# 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]

### ISO定義

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)

## 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. The Physics Teacher. 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. Richard Alan Strehlow (编). Standardization of Technical Terminology: Principles and Practice – second volume. ASTM International. 1988: 45–48 [2018-01-30]. ISBN 978-0-8031-1183-7. （原始内容存档于2021-04-29）.
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 [2018-01-30]. Bibcode:2003AmJPh..71.1127G. doi:10.1119/1.1607336. （原始内容存档 (PDF)于2021-01-16）.
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） （英语及法语）.
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 [2018-01-30]. ISBN 978-0-7487-3332-3. （原始内容存档于2021-04-28）.
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）.