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Encyclopedia > Mass
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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. Look up mass in Wiktionary, the free dictionary. ... Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Web-based project to create a free content dictionary, available in over 151 languages. ... Wikipedia does not have an article with this exact name. ... Wikipedia does not have an article with this exact name. ... Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... Newtons First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. ... The Greeks, and Aristotle in particular, were the first to propose that there are abstract principles governing nature. ... This article is about the idea of space. ... This article is about the concept of time. ... For other uses, see Force (disambiguation). ... This article is about momentum in physics. ... Newtons First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. ... Lagrangian mechanics is a re-formulation of classical mechanics that combines conservation of momentum with conservation of energy. ... Hamiltonian mechanics is a re-formulation of classical mechanics that was invented in 1833 by William Rowan Hamilton. ... Applied mechanics, also known as theoretical and applied mechanics, is a branch of the physical sciences and the practical application of mechanics. ... Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects. ... Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. ... See also list of optical topics. ... Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... Galileo redirects here. ... Kepler redirects here. ... Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Pierre-Simon, marquis de Laplace (March 23, 1749 - March 5, 1827) was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy. ... For other persons named William Hamilton, see William Hamilton (disambiguation). ... Jean le Rond dAlembert, pastel by Maurice Quentin de La Tour Jean le Rond dAlembert (November 16, 1717 – October 29, 1783) was a French mathematician, mechanician, physicist and philosopher. ... Augustin Louis Cauchy (August 21, 1789 – May 23, 1857) was a French mathematician. ... Joseph-Louis, comte de Lagrange (January 25, 1736 Turin, Kingdom of Sardinia - April 10, 1813 Paris) was an Italian-French mathematician and astronomer who made important contributions to all fields of analysis and number theory and to classical and celestial mechanics as arguably the greatest mathematician of the 18th century. ... Euler redirects here. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... Intuition has many meanings across many cultures, including: quick and ready insight seemingly independent of previous experiences and empirical knowledge immediate apprehension or cognition knowledge or conviction gained by intuition the power or faculty of attaining to direct knowledge or cognition without evident rational thought and inference. ... This article is about matter in physics and chemistry. ... Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... The term mass in special relativity can be used in different ways, occasionally leading to confusion. ... The concept of mass in general relativity (GR) is more complex than the concept of mass in special relativity. ... The invariant mass or intrinsic mass or proper mass or just mass is a measurement or calculation of the mass of an object that is the same for all frames of reference. ... A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ...


In everyday usage, mass is more commonly referred to as weight, but in physics and engineering, weight means the strength of the gravitational pull on the object; that is, how heavy it is, measured in units of force. In everyday situations, the weight of an object is proportional to its mass, which usually makes it unproblematic to use the same word for both concepts. However, the distinction between mass and weight 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 for places far from the surface of the Earth, such as in space or on other planets. For other uses, see Weight (disambiguation). ... For other uses, see Force (disambiguation). ... In the physical sciences, mass and weight are different properties. ...

Contents

Units of mass

In the SI system of units, mass is measured in kilograms, kg. Many other units of mass are also employed, such as: “SI” redirects here. ... Kg redirects here. ...

Outside the SI system, a variety of different mass units are used, depending on context. BIC pen cap, about 1 gram. ... This article is about the metric tonne. ... The unified atomic mass unit (u), or dalton (Da), is a small unit of mass used to express atomic and molecular masses. ... The Planck mass is the natural unit of mass, denoted by mP. It is the mass for which the Schwarzschild radius is equal to the Compton length divided by π. ≈ 1. ... In astronomy, the solar mass is a unit of mass used to express the mass of stars and larger objects such as galaxies. ... The electronvolt (symbol eV) is a unit of energy. ... A line showing the speed of light on a scale model of Earth and the Moon, taking about 1⅓ seconds to traverse that distance. ...


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 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 length. Here one identifies the mass of a particle with its inverse Compton wavelength (1 cm-1 ≈ 3.52×10-41 kg). The invariant mass or intrinsic mass or proper mass or just mass is a measurement or calculation of the mass of an object that is the same for all frames of reference. ... The term mass in special relativity can be used in different ways, occasionally leading to confusion. ... Thousands of particles explode from the collision point of two relativistic (100 GeV per nucleon) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ...


