1 occurring widely (as to many people); "mass destruction" [syn: large-scale]
2 gathered or tending to gather into a mass or whole; "aggregate expenses include expenses of all divisions combined for the entire year"; "the aggregated amount of indebtedness" [syn: aggregate, aggregated, aggregative]
1 the property of a body that causes it to have weight in a gravitational field
2 (often followed by `of') a large number or amount or extent; "a batch of letters"; "a deal of trouble"; "a lot of money"; "he made a mint on the stock market"; "it must have cost plenty" [syn: batch, deal, flock, good deal, great deal, hatful, heap, lot, mess, mickle, mint, muckle, peck, pile, plenty, pot, quite a little, raft, sight, slew, spate, stack, tidy sum, wad, whole lot, whole slew]
3 an ill-structured collection of similar things (objects or people)
4 (Roman Catholic Church and Protestant Churches) the celebration of the Eucharist
5 a body of matter without definite shape; "a huge ice mass"
6 the common people generally; "separate the warriors from the mass"; "power to the people" [syn: multitude, masses, hoi polloi, people]
7 the property of something that is great in magnitude; "it is cheaper to buy it in bulk"; "he received a mass of correspondence"; "the volume of exports" [syn: bulk, volume]
8 a musical setting for a Mass; "they played a Mass composed by Beethoven"
9 a sequence of prayers constituting the Christian eucharistic rite; "the priest said Mass" v : join together into a mass or collect or form a mass; "Crowds were massing outside the palace" [also: masses (pl)]
Etymology 1From mæsse, from missa, noun use of feminine past participle of classical mittere.
- a US /mæs/, /m
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 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.
Units of massIn the SI system of units, mass is measured in kilograms, kg. Many other units of mass are also employed, such as: Outside the SI system, a variety of different mass units are used, depending on context.
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).
For more information on the different units of mass, see Orders of magnitude (mass).
Inertial and gravitational mass
One may distinguish conceptually between three types of mass or properties called mass:
- 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.
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".
- This section uses mathematical equations involving differential calculus.
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
- f = \frac (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.
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.
When the mass of a body is constant, Newton's second law becomes
- f = m \frac = m a
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
- f_ = m_B a_B \, and f_ = 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_ = - f_. \,
Substituting this into the previous equations, we obtain
- m_A = - \frac \, 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 massGravitational 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
- |f| =
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
- 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.
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
- a = \frac 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.)
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.
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.
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.
- R.V. Eötvös et al, Ann. Phys. (Leipzig) 68 11 (1922)
- Spacetime Physics
- Usenet Physics FAQ
- The Origin of Mass and the Feebleness of Gravity (video) - a colloquium lecture by the Nobel Laureate Frank Wilczek
- Mass conversions
- Mass & energy
- Photons, Clocks, Gravity and the Concept of Mass by L.B.Okun
- The Apollo 15 Hammer-Feather Drop
- Apollo 15 Hammer-Feather gravity demonstration video (higher quality)
- Online mass units conversion
- Scientific American Magazine (July 2005 Issue) The Mysteries of Mass
mass in Afrikaans: Massa
mass in Tosk Albanian: Masse (Physik)
mass in Arabic: كتلة
mass in Asturian: Masa
mass in Azerbaijani: Kütlə (fiziki kəmiyyət)
mass in Min Nan: Chit-liōng
mass in Belarusian: Маса
mass in Belarusian (Tarashkevitsa): Маса
mass in Bosnian: Masa
mass in Breton: Mas
mass in Bulgarian: Маса (величина)
mass in Catalan: Massa
mass in Czech: Hmotnost
mass in Welsh: Màs
mass in Danish: Masse (fysik)
mass in German: Masse (Physik)
mass in Estonian: Mass
mass in Modern Greek (1453-): Μάζα
mass in Spanish: Masa
mass in Esperanto: Maso
mass in Basque: Masa
mass in Persian: جرم
mass in French: Masse
mass in Galician: Masa
mass in Gujarati: દળ
mass in Korean: 질량
mass in Croatian: Masa
mass in Ido: Maso
mass in Indonesian: Massa
mass in Interlingua (International Auxiliary Language Association): Massa
mass in Icelandic: Massi
mass in Italian: Massa (fisica)
mass in Hebrew: מסה
mass in Georgian: მასა
mass in Kurdish: Bariste
mass in Latin: Pondus et Massa
mass in Latvian: Masa
mass in Luxembourgish: Mass (Physik)
mass in Lithuanian: Masė
mass in Lingala: Libóndó
mass in Hungarian: Tömeg
mass in Macedonian: Маса
mass in Malayalam: പിണ്ഡം
mass in Malay (macrolanguage): Jisim
mass in Dutch: Massa (natuurkunde)
mass in Japanese: 質量
mass in Norwegian: Masse
mass in Norwegian Nynorsk: Masse
mass in Novial: Mase
mass in Occitan (post 1500): Massa
mass in Low German: Masse (Physik)
mass in Polish: Masa (fizyka)
mass in Portuguese: Massa
mass in Romanian: Masă
mass in Quechua: Wisnu
mass in Russian: Масса
mass in Albanian: Masa
mass in Sicilian: Massa
mass in Simple English: Mass
mass in Slovak: Hmotnosť
mass in Slovenian: Masa
mass in Serbian: Маса
mass in Serbo-Croatian: Masa
mass in Finnish: Massa
mass in Swedish: Massa
mass in Thai: มวล
