重量

本条目介绍的是一个物理概念。口语上，「重量」也可能指「质量」。

在科学与工程学上，物体的重量指的通常是重力作用在它身上的力。重量是向量，它的量（纯量）一般用斜体 <math>W</math> 表示。重量是质量 <math>m</math> 和当地重力加速度 <math>g</math> 的乘积，即为：<math>W=mg</math>。重力的计量单位和力一样，也就是国际单位制（SI）的「牛顿」。举例而言，一件质量为一公斤的物体在地球表面重9.8牛顿，而在月球上则重9.8牛顿的六分之一。根据这个定义，若要一个物体没有重量，原则上只有无限远离所有其他具有质量的物体才可能发生。虽然科学上重量和质量是不同的量，日常生活中常会将两者混用。例如转换或比较以磅力为单位的力和以公斤为单位的质量，反之亦然。

牛顿物理学和工程学也有个传统：视一物体的重量为其秤起来的重量。这裡的重量是施在一物上的反作用力。一般而言，测量物体的重量时，物体会被放置在相对于地球处于静止状态的秤上，而这个定义也能延伸到其他的运动状态。因此，自由落体的物体重量为零。这第二种重量的定义，允许地面上的物体处于失重状态。若忽略空气阻力，艾萨克牛顿那颗著名的苹果从树上掉下来接触地面之前是没有重量的。

另外，根据相对论，重力是时空弯曲的结果。教学界已经为「如何向学生定义重量」争论超过半世纪。目前的情况是多种概念并存，视情况使用不同概念。

目录

历史

有关「轻」、「重」概念的讨论可以追溯至古希腊的哲学家。轻重曾被视为物体内在的性质。柏拉图将重量描述为物体寻找同类的自然倾向。对亚里斯多德而言，轻重则代表恢复基本元素（空气、土、火、水）的自然秩序的倾向。他将「重」归因于土，而「轻」归因于火。阿基米德将重量视为与浮力相反的量，因为这两者决定了物体会浮起来或沉下去。而欧几里得给出了重量的第一个操作定义：重量是一物和他物相比的轻重，可用天秤测量。比起操作定义，用秤测量重量的历史自有文字记载就开始了。

根据亚里斯多德，重量是物体坠落的直接原因，其坠落速率应与重量成正比。后来，中世纪学者发现物体坠落的速率随时间增加。为了维持这种因果关系，重量的概念被修改，分成两部分：静止的重量（still weight）和因重力导致的重量（actual gravity）。前者为物体的本质，后者反应了坠落速率增加的原因。「重力导致的重量」这概念之后被让·布里丹的「衝力」取代。其中衝力为动量的前身。

哥白尼世界观的兴起重振了「同类相吸」的想法（柏拉图），以解释天体间的互相吸引。17世纪，伽利略在重量的观念上取得重大进展。他提出一种测量方法，来衡量运动中的物体和静止物体的重量差异。最终，他认爲物体的重量与物质的量成正比，而非速率（亚里斯多德）。

牛顿

牛顿运动定律和万有引力定律的引入，进一步发展了重量的概念。重量和质量（物质的量）被区分开来。质量被认为是物体的基本性质，与其惯性相关；而重量则是重力作用于物体的结果，与物体的情况有关。特别的是，牛顿认为重量是相对的，是一对物体间的性质。例如，他曾写道：「行星们『对太阳的重量』必须是它们物质的量」。牛顿对重量的操作定义为：它与阻碍物体下降的力相反、值相等。

牛顿认为时间和空间是绝对的，这让他有「真实的」（ture，对应于 relative，「相对的」）位置或真实的速度这类的概念。他也知道秤量的重量会受浮力等环境因素影响，因此引入了「视重」（apparent weight）这个词来表达因不完善测量条件造成的假重量，以区隔由重力定义的「真实重量」。这裡的视重和现代的不太一样，现代的视重通常与惯性力有关，例如用来解释地理上纬度和离心力的关系。

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。

定义

「重量」有数种不同的定义，互相不见得等价。

重力定义

重量最常见的定义为「重力作用在物体上的力」，可在入门等级的物理教科书中找到。公式通常可表达为<math>W = mg</math>，其中<math>W</math>为重量，<math>m</math>为物体质量，<math>g</math>为重力加速度。

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： Template:Quotation 这项决议将重量定义为向量（由于力是向量）。然而，一些教科书使用了下列定义，将重量当成纯量： Template:Quotation

不同地点的重力加速度不一样。有时会直接使用标准重力提供的标准值<math>9.80665 m/s^2</math>。

量值等于<math>mg</math>牛顿的力也会写为 kg-wt（m kilogram weight 的缩写）。

Measuring weight versus mass

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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.

操作定义

重量的操作定义为「秤重」物体得到的重量，也就是「支撑物体的力」。

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. 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.

视重

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. 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 to as the apparent weight.

质量

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. 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% 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.

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

地点	纬度	m/s2
赤道	0°	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制单位

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).

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).

其他单位

In United States customary units, the pound can be either a unit of force or a unit of mass. Related units used in some distinct, separate subsystems of units include the 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.

延伸阅读

• 体重

参考资料

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