For more information on the different units of mass, see Orders of magnitude (mass). To help compare different orders of magnitude, the following list describes various mass levels between 10−36 kg and 1053 kg. ...


Inertial and gravitational mass

One may distinguish conceptually between three types of mass or properties called mass:[1]

  • Inertial mass is a measure of an object's resistance to changing its state of motion when a force is applied. An object with small inertial mass changes its motion more readily, and an object with large inertial mass does so less readily.
  • Passive gravitational mass is a measure of the strength of an object's interaction with a gravitational field. Within the same gravitational field, an object with a smaller passive gravitational mass experiences a smaller force than an object with a larger passive gravitational mass.
  • Active gravitational mass is a measure of the strength of the gravitational field due to a particular object. For example, the gravitational field that one experiences on the Moon is weaker than that of the Earth because the Moon has less active 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 inertial mass. That it does is merely an empirical fact. For other uses, see Force (disambiguation). ... A gravitational field is a model used within physics to explain how gravity exists in the universe. ... This article is about Earths moon. ... Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ...


Albert Einstein developed his general theory of relativity starting from the assumption that this correspondence between inertial and (passive) gravitational mass is not accidental: that no experiment will ever detect a difference between them (the weak version of the equivalence principle). 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 [...] remains as puzzling as ever".[2] “Einstein” redirects here. ... General relativity (GR) or general relativity theory (GRT) is the theory of gravitation published by Albert Einstein in 1915. ... In the physics of relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. ...


Inertial mass

This section uses mathematical equations involving differential calculus.

Inertial mass is the mass of an object measured by its resistance to acceleration. Differential calculus is the theory of and computations with differentials; see also derivative and calculus. ...


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. Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... Newtons First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. ... For a less technical and generally accessible introduction to the topic, see Introduction to special relativity. ...


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

 f = frac{mathrm{d}}{mathrm{d}t} (mv)

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. For other uses, see Force (disambiguation). ... This article is about velocity in physics. ...


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 be 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. The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov-Lavoisier law), states that the mass of a closed system of substances will remain constant, regardless of the processes acting inside the system. ... For a less technical and generally accessible introduction to the topic, see Introduction to special relativity. ... This article is about vehicles powered by rocket engines. ...


When the mass of a body is constant, Newton's second law becomes

 f = m frac{mathrm{d}v}{mathrm{d}t} = m a

where a denotes the acceleration of the body. Acceleration is the time rate of change of velocity and/or direction, and at any point on a velocity-time graph, it is given by the slope of the tangent to the curve at that point. ...


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

f_{AB} = m_B a_B , and f_{BA} = m_A a_A ,

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

f_{AB} = - f_{BA}. ,

Substituting this into the previous equations, we obtain

m_A = - frac{a_B}{a_A} , m_B.

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 any 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.


The concept of gravitational mass rests on Newton's law of gravitation. Let us suppose we have two objects A and B, separated by a distance |rAB|. The law of gravitation states that if A and B have gravitational masses MA and MB respectively, then each object exerts a gravitational force on the other, of magnitude Isaac Newtons theory of universal gravitation (part of classical mechanics) states the following: Every single point mass attracts every other point mass by a force pointing along the line combining the two. ...

|f| = {G M_A M_B over |r_{AB}|^2}

where G is the universal gravitational constant. The above statement may be reformulated in the following way: if g is the acceleration of a reference mass at a given location in a gravitational field, then the gravitational force on an object with gravitational mass M is The gravitational constant G is a key element in Newtons law of universal gravitation. ...

f = Mg. ,

This is the basis by which masses are determined by weighing. In simple bathroom scales, for example, the force f is proportional to the displacement of the spring beneath the weighing pan (see Hooke's law), and the scales are calibrated to take g into account, allowing the mass M to be read off. Note that a balance (see the subheading within Weighing scale) as used in the laboratory or the health club measures gravitational mass; only the spring scale measures weight. A scale is either a device used for measurement of weights, or a series of ratios against which different measurements can be compared. ... Digital kitchen scales. ... For other uses, see Spring. ... Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ... calibration refers to the process of determining the relation between the output (or response) of a measuring instrument and the value of the input quantity or attribute, a measurement standard. ... Digital kitchen scales. ...


