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W n n = W m m {\displaystyle {\frac {W_{n}}{n}}={\frac {W_{m}}{m}}} , or equivalently W n W m = n m . {\displaystyle {\frac {W_{n}}{W_{m}}}={\frac {n}{m}}.} the electronvolt (eV), a unit of energy, used to express mass in units of eV/ c 2 through mass–energy equivalence The force known as "weight" is proportional to mass and acceleration in all situations where the mass is accelerated away from free fall. For example, when a body is at rest in a gravitational field (rather than in free fall), it must be accelerated by a force from a scale or the surface of a planetary body such as the Earth or the Moon. This force keeps the object from going into free fall. Weight is the opposing force in such circumstances and is thus determined by the acceleration of free fall. On the surface of the Earth, for example, an object with a mass of 50kilograms weighs 491 newtons, which means that 491 newtons is being applied to keep the object from going into free fall. By contrast, on the surface of the Moon, the same object still has a mass of 50kilograms but weighs only 81.5newtons, because only 81.5 newtons is required to keep this object from going into a free fall on the moon. Restated in mathematical terms, on the surface of the Earth, the weight W of an object is related to its mass m by W = mg, where g = 9.80665m/s 2 is the acceleration due to Earth's gravitational field, (expressed as the acceleration experienced by a free-falling object). the solar mass ( M ☉), defined as the mass of the Sun, primarily used in astronomy to compare large masses such as stars or galaxies (≈ 1.99 ×10 30kg)
Inertial mass measures an object's resistance to being accelerated by a force (represented by the relationship F = ma). AU 3 y 2 = 3.986 ⋅ 10 14 m 3 s 2 {\displaystyle 1.2\pi Humans, at some early era, realized that the weight of a collection of similar objects was directly proportional to the number of objects in the collection: Galilean free fall Galileo Galilei (1636) Distance traveled by a freely falling ball is proportional to the square of the elapsed time. A stronger version of the equivalence principle, known as the Einstein equivalence principle or the strong equivalence principle, lies at the heart of the general theory of relativity. Einstein's equivalence principle states that within sufficiently small regions of space-time, it is impossible to distinguish between a uniform acceleration and a uniform gravitational field. Thus, the theory postulates that the force acting on a massive object caused by a gravitational field is a result of the object's tendency to move in a straight line (in other words its inertia) and should therefore be a function of its inertial mass and the strength of the gravitational field.
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the pound (lb), a unit of mass (about 0.45kg), which is used alongside the similarly named pound (force) (about 4.5N), a unit of force [note 3] For other situations, such as when objects are subjected to mechanical accelerations from forces other than the resistance of a planetary surface, the weight force is proportional to the mass of an object multiplied by the total acceleration away from free fall, which is called the proper acceleration. Through such mechanisms, objects in elevators, vehicles, centrifuges, and the like, may experience weight forces many times those caused by resistance to the effects of gravity on objects, resulting from planetary surfaces. In such cases, the generalized equation for weight W of an object is related to its mass m by the equation W = – ma, where a is the proper acceleration of the object caused by all influences other than gravity. (Again, if gravity is the only influence, such as occurs when an object falls freely, its weight will be zero). Active gravitational mass determines the strength of the gravitational field generated by an object. Passive gravitational mass measures the gravitational force exerted on an object in a known gravitational field.
In physical science, one may distinguish conceptually between at least seven different aspects of mass, or seven physical notions that involve the concept of mass. [5] Every experiment to date has shown these seven values to be proportional, and in some cases equal, and this proportionality gives rise to the abstract concept of mass. There are a number of ways mass can be measured or operationally defined: An early use of this relationship is a balance scale, which balances the force of one object's weight against the force of another object's weight. The two sides of a balance scale are close enough that the objects experience similar gravitational fields. Hence, if they have similar masses then their weights will also be similar. This allows the scale, by comparing weights, to also compare masses.the dalton (Da), equal to 1/12 of the mass of a free carbon-12 atom, approximately 1.66 ×10 −27kg. [note 2]
a large vessel of water placed in an elevated position; to the bottom of this vessel was soldered a pipe of small diameter giving a thin jet of water, which we collected in a small glass during the time of each descent, whether for the whole length of the channel or for a part of its length; the water thus collected was weighed, after each descent, on a very accurate balance; the differences and ratios of these weights gave us the differences and ratios of the times, and this with such accuracy that although the operation was repeated many, many times, there was no appreciable discrepancy in the results. [12] the mass of a particle, as identified with its inverse Compton wavelength ( 1cm −1 ≘ 3.52 ×10 −41kg) The particular equivalence often referred to as the "Galilean equivalence principle" or the " weak equivalence principle" has the most important consequence for freely falling objects. Suppose an object has inertial and gravitational masses m and M, respectively. If the only force acting on the object comes from a gravitational field g, the force on the object is:Consequently, historical weight standards were often defined in terms of amounts. The Romans, for example, used the carob seed ( carat or siliqua) as a measurement standard. If an object's weight was equivalent to 1728 carob seeds, then the object was said to weigh one Roman pound. If, on the other hand, the object's weight was equivalent to 144 carob seeds then the object was said to weigh one Roman ounce (uncia). The Roman pound and ounce were both defined in terms of different sized collections of the same common mass standard, the carob seed. The ratio of a Roman ounce (144 carob seeds) to a Roman pound (1728 carob seeds) was: The universality of free-fall only applies to systems in which gravity is the only acting force. All other forces, especially friction and air resistance, must be absent or at least negligible. For example, if a hammer and a feather are dropped from the same height through the air on Earth, the feather will take much longer to reach the ground; the feather is not really in free-fall because the force of air resistance upwards against the feather is comparable to the downward force of gravity. On the other hand, if the experiment is performed in a vacuum, in which there is no air resistance, the hammer and the feather should hit the ground at exactly the same time (assuming the acceleration of both objects towards each other, and of the ground towards both objects, for its own part, is negligible). This can easily be done in a high school laboratory by dropping the objects in transparent tubes that have the air removed with a vacuum pump. It is even more dramatic when done in an environment that naturally has a vacuum, as David Scott did on the surface of the Moon during Apollo 15.
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