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重量

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重量
Weeghaak.JPG
用來測量物體重量的弹簧秤
常見符號
國際單位 牛頓(N)
其他單位
磅力 (lbf)
基本單位 kg⋅m⋅s−2
單位因次
外延?
內含?
守恆?
從其他物理量的推衍
因次

科学工程学上,物體的重量指的通常是重力作用在它身上的[1][2]重量是向量,它的量(純量)一般用斜體 表示。重量是質量 和當地重力加速度 的乘積[3],即為:。重力的计量单位一樣,也就是国际单位制SI)的「牛頓」。舉例而言,一件質量為一公斤的物體在地球表面重9.8牛頓,而在月球上則重9.8牛頓的六分之一。根據這個定義,若要一個物體沒有重量,原則上只有無限遠離所有其他具有質量的物體才可能發生。雖然科學上重量和質量是不同的量,日常生活中常會將兩者混用。例如轉換或比較以磅力為單位的力和以公斤為單位的質量,反之亦然。[4]

牛頓物理學和工程學也有個傳統:視一物體的重量為其秤起來的重量。這裡的重量是施在一物上的反作用力。一般而言,測量物體的重量時,物體會被放置在相對於地球處於靜止狀態的秤上,而這個定義也能延伸到其他的運動狀態。因此,自由落體的物體重量為零。這第二種重量的定義,允許地面上的物體處於失重狀態。若忽略空氣阻力艾薩克牛頓那顆著名的蘋果從樹上掉下來接觸地面之前是沒有重量的。

另外,根據相对论,重力是时空彎曲的結果。教學界已經為「如何向學生定義重量」爭論超過半世紀。目前的情況是多種概念並存,視情況使用不同概念。[2]

歷史[编辑]

公元前六世紀前後的古希腊官方青銅器(標示重量用),展示於雅典的古代亞哥拉博物館
秤穀類(Weighing Grain)。來自巴布林回憶錄英语Baburnama[5]

有關「輕」、「重」概念的討論可以追溯至古希臘的哲學家。輕重曾被視為物體內在的性質。柏拉图將重量描述為物體尋找同類的自然傾向。對亞里斯多德而言,輕重則代表恢復基本元素(空氣、土、火、水)的自然秩序的傾向。他將「重」歸因於土,而「輕」歸因於火。阿基米德將重量視為與浮力相反的量,因為這兩者決定了物體會浮起來或沉下去。而欧几里得給出了重量的第一個操作定義:重量是一物和他物相比的輕重,可用天秤測量。比起操作定義,用秤測量重量的歷史自有文字記載就開始了。[2]

根據亞里斯多德,重量是物體墜落的直接原因,其墜落速率應與重量成正比。後來,中世紀學者發現物體墜落的速率隨時間增加。為了維持這種因果關係,重量的概念被修改,分成兩部分:靜止的重量(still weight)和因重力導致的重量(actual gravity)。前者為物體的本質,後者反應了墜落速率增加的原因。「重力導致的重量」這概念之後被让·布里丹的「衝力」取代。其中衝力為动量的前身。[2]

哥白尼世界觀英语Copernican heliocentrism的興起重振了「同類相吸」的想法(柏拉圖),以解釋天體間的互相吸引。17世紀,伽利略在重量的觀念上取得重大進展。他提出一種測量方法,來衡量運動中的物體和靜止物體的重量差異。最終,他認爲物體的重量與物質的量成正比,而非速率(亞里斯多德)。[2]

牛頓[编辑]

牛頓運動定律萬有引力定律的引入,進一步發展了重量的概念。重量和质量(物質的量)被區分開來。質量被認為是物體的基本性質,與其慣性相關;而重量則是重力作用於物體的結果,與物體的情況有關。特別的是,牛頓認為重量是相對的,是一對物體間的性質。例如,他曾寫道:「行星們『對太陽的重量』必須是它們物質的量」[註 1]。牛頓對重量的操作定義為:它與阻礙物體下降的力相反、值相等。[2]

牛頓認為時間和空間是絕對的,這讓他有「真實的」(ture,對應於 relative,「相對的」)位置或真實的速度這類的概念。他也知道秤量的重量會受浮力等環境因素影響,因此引入了「視重」(apparent weight)這個詞來表達因不完善測量條件造成的假重量,以區隔由重力定義的「真實重量」。這裡的視重和現代的不太一樣,現代的視重通常與慣性力有關,例如用來解釋地理上緯度和離心力的關係。[2]

相對論[编辑]

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[编辑]

這輛火箭車英语top fuel能在0.86秒內從0加速到每小時160公里,水平加速度達5.3。結合車輛靜止時垂直向下的重力,由勾股定理可知,G力將達5.4。若使用操作定義,G力將改變駕駛的重量;如果使用重力定義,駕駛的重量則不因車輛移動而改變。

「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[编辑]

重量最常見的定義為「重力作用在物體上的力」,可在入門等級的物理教科書中找到。[1][8]公式通常可表達為,其中為重量,為物體質量,重力加速度

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]

這項決議將重量定義為向量(由於力是向量)。然而,一些教科書使用了下列定義,將重量當成純量:

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

不同地點的重力加速度不一樣。有時會直接使用標準重力提供的標準值[10]

量值等於牛頓的力也會寫為 kg-wtm kilogram weight 的縮寫)。[13]

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.

操作定義[编辑]

重量的操作定義為「秤重」物體得到的重量,也就是「支撐物體的」。[6]

ISO定義[编辑]

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

,
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[编辑]

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[编辑]

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 moments英语Moment (physics) acting on it sum to zero).

In modern scientific usage, weight and mass are fundamentally different quantities: mass is an intrinsic英语Intrinsic and extrinsic properties 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]

地點 緯度 m/s2
赤道 9.7803
悉尼 33°52′ S 9.7968
阿伯丁 57°9′ N 9.8168
北极点 90° N 9.8322

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[编辑]

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[编辑]

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.

延伸閱讀[编辑]

註釋[编辑]

  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[编辑]

  1. ^ 1.0 1.1 Richard C. Morrison. Weight and gravity - the need for consistent definitions. The Physics Teacher英语The Physics Teacher. 1999, 37: 51. Bibcode:1999PhTea..37...51M. doi:10.1119/1.880152. 
  2. ^ 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 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. ^ 3.0 3.1 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. ^ 4.0 4.1 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. ^ 6.0 6.1 Allen L. King. Weight and weightlessness. American Journal of Physics英语American Journal of Physics. 1963, 30: 387. Bibcode:1962AmJPh..30..387K. doi:10.1119/1.1942032. 
  7. ^ 7.0 7.1 A. P. French. On weightlessness. American Journal of Physics英语American Journal of Physics. 1995, 63: 105–106. Bibcode:1995AmJPh..63..105F. doi:10.1119/1.17990. 
  8. ^ 8.0 8.1 Galili, I.; Lehavi, Y. The importance of weightlessness and tides in teaching gravitation (PDF). American Journal of Physics英语American Journal of Physics. 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. ^ 10.0 10.1 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. ^ 17.0 17.1 17.2 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).