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Mass is a fundamental concept in Physics , roughly corresponding to the intuitive idea of "how much matter there is in an object?". Mass is a central concept of Classical Mechanics and related subjects, and there are several definitions of mass within the framework of relativistic kinematics (see Mass In Special Relativity and Mass In General Relativity ). In the theory of relativity, the quantity Invariant Mass , which in concept is close to the classical idea of mass, does not vary between single observers in different Reference Frames . In informal everyday usage, mass is more commonly referred to as weight, but in physics and engineering, Weight strictly means the size of the gravitational pull on the object; that is, how heavy it is, measured in units of Force . In everyday situations, the mass of an object is proportional to its weight, which usually makes it unproblematic to use the same word for both. Distinguishing them becomes important for measurements with a precision better than a few percent, due to slight differences in the strength of the Earth's gravitational field at different places, and is essential when one considers places far from the surface of the Earth, such as in space or on other planets. UNITS OF MASS In the s (g), Tonne s, Pound s, Ounce s, Long and Short Ton s, Quintals , Slug s, Atomic Mass Unit s, Planck Mass es, Solar Mass es, and EV /'' C ''2. Because of the relativistic connection between Mass and energy (see Mass In Special Relativity ), it is possible to use any unit of energy as a unit of mass instead. For example, the eV energy unit based on the Electron Volt is normally used as a unit of mass (roughly 1.783 × 10-36 kg) in Particle Physics . A mass can sometimes also be expressed in terms of inverse length. Here one identifies the mass of a particle with its inverse Compton wavelength ( kg). Because the Gravitational Acceleration (g) is approximately constant on the surface of the Earth , and also because mass balances do not depend on the local value of g, a unit like the Pound is often used to measure ''either'' mass or Force (e.g. weight). When the pound is used as a measure of mass (where g does not enter in), it is officially in the English system defined in terms of the kg, as 1 lb = 0.453 592 37 kg (see Force ). In this case the English system unit of force is the Poundal . By contrast, when the pound is used as the unit of force, the English unit of mass is the Slug (mass) . For more information on the different units of mass, see Orders Of Magnitude (mass) . INERTIAL AND GRAVITATIONAL MASS
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 intertial mass. That it does is merely an empirical fact. ) because "acceleration" (due to an external force) and "weight" (due to a gravitational field) are themselves identical. However, in the resulting theory gravitation is not a force and thus not subject to Newton's third law, so "the equality of inertial and ''active'' gravitational mass {Link without Title} remains as puzzling as ever".Rindler, ''supra'', end of Section 1.14 Inertial mass ''Inertial mass'' is the mass of an object measured by its resistance to acceleration. To understand what the inertial mass of a body is, one begins with Classical Mechanics and Newton's Laws Of Motion . Later on, we will see how our classical definition of mass must be altered if we take into consideration the theory of Special Relativity , which is more accurate than classical mechanics. However, the implications of special relativity will not change the meaning of "mass" in any essential way. According to Newton's second law, we say that a body has a mass ''m'' if, at any instant of time, it obeys the equation of motion : where ''f'' is the Force acting on the body and ''v'' is its Velocity . For the moment, we will put aside the question of what "force acting on the body" actually means. Now, suppose that the mass of the body in question is a constant. This assumption, known as the Conservation Of Mass , rests on the ideas that (i) mass is a measure of the amount of matter contained in a body, and (ii) matter can never be created or destroyed, only split up or recombined. These are very reasonable assumptions for everyday objects, though, as we will see, mass can indeed by created or destroyed when we take Special Relativity into account. Another point to note is that, even in classical mechanics, it is sometimes useful to treat the mass of an object as changing with time. For example, the mass of a Rocket decreases as the rocket fires. However, this is an ''approximation'', based on ignoring pieces of matter which enter or leave the system. In the case of the rocket, these pieces correspond to the ejected propellant; if we were to measure the total mass of the rocket and its propellant, we would find that it is conserved. When the mass of a body is constant, Newton's second law becomes : where ''a'' denotes the Acceleration of the body. This equation illustrates how mass relates to the inertia of a body. Consider two objects with different masses. If we apply an identical force to each, the object with a bigger mass will experience a smaller acceleration, and the object with a smaller mass will experience a bigger acceleration. We might say that the larger mass exerts a greater "resistance" to changing its state of motion in response to the force. However, this notion of applying "identical" forces to different objects brings us back to the fact that we have not really defined what a force is. We can sidestep this difficulty with the help of Newton's third law, which states that if one object exerts a force on a second object, it will experience an equal and opposite force. To be precise, suppose we have two objects A and B, with constant inertial masses ''mA'' and ''mB''. We isolate the two objects from all other physical influences, so that the only forces present are the force exerted on A by B, which we denote ''fAB'', and the force exerted on B by A, which we denote ''fBA''. As we have seen, Newton's second law states that : and where ''aA'' and ''aB'' are the accelerations of A and B respectively. Suppose that these accelerations are non-zero, so that the forces between the two objects are non-zero. This occurs, for example, if the two objects are in the process of colliding with one another. Newton's third law then states that : Substituting this into the previous equations, we obtain : Note that our requirement that ''aA'' be non-zero ensures that the fraction is well-defined. This is, in principle, how we would measure the inertial mass of an object. We choose a "reference" object and define its mass ''mB'' as (say) 1 kilogram. Then we can measure the mass of every other object in the universe by colliding it with the reference object and measuring the accelerations. Gravitational mass ''Gravitational mass'' is the mass of an object measured using the effect of a gravitational field on the object. |
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