Equivalence of inertial and gravitational masses

The equivalence of inertial and gravitational masses is sometimes referred to as the Galilean equivalence principle or weak equivalence principle. The most important consequence of this equivalence principle applies to freely falling objects. Suppose we have an object with inertial and gravitational masses m and M respectively. If the only force acting on the object comes from a gravitational field g, combining Newton's second law and the gravitational law yields the acceleration In relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. ...

a = frac{M}{m} g.

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 to be 1 by defining our units appropriately.) ↔ ⇔ ≡ logical symbols representing iff. ...


The first experiments demonstrating the universality of free-fall were conducted by Galileo. It is commonly stated that Galileo obtained his results by dropping objects from the Leaning Tower of Pisa, but this is most likely apocryphal; actually, he performed his experiments with balls rolling down inclined planes. Increasingly precise experiments have been performed, such as those performed by Loránd Eötvös, using the torsion balance pendulum, in 1889. As of 2008, no deviation from universality, and thus from Galilean equivalence, has ever been found, at least to the accuracy 1/1012. More precise experimental efforts are still being carried out. Galileo redirects here. ... The Leaning Tower of Pisa (Italian: ) or simply The Tower of Pisa (La Torre di Pisa) is the campanile, or freestanding bell tower, of the cathedral of the Italian city of Pisa. ... The inclined plane is one of the classical simple machines; as the name suggests, it is a flat surface whose endpoints are at different heights. ... Image:Lorand Eotvos. ... A torsion spring is a ribbon, bar, or coil that reacts against twisting motion. ... Year 1889 (MDCCCLXXXIX) was a common year starting on Tuesday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Sunday of the 12-day slower Julian calendar). ... 2008 (MMVIII) will be a leap year starting on Tuesday of the Gregorian calendar. ...


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 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 demonstration is easily done in a high-school laboratory, using two transparent tubes connected to a vacuum pump. For other uses, see Friction (disambiguation). ... For a solid object moving through a fluid or gas, drag is the sum of all the aerodynamic or hydrodynamic forces in the direction of the external fluid flow. ... Although related to the more mathematical concepts of infinitesimal , the idea of something being negligible is particularly useful in practical disciplines like physics, chemistry, mechanical and electronic engineering, computer programming and in everyday decision-making. ... Look up Vacuum in Wiktionary, the free dictionary. ...


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 inertial and gravitational masses are fundamentally the same thing. For a generally accessible and less technical introduction to the topic, see Introduction to general relativity. ...


See also

For other uses, see Weight (disambiguation). ... For other uses, see Density (disambiguation). ... The Higgs boson, also known as the God particle, is a hypothetical massive scalar elementary particle predicted to exist by the Standard Model of particle physics. ... The term mass in special relativity can be used in different ways, occasionally leading to confusion. ... The concept of mass in general relativity (GR) is more complex than the concept of mass in special relativity. ... To help compare different orders of magnitude, the following list describes various mass levels between 10−36 kg and 1053 kg. ... In physics, Planck units are one of several systems of natural units, units of measurement that normalize certain fundamental physical constants to 1. ... For other uses, see Volume (disambiguation). ...

References

  1. ^ Rindler, Wolfgang (2001). Relativity: Special, General and Cosmological. Oxford University Press.  Section 1.12
  2. ^ Rindler, supra, end of Section 1.14
  • R.V. Eötvös et al, Ann. Phys. (Leipzig) 68 11 (1922)
  • Taylor, Edwin F.; John Archibald Wheeler (1992). Spacetime Physics. New York: W.H. Freeman and Company. ISBN 0-7167-2327-1. 

Wolfgang Rindler is a leading physicist working in the field of General Relativity where he is well known for introducing the term event horizon, rindler coordinates, and (in collaboration with Roger Penrose) for popularizing the use of spinors in general relativity. ...

External links

Frank Wilczek (born May 15, 1951) is a Nobel prize winning American physicist. ...

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