Mass is an intrinsic physical quantity of a body which in modern physics is generally defined as the strength of an object's gravitational attraction to other bodies. The unit of mass in the International System of Units (SI) is the kilogram (kg). Mass can also be understood as a measure of the energy content of a body (see E=mc²).
Mass can be experimentally defined as a measure of the body's inertia, meaning the resistance to acceleration (change of velocity) when a net force is applied.
In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity, but it would still have the same mass. This is because weight is a force, while mass is the property that (along with gravity) determines the strength of this force.
In the Standard Model of physics, the mass of elementary particles is believed to be a result of their coupling with the Higgs boson in what is known as the Brout–Englert–Higgs mechanism.
Phenomena 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, current experiments have found no difference in results regardless of how it is measured: Inertial mass measures an object's resistance to being accelerated by a force (represented by the relationship ). Active gravitational mass determines the strength of the gravitational field generated by an object. Passive gravitational mass measures the gravitational force exerted on an object in a known gravitational field.
The mass of an object determines its acceleration in the presence of an applied force. The inertia and the inertial mass describe this property of physical bodies at the qualitative and quantitative level respectively. According to Newton's second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A body's mass also determines the degree to which it generates and is affected by a gravitational field. If a first body of mass mA is placed at a distance r (center of mass to center of mass) from a second body of mass mB, each body is subject to an attractive force , where is the "universal gravitational constant". This is sometimes referred to as gravitational mass.When a distinction is necessary, the active and passive gravitational masses may be distinguished. Repeated experiments since the 17th century have demonstrated that inertial and gravitational mass are identical; since 1915, this observation has been incorporated a priori in the equivalence principle of general relativity.
Units of mass
The International System of Units (SI) unit of mass is the kilogram (kg). It is defined in terms of three constants, Planck constant, the speed of light, and the definition of the second (itself defined by fixing the caesium hyperfine frequency). The specific values of these constants were selected to closely approximate the older definition of the kilogram, the platinum–iridium International Prototype of the Kilogram.
Non-SI-units that continue to be widely used include: the tonne (t) (or "metric ton"), equal to 1000 kg the dalton (Da) or unified atomic mass (u), equal to 1/12 of the mass of a free carbon-12 atom, approximately . The dalton is convenient for expressing the masses of atoms and molecules. Other units of mass include: the electronvolt (eV), a unit of energy, used in high energy physics to express mass in units of GeV/c2 () through mass–energy equivalence, the pound (lb), a unit of mass (about 0.45 kg). the Planck mass () a quantity derived from fundamental constants the solar mass (), defined as the mass of the Sun, primarily used in astronomy to compare large masses such as stars or galaxies (≈ )
History of units of mass
The kilogram was first defined in 1795 as the mass of one cubic decimetre of water at the melting point of ice. However, because precise measurement of a cubic decimetre of water at the specified temperature and pressure was difficult, in 1889 the kilogram was redefined as the mass of a metal object, and thus became independent of the metre and the properties of water, this being a copper prototype of the grave in 1793, the platinum Kilogramme des Archives in 1799, and the platinum–iridium International Prototype of the Kilogram (IPK) in 1889.
However, the mass of the IPK and its national copies have been found to drift over time. The re-definition of the kilogram and several other units came into effect on 20 May 2019, following a final vote by the CGPM in November 2018. The new definition uses only invariant quantities of nature: the speed of light, the caesium hyperfine frequency, the Planck constant and the elementary charge.
Definition In general relativity mass creates the gravitational field. Newtonian gravity distinguishes between active gravitational mass that creates the field and passive gravitational mass that responds to the field and between gravitational mass involved in the force of gravity and inertial mass measuring a body's response to acceleration. However, the combination of Newton's law of gravity and his third law of motion,
shows that the active and passive masses are the same. Empirical measurements have shown that inertial and gravitational mass are identical to one part in a trillion. General relativity assumes this identity, known as the equivalence principle.
Weight vs. mass
In everyday usage, mass and "weight" are often used interchangeably. For instance, a person's weight may be stated as 75 kg. In a constant gravitational field, the weight of an object is proportional to its mass, and it is unproblematic to use the same unit for both concepts. But because of slight differences in the strength of the Earth's gravitational field at different places, the distinction becomes important for measurements with a precision better than a few percent, and for places far from the surface of the Earth, such as in space or on other planets. Conceptually, "mass" (measured in kilograms) refers to an intrinsic property of an object, whereas "weight" (measured in newtons) measures an object's resistance to deviating from its current course of free fall, which can be influenced by the nearby gravitational field. No matter how strong the gravitational field, objects in free fall are weightless, though they still have mass.
The force known as "weight" is proportional to mass and acceleration in all situations where the mass is accelerated away from free fall. For example, when a body is at rest in a gravitational field (rather than in free fall), it must be accelerated by a force from a scale or the surface of a planetary body such as the Earth or the Moon. This force keeps the object from going into free fall. Weight is the opposing force in such circumstances and is thus determined by the acceleration of free fall. On the surface of the Earth, for example, an object with a mass of 50 kilograms weighs 491 newtons, which means that 491 newtons is being applied to keep the object from going into free fall. By contrast, on the surface of the Moon, the same object still has a mass of 50 kilograms but weighs only 81.5 newtons, because only 81.5 newtons is required to keep this object from going into a free fall on the moon. Restated in mathematical terms, on the surface of the Earth, the weight W of an object is related to its mass m by , where is the acceleration due to Earth's gravitational field, (expressed as the acceleration experienced by a free-falling object).
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 , 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).
Inertial vs. 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 an established empirical fact to one part in a trillion.
Albert Einstein developed his general theory of relativity starting with the assumption that the inertial and passive gravitational masses are the same. This is known as the equivalence principle.
The particular equivalence often referred to as the "Galilean equivalence principle" or the "weak equivalence principle" has the most important consequence for freely falling objects. Suppose an object has inertial and gravitational masses m and M, respectively. If the only force acting on the object comes from a gravitational field g, the force on the object is:
Given this force, the acceleration of the object can be determined by Newton's second law:
Putting these together, the gravitational acceleration is given by:
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.
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, using the torsion balance pendulum, in 1889. , 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.