# 重量

${\displaystyle W}$

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

## 历史

### 相对论

20世纪，牛顿的绝对时空观受到相对论的挑战。爱因斯坦的等效原理认为不同参考系的观察者是平等的，这会使得观察者无法区分自己是处在加速中的参考系或是重力场之中，进而促使“重力”的概念与“重量”分离。至此，重量这个概念在科学上的历史可视为终结了。不过在日常生活和物理教学上，重量的概念依然有用。相对论的引入，使教学界自1960年代以来对“如何向学生定义重量”进行了相当多辩论。教师们可以选择使用“因重力引起的力”（名义定义）或是“秤重”这个行为（操作定义）来定义重量。[2]

## 定义

“重量”有数种不同的定义，互相不见得等价。[3][6][7][8]

### 重力定义

1901年，第三届国际度量衡大会（CGPM）确立了他们正式的重量定义：

"The word weight denotes a quantity of the same nature[注 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]

### ISO定义

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)

## 注释

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]

## 参考资料

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）.