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Mass is a property of a Physical object that quantifies the amount of Matter and Energy it contains. Unlike Weight , the mass of something stays the same regardless of location. In relativity, the quantity Invariant Mass , which is closest in content to the classical idea of mass, also does not vary between single observers in different Reference Frames . Mass is a central concept of Classical Mechanics and related subjects, and also several forms of mass appear in relativistic kinematics (see Mass In Special Relativity ). There are three different quantities called ''mass'':
INTRODUCTION Although inertial mass, passive gravitational mass and active gravitational mass are conceptually distinct, no experiment has ever unambiguously demonstrated any difference between them. One of the consequences of the equivalence of inertial mass and passive gravitational mass is the fact, famously demonstrated by Galileo Galilei , that objects with different masses fall at the same rate, assuming factors like Air Resistance are Negligible . The theory of General Relativity , the most accurate theory of gravitation known to physicists to date, rests on the assumption that inertial and passive gravitational mass are ''completely'' equivalent. This is known as the Weak Equivalence Principle . Classically , active and passive gravitational mass were equivalent as a consequence of Newton's Third Law , but a new axiom is required in the context of relativity's reformulation of gravity and mechanics. Thus, standard general relativity also assumes the equivalence of inertial mass and active gravitational mass; this equivalence is sometimes called the strong equivalence principle. If one were to treat Inertial Mass ''m''i, Passive Gravitational Mass ''m''p, and Active Gravitational Mass ''m''a distinctly, Newton's Law Of Universal Gravitation would give as force on the second mass due to the first mass : , of reciprocal actions, shows that active and passive mass are proportional. As a result they can be ''defined'' to be equal. UNITS OF MASS In the s (g), Metric Ton 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. The eV/''c''2 unit is based on the Electron Volt (eV), which is normally used as a unit of Energy . However, because of the relativistic connection between (rest) mass and energy, ''E'' = ''mc''2 (see Below ), it is possible to use any unit of energy as a unit of mass instead. Thus, in Particle Physics where mass and energy are often interchanged, it is common to use not only eV/''c''2 but even simply eV as a unit of mass (roughly 1.783 × 10-36 kg). Because the Gravitational Acceleration is approximately constant on the surface of the Earth , a unit like the Pound is often used to measure ''either'' mass or Force (e.g. weight), although the pound is officially defined as a unit of force. For more information on the different units of mass, see Orders Of Magnitude (mass) . 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, the situation gets more complicated 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. | ||
| :<math>F | {G M_A M_B \over r_{AB}^2}</math> |
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