mass in Vietnamese: Khối lượng
mass in Tajik: Масса
mass in Turkish: Kütle
mass in Ukrainian: Маса
mass in Yiddish: מאסע
mass in Contenese: 質量
mass in Chinese: 质量
G, G suit, Negro spiritual, a mass of, a world of, abundance, accouple, accumulate, accumulation, acervation, acres, adhere, agglomerate, agglomeration, agglutinate, aggregate, aggregation, aggroup, amass, amassment, amount, amplitude, anthem, apogeotropism, area, army, articulate, assemblage, assemble, associate, assortment, backlog, bag, bags, band, bank, barrel, barrels, batch, best part, better part, bevy, bigness, block, bodily size, body, bond, bottle, box, bracket, breadth, breccia, bridge, bridge over, bring together, budget, bulk, bunch, bunch together, bunch up, bundle, burden, bushel, cake, caliber, can, canaille, cantata, canticle, carat, cement, centigram, chain, chorale, chunk, church music, clap together, clasp, cleave, clinch, cling, cling to, clod, clot, cloud, clump, cluster, clutter, coagulate, coarseness, cohere, cohue, collect, collection, colligate, collocate, combine, come together, commissariat, commissary, compare, compile, comprise, concatenate, concrete, concreteness, concretion, congeal, congeries, conglobation, conglobulate, conglomerate, conglomeration, congregate, conjoin, conjugate, connect, convene, converge, copiousness, copulate, core, cornucopia, corpulence, corpus, corral, countlessness, couple, cover, coverage, covey, crate, crowd, crush, cumulate, cumulation, date, decagram, decigram, deluge, density, depth, diameter, dig up, dimension, dimensions, distance through, doxology, dram, dram avoirdupois, draw together, dredge up, dregs, drive together, dump, durability, dyne, embrace, encompass, enormousness, essence, expanse, expansion, extension, extent, fatness, fill, firmness, flight, flock, flock together, flocks, flood, flow together, force, forgather, freeze to, freight, fuse, galaxy, gang around, gang up, gather, gather around, gather in, gather together, gathering, gauge, generality, geotropism, get in, get together, girth, gist, glomeration, glue, gob, gospel, gospel music, grain, gram, grasp, gravamen, gravitation, graviton, gravity, great deal, greatness, grossness, group, grow together, hail, hang on, hang together, heap, heap up, height, herd together, herds, hill, hive, hoard, hoi polloi, hold, hold on, hold together, horde, host, huddle, hug, hundredweight, hunk, hymn, hymn-tune, hymnody, hymnology, immensity, include, introit, inventory, jam, join, juxtapose, kilo, kilogram, knot, lade, larder, large amount, largeness, lay together, league, legion, legions, length, link, load, loads, loaf, lot, lots, lump, lump together, magnitude, main body, major part, majority, many, marry, marshal, masses of, massiveness, match, material, materiality, materials, materiel, matter, measure, measurement, meat, meet, megaton, merge, mess, mill, milligram, miscellany, mob, mobilize, mole, more than half, most, motet, mound, mountain, much, muchness, multitude, munitions, muster, nest, node, nugget, numbers, numerousness, object, ocean, oceans, offertory, offertory sentence, oodles, oratorio, ounce, ounce avoirdupois, ounce troy, pack, pack away, paean, pair, palpability, panoply, partner, passion, pat, peck, pennyweight, persist, piece together, pile, pile up, piles, plenitude, plenty, plurality, pocket, ponderability, pound, pound avoirdupois, pound troy, poundal, preponderance, preponderancy, press, profusion, proletariat, proportion, proportions, prosodion, provisionment, provisions, psalm, psalmody, put together, pyramid, quantities, quantity, quantum, quite a few, rabble, radius, ragtag and bobtail, raise, rake up, rally, rally around, range, rations, reach, recessional, rendezvous, repertoire, repertory, requiem, requiem mass, rick, riffraff, roll into one, round up, rout, ruck, sack, sacred music, scads, scale, scope, scores, scrape together, scruple, scum, sea, seethe, set, ship, shoal, shock, size, slews, slug, snowball, solder, solid, solid body, solidify, solidity, soundness, span, spate, specific gravity, spiritual, splice, spread, stability, stack, staple, stay, stay put, steadiness, stick, stick together, stock, stock-in-trade, stockpile, stone, store, stores, stoutness, stow, stream, strength, sturdiness, substance, substantiality, substantialness, sum, superabundance, superfluity, supplies, supply on hand, surge, swarm, swarms, take hold of, take in, take up, tangibility, tape, the common herd, the greatest number, the masses, the third dimension, thickness, throng, thrust, tidy sum, tie, ton, tons, toughness, trash, treasure, treasury, unify, unite, units of weight, unwashed, volume, wad, weight, weld, whip in, white spiritual, whole, width, world, worlds, worlds of, yokeAgnus Dei, Alleluia, Anamnesis, Blessing, Canon, Collect, Communion, Consecration, Credo, Dismissal, Dry Mass, Epistle, Eucharistic rites, Fraction, Gloria, Gospel, Gradual, Introit, Kyrie, Kyrie Eleison, Lady Mass, Last Gospel, Lavabo, Low Mass, Missa, Missa bassa, Missa cantata, Missa legata, Missa media, Missa praesanctificatorum, Missa privata, Missa publica, Missa sicca, Offertory, Paternoster, Pax, Post-Communion, Preface, Requiem Mass, Rosary, Rosary Mass, Sanctus, Secreta, Tersanctus, Tract, bedtime prayer, camp meeting, church, church service, compline, devotions, dirge, divine service, duty, evening devotions, evensong, exercises, lauds, liturgy, matins, meeting, morning devotions, night song, none, nones, novena, office, praise meeting, prayer, prayer meeting, prayers, prime, prime song, public worship, requiem, revival, revival meeting, service, sext, tent meeting, the Divine Liturgy, the Liturgy, tierce, undersong, vesper, vespers, vigils, watch meeting, watch night, watch-night service