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On 25 August 1609, Galileo Galilei demonstrated his first telescope to a group of Venetian merchants, and in early January 1610, Galileo observed four dim objects near Jupiter, which he mistook for stars. However, after a few days of observation, Galileo realized that these "stars" were in fact orbiting Jupiter. These four objects (later named the Galilean moons in honor of their discoverer) were the first celestial bodies observed to orbit something other than the Earth or Sun. Galileo continued to observe these moons over the next eighteen months, and by the middle of 1611, he had obtained remarkably accurate estimates for their periods.
where W is the weight of the collection of similar objects and n is the number of objects in the collection. Proportionality, by definition, implies that two values have a constant ratio: Work done: Work done by a constant force is the work done by a constant force of 2 Newtons on an object having a mass of 3 kilograms. As stated previously, the mole is a unit that relates a variety of measurements to one another and to chemically-significantquantities. The previous sections of this chapter have defined and discussed Avogadro's number, 6.02× 10 23, which quantifies the number of individual atoms, ions, or moleculesthat are present within a substance, and" component within" molar quantities, whichindicate the relative ratios of the elements that are present within a compound or molecule. There are several distinct phenomena that can be used to measure mass. Although some theorists have speculated that some of these phenomena could be independent of each other, [2] current experiments have found no difference in results regardless of how it is measured: 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:In mechanics’ mass, length, and time are selected as three base dimensions from which other derived quantities such as velocity, force, energy are derived. The fundamental units are expressed as Galilean free fall Galileo Galilei (1636) Distance traveled by a freely falling ball is proportional to the square of the elapsed time. 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}}.} 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).
Although inertial mass, passive gravitational mass and active gravitational mass are conceptually distinct, no experiment has ever unambiguously demonstrated any difference between them. In classical mechanics, Newton's third law implies that active and passive gravitational mass must always be identical (or at least proportional), but the classical theory offers no compelling reason why the gravitational mass has to equal the inertial mass. That it does is merely an empirical fact. As stated earlier, the constant force is directly proportional to that of acceleration produced in a body. Moreover, the direction of the constant force will be in the direction of the acceleration. Inertial mass measures an object's resistance to being accelerated by a force (represented by the relationship F = ma). Donnerstein, Edward. "Mass Media, General View." Encyclopedia of Violence, Peace, & Conflict (Second Edition). Ed. Kurtz, Lester. Oxford: Academic Press, 2008. 1184-92. Print. An object which has constant restoring force regardless of displacement. This is derived from Newton’s second law of motion, which states:According to relativity, mass is nothing else than the rest energy of a system of particles, meaning the energy of that system in a reference frame where it has zero momentum. Mass can be converted into other forms of energy according to the principle of mass–energy equivalence. This equivalence is exemplified in a large number of physical processes including pair production, beta decay and nuclear fusion. Pair production and nuclear fusion are processes in which measurable amounts of mass are converted to kinetic energy or vice versa. the dalton (Da), equal to 1/12 of the mass of a free carbon-12 atom, approximately 1.66 ×10 −27kg. [note 2]
A constant force is defined as the force applied in a constant manner on a particular object in a direction parallel to that of the direction of the acceleration produced in the body.
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Passive gravitational mass is a measure of the strength of an object's interaction with a gravitational field. Passive gravitational mass is determined by dividing an object's weight by its free-fall acceleration. Two objects within the same gravitational field will experience the same acceleration; however, the object with a smaller passive gravitational mass will experience a smaller force (less weight) than the object with a larger passive gravitational mass. Galileo had shown that objects in free fall under the influence of the Earth's gravitational field have a constant acceleration, and Galileo's contemporary, Johannes Kepler, had shown that the planets follow elliptical paths under the influence of the Sun's gravitational mass. However, Galileo's free fall motions and Kepler's planetary motions remained distinct during Galileo's lifetime. In everyday usage, mass and " weight" are often used interchangeably. For instance, a person's weight may be stated as 75kg. In a constant gravitational field, the weight of an object is proportional to its mass, and it is unproblematic to use the same unit for both concepts. But because of slight differences in the strength of the Earth's gravitational field at different places, the distinction becomes important for measurements with a precision better than a few percent, and for places far from the surface of the Earth, such as in space or on other planets. Conceptually, "mass" (measured in kilograms) refers to an intrinsic property of an object, whereas "weight" (measured in newtons) measures an object's resistance to deviating from its current course of free fall, which can be influenced by the nearby gravitational field. No matter how strong the gravitational field, objects in free fall are weightless, though they still have mass. [6]
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