Information about Mass
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.
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 imperial 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 imperial unit of mass is the slug (mass).
For more information on the different units of mass, see Orders of magnitude (mass).
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) 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 [...] remains as puzzling as ever".[2]
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
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.
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
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
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.
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. To date, 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 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.
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 SI system of units, mass is measured in kilograms, originally defined as the mass of one litre of water. Many other units of mass are also employed, such as: grams (g), tonnes, pounds, ounces, long and short tons, quintals, slugs, atomic mass units, Planck masses, solar masses, and eV/c2.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 imperial 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 imperial 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
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.
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) 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 [...] remains as puzzling as ever".[2]
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.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
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
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
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. To date, 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 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.
Relationship between mass and energy
In special relativity, mass and energy are intimately related, as described by the famous equation E = mc2; see mass-energy equivalence and mass in special relativity.References
1. ^ Rindler, Wolfgang (2001). Relativity: Special, General and Cosmological. Oxford University Press. Section 1.12
2. ^ Rindler, supra, end of Section 1.14
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.
See also
- Weight
- Density
- Higgs boson
- Mass in special relativity
- Mass in general relativity
- Orders of magnitude (mass)
- Planck units
- Volume
External links
- Usenet Physics FAQ
- Does mass change with velocity?
- Does light have mass?
- 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
Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
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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.
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relativistic mass is also used, this occasionally leads to confusion.
The invariant mass of an object (also known as the rest mass, intrinsic mass or proper mass) is an observer-independent quantity that is synonymous with mass.
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The invariant mass of an object (also known as the rest mass, intrinsic mass or proper mass) is an observer-independent quantity that is synonymous with mass.
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The concept of mass in general relativity (GR) is more complex than the concept of mass in special relativity. In fact, general relativity does not offer a single definition for the term mass, but offers several different definitions which are applicable under different
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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.
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A frame of reference is a particular perspective from which the universe is observed. Specifically, in physics, it refers to a provided set of axes from which an observer can measure the position and motion of all points in a system, as well as the orientation of objects in it.
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weight is a measurement of the gravitational force acting on an object. Near the surface of the Earth, the acceleration due to gravity is approximately constant; this means that an object's weight is roughly proportional to its mass.
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In physics, force is an action or agency that causes a body of mass m to accelerate. It may be experienced as a lift, a push, or a pull. The acceleration of the body is proportional to the vector sum of all forces acting on it (known as net force or resultant force).
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Si, si, or SI may refer to (all SI unless otherwise stated):
In language:
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In language:
- One of two Italian words:
- sì (accented) for "yes"
- si
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kilogram or kilogramme (symbol: kg) is the SI base unit of mass. The kilogram is defined as being equal to the mass of the International Prototype Kilogram (IPK), which is almost exactly equal to the mass of one liter of water.
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The litre or liter (see spelling differences) is a unit of volume. There are two official symbols, namely the Latin letter L both in lower and upper case: l and L.
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Gram
Unit sign g
Measure Mass
Base Unit Kilogram
Multiple of Base 10−3
System SI, CGS, other
Common usage Commonly used in cooking and food labeling
Examples
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Unit sign g
Measure Mass
Base Unit Kilogram
Multiple of Base 10−3
System SI, CGS, other
Common usage Commonly used in cooking and food labeling
Examples
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tonne (t) or metric ton (M/T), also referred to as a metric tonne, is a measurement of mass equal to 1,000 kilograms. It is not an SI unit but is accepted for use with the SI.
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pound or pound-mass (abbreviations: lb, ℔, lbm, or sometimes in the United States: #) is a unit of mass (sometimes called 'weight' in everyday parlance) in a number of different systems, including English units, Imperial units, and United
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ounce (abbreviation: oz) is the name of a unit of mass in a number of different systems, including various systems of mass that form part of English units, Imperial units, and United States customary units. Its size can vary from system to system.
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Long Ton (L/T sometimes known as a Gross Ton, Weight Ton, or Imperial Ton) is the name for the unit called the "Ton" in the Avoirdupois or Imperial system of measurements, as formerly used in the United Kingdom and several other Commonwealth countries.
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The short ton (S/T) is a unit of mass equal to 2,000 lb (exactly 907.18474 kg). In the United States it is often called simply ton without distinguishing it from the metric ton (or tonne
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The quintal or centner is a historical unit of mass with many different definitions in different countries, but usually it is 100 base units of mass, e.g. pounds.
Both terms share their roots in the Classical Latin centenarius, meaning hundredlike
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Both terms share their roots in the Classical Latin centenarius, meaning hundredlike
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The slug is an English unit of mass. It is a mass that accelerates by 1 ft/s² when a force of one pound-force (lbf) is exerted on it. Therefore a slug has a mass of about 32.17405 pound-mass or 14.5939 kg.
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The unified atomic mass unit (u), or dalton (Da), is a small unit of mass used to express atomic and molecular masses. It is defined to be one twelfth of the mass of an unbound atom of the carbon-12 nuclide, at rest and in its ground state.
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The Planck mass is the unit of mass, denoted by mP, in the system of natural units known as Planck units. Named after Max Planck, it is the mass for which the Schwarzschild radius is equal to the Compton length divided by π.
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- ≈ 1.
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The solar mass is a standard way to express mass in astronomy, used to describe the masses of other stars and galaxies. It is equal to the mass of the Sun, about two nonillion kilograms or about 332,950 times the mass of the Earth.
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The electronvolt (symbol eV) is a unit of energy. In theoretical physics, where distinctions between mass and energy are not concrete, it is often used also as a unit of mass (AAAS Science journal, 2006).
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speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning "swiftness".[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum.
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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.
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relativistic mass is also used, this occasionally leads to confusion.
The invariant mass of an object (also known as the rest mass, intrinsic mass or proper mass) is an observer-independent quantity that is synonymous with mass.
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The invariant mass of an object (also known as the rest mass, intrinsic mass or proper mass) is an observer-independent quantity that is synonymous with mass.
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The electronvolt (symbol eV) is a unit of energy. In theoretical physics, where distinctions between mass and energy are not concrete, it is often used also as a unit of mass (AAAS Science journal, 2006).
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Particle physics is a branch of physics that studies the elementary constituents of matter and radiation, and the interactions between them. It is also called "high energy physics"
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In physics, gravitational acceleration is the acceleration of an object caused by the force of gravity from another object. An interesting fact is that any object will accelerate towards a large object at the same rate, regardless of the mass of the object.
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EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001. Their greatest hit, their debut single "time after time", peaked at #13 in the Oricon singles chart.
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