gravitation" (PDF). American Journal of Physics. 71 (11): 1127–1135. Bibcode:2003AmJPh..71.1127G. doi:10.1119/1.1607336.
  14. ^ Working Group 2 of the Joint Committee for Guides in Metrology (JCGM/WG 2) (2008). International vocabulary of metrology – Basic and general concepts and associated terms (VIM) – Vocabulaire international de métrologie – Concepts fondamentaux et généraux et termes associés (VIM) (PDF) (JCGM 200:2008) (in English and French) (3rd ed.). BIPM. Note 3 vĩ đại Section 1.2.
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  19. ^ ISO 80000-4:2006, Quantities and units - Part 4: Mechanics
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  22. ^ a b c A. Thompson & B. N. Taylor (March 3, 2010) [July 2, 2009]. "The NIST Guide for the use of the International System of Units, Section 8: Comments on Some Quantities and Their Units". Special Publication 811. NIST. Retrieved 2010-05-22.
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  24. ^ Clark, John B (1964). Physical and Mathematical Tables. Oliver and Boyd.
  25. ^ "Common Conversion Factors, Approximate Conversions from U.S. Customary Measures vĩ đại Metric". Nist. National Institute of Standards and Technology. 13 January 2010. Retrieved 2013-09-03.
  26. ^ This value excludes the adjustment for centrifugal force due vĩ đại Earth’s rotation and is therefore greater than vãn the 9.80665 m/s2 value of standard gravity.