重量

${\displaystyle W}$

• ${\displaystyle W=mg}$
• ${\displaystyle W=ma}$

歷史

相對論

20世紀，牛頓的絕對時空觀受到相對論的挑戰。愛因斯坦的等效原理認為不同參考系的觀察者是平等的，這會使得觀察者無法區分自己是處在加速中的參考系或是重力場之中，進而促使「重力」的概念與「重量」分離。至此，重量這個概念在科學上的歷史可視為終結了。不過在日常生活和物理教學上，重量的概念依然有用。相對論的引入，使教學界自1960年代以來對「如何向學生定義重量」進行了相當多辯論。教師們可以選擇使用「因重力引起的力」（名義定義）或是「秤重」這個行為（操作定義）來定義重量。[2]

定義

「重量」有數種不同的定義，互相不見得等價。[3][6][7][8]

重力定義

1901年，第三屆國際度量衡大會（CGPM）確立了他們正式的重量定義：

"The word weight denotes a quantity of the same nature[註 2] 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[10][11]

"The weight W of a body is equal to the magnitude Fg of the gravitational force on the body."[12]

Measuring weight versus mass
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 to references. On the Moon, an object would give the same reading, because the object and references would both become lighter.

ISO定義

In the ISO International standard ISO 80000-4(2006),[14] 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:

Definition

${\displaystyle F_{g}=mg\,}$,
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.[7] 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.

視重

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, 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.[15] The apparent weight may be similarly affected by levitation英语levitation 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.[16]

質量

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

In modern scientific usage, weight and mass are fundamentally different quantities: mass is an 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.[4][17] 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 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 (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 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, 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%[18] at different locations on Earth (see Earth's gravity). 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 scales, 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.[來源請求]

This table shows the variation of acceleration due to gravity (and hence the variation of weight) at various locations on the Earth's surface.[19]

The historic 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 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 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 extrinsic 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 when visiting the Moon.

SI制單位

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 meters per second squared).[17]

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 (kg).[17]

其他單位

In United States customary units, the pound can be either a unit of force or a unit of mass.[20] Related units used in some distinct, separate subsystems of units include the poundal英语poundal and the slug. The poundal is defined as the force necessary to accelerate an object of one-pound mass at 1 ft/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 1 ft/s2 when one pound-force is exerted on it, and is equivalent to 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 to 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.

註釋

1. ^ 原文："the weights of the planets towards the sun must be as their quantities of matter"
2. ^ 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.[9]

參考資料

1. Richard C. Morrison. Weight and gravity - the need for consistent definitions. . 1999, 37: 51. Bibcode:1999PhTea..37...51M. doi:10.1119/1.880152.
2. Igal Galili. Weight versus gravitational force: historical and educational perspectives. International Journal of Science Education. 2001, 23: 1073. Bibcode:2001IJSEd..23.1073G. doi:10.1080/09500690110038585.
3. Gat, Uri. The weight of mass and the mess of weight. (编) Richard Alan Strehlow. Standardization of Technical Terminology: Principles and Practice – second volume. ASTM International. 1988: 45–48. ISBN 978-0-8031-1183-7.
4. 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 5 kg," is correct.
5. ^ Sur Das. Weighing Grain. Baburnama. 1590s. （原始内容存档于2013-07-14）.
6. Allen L. King. Weight and weightlessness. . 1963, 30: 387. Bibcode:1962AmJPh..30..387K. doi:10.1119/1.1942032.
7. A. P. French. On weightlessness. . 1995, 63: 105–106. Bibcode:1995AmJPh..63..105F. doi:10.1119/1.17990.
8. Galili, I.; Lehavi, Y. The importance of weightlessness and tides in teaching gravitation (PDF). . 2003, 71 (11): 1127–1135. Bibcode:2003AmJPh..71.1127G. doi:10.1119/1.1607336.
9. ^ Working Group 2 of the Joint Committee for Guides in Metrology (JCGM/WG 2). 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) 3rd. BIPM. 2008. Note 3 to Section 1.2. （原始内容存档 (PDF)于2018-01-27） （English及French）.
10. Resolution of the 3rd meeting of the CGPM (1901). BIPM. （原始内容存档于2018-01-17）.
11. ^ Barry N. Taylor; Ambler Thompson (编). The International System of Units (SI) (PDF). NIST Special Publication 330 2008. NIST. 2008: 52. （原始内容 (PDF)存档于2017-06-22）.
12. ^ Halliday, David; Resnick, Robert; Walker, Jearl. Fundamentals of Physics 1 8th. Wiley. 2007: 95. ISBN 978-0-470-04473-5.
13. ^ Chester, W. Mechanics. London: George Allen & Unwin. 1979: 83. ISBN 0-04-510059-4.
14. ^ ISO 80000-4:2006, Quantities and units - Part 4: Mechanics
15. ^ Bell, F. Principles of mechanics and biomechanics. Stanley Thornes Ltd. 1998: 174–176. ISBN 978-0-7487-3332-3.
16. ^ Galili, Igal. Weight and gravity: teachers’ ambiguity and students’ confusion about the concepts. International Journal of Science Education. 1993, 15 (2): 149–162. Bibcode:1993IJSEd..15..149G. doi:10.1080/0950069930150204.
17. A. Thompson & B. N. Taylor. 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. 2010-03-03 [2009-07-02] [2010-05-22]. （原始内容存档于2018-01-30）.
18. ^ Hodgeman, Charles (编). Handbook of Chemistry and Physics 44th. Cleveland, USA: Chemical Rubber Publishing Co. 1961: 3480–3485.
19. ^ Clark, John B. Physical and Mathematical Tables. Oliver and Boyd. 1964.
20. ^ Common Conversion Factors, Approximate Conversions from U.S. Customary Measures to Metric. National Institute of Standards and Technology. [2018-01-30]. （原始内容存档于2018-01-30）.