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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. 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). A constant force is defined as the force applied in a concerted manner over an object. At the same time, the direction of the constant force is parallel to that of the direction of the acceleration produced in the body. However, the work done by a constant force is denoted by the product of the acceleration produced in the body as well as the force applied on the body. Intermolecular force: The force that is applied between the molecules is called the intermolecular forces. These intermolecular forces are applied in a constant manner so as to maintain the stability of the molecule.

the electronvolt (eV), a unit of energy, used to express mass in units of eV/ c 2 through mass–energy equivalence 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: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: This says that the ratio of gravitational to inertial mass of any object is equal to some constant K if and only if all objects fall at the same rate in a given gravitational field. This phenomenon is referred to as the "universality of free-fall". In addition, the constant K can be taken as 1 by defining our units appropriately. 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: 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. Inertial mass is a measure of an object's resistance to acceleration when a force is applied. It is determined by applying a force to an object and measuring the acceleration that results from that force. An object with small inertial mass will accelerate more than an object with large inertial mass when acted upon by the same force. One says the body of greater mass has greater inertia.

Active gravitational mass determines the strength of the gravitational field generated by an object. Isaac Newton, Mathematical principles of natural philosophy, Definition I. Newtonian mass Earth's Moon In 1600 AD, Johannes Kepler sought employment with Tycho Brahe, who had some of the most precise astronomical data available. Using Brahe's precise observations of the planet Mars, Kepler spent the next five years developing his own method for characterizing planetary motion. In 1609, Johannes Kepler published his three laws of planetary motion, explaining how the planets orbit the Sun. In Kepler's final planetary model, he described planetary orbits as following elliptical paths with the Sun at a focal point of the ellipse. Kepler discovered that the square of the orbital period of each planet is directly proportional to the cube of the semi-major axis of its orbit, or equivalently, that the ratio of these two values is constant for all planets in the Solar System. [note 5] 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. DeFleur, Melvin L., and Everette E. Dennis. "Understanding Mass Communication." (Fifth Edition, 1991). Houghton Mifflin: New York.Buoyant force (Up-thrust): When a body is floating over liquid, it experiences a force of buoyancy, which acts in a constant manner to maintain the stability of the object over the liquid. 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: Galilean free fall Galileo Galilei (1636) Distance traveled by a freely falling ball is proportional to the square of the elapsed time. Pennington, Robert. "Mass Media Content as Cultural Theory." The Social Science Journal 49.1 (2012): 98-107. Print. The first experiments demonstrating the universality of free-fall were—according to scientific 'folklore'—conducted by Galileo obtained by dropping objects from the Leaning Tower of Pisa. This is most likely apocryphal: he is more likely to have performed his experiments with balls rolling down nearly frictionless inclined planes to slow the motion and increase the timing accuracy. Increasingly precise experiments have been performed, such as those performed by Loránd Eötvös, [7] using the torsion balance pendulum, in 1889. As of 2008 [update], no deviation from universality, and thus from Galilean equivalence, has ever been found, at least to the precision 10 −6. More precise experimental efforts are still being carried out. [8] Astronaut David Scott performs the feather and hammer drop experiment on the Moon.

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:Atomic weightand molecular weightare molar quantities that relate to the mass of an element or a compound, respectively. Therefore, the word " mass"is the first indicator word that is associated with applying one of these values in a problem-solving context. Alternatively, mass units, such as" grams,"" kilograms," or " milligrams," also serveasindicators for utilizing these molar relationships.