Mass Measure

A Mass Measure is a physical measure of the amount of matter and energy in a physical object .

• Context:
  • It can be defined as the inertial mass [math]\displaystyle{ F=ma }[/math] where F is the external force, m is the constant mass and a is the acceleration (Newtonian Physics)
  • It can be defined energy-mass (a.k.a mass-energy) [math]\displaystyle{ E=mc^2 }[/math] (Theory of Relativity) where E is the energy, m is the mass, and c the speed of light.
  • It can be defined as gravitational mass [math]\displaystyle{ F=mg }[/math] where F is the gravitational force, where g is the magnitude at a given location in the gravitational field, m is the mass. (Gravitational Law)
• Example(s):
  • Inertial mass.
  • Mass-Energy.
  • Gravitational mass.
  • Stellar Mass.
  • Electromagnetic Mass.
• Counter-Example(s):
  • Weight.
  • Density.
  • Volume.
• See: Acceleration, Force, Velocity, Motion, Inertia, Newton's Second Law.

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References

2015

• (Wikipedia, 2015) ⇒ https://www.wikiwand.com/en/Mass
  • In physics, mass is a property of a physical body. It is generally a measure of an object's resistance to changing its state of motion when a force is applied. It is determined by the strength of its mutual gravitational attraction to other bodies, its resistance to acceleration or directional changes, and in the theory of relativity gives the mass–energy content of a system. The SI unit of mass is the kilogram (kg).

Mass is not the same as weight, even though we often calculate an object's mass by measuring its weight with a spring scale instead of comparing it to known masses. An object on the Moon would weigh less than it would 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) causes this force.

In Newtonian physics, mass can be generalized as the amount of matter in an object. However, at very high speeds or for subatomic particles, special relativity shows that energy is an additional source of mass. Thus, any stationary body having mass has an equivalent amount of energy, and all forms of energy resist acceleration by a force and have gravitational attraction. In addition, "matter" is a loosely defined term in science, and thus cannot be precisely measured.

There are several distinct phenomena which can be used to measure mass. Although some theorists have speculated some of these phenomena could be independent of each other current experiments have found no difference among any of the ways used to measure mass:

• Inertial mass measures an object's resistance to being accelerated by a force (represented by the relationship F = ma).
• Active gravitational mass measures the gravitational force exerted by an object.
• Passive gravitational mass measures the gravitational force experienced by an object in a known gravitational field.
• Mass–energy measures the total amount of energy contained within a body, using E = mc².

The mass of an object determines its acceleration in the presence of an applied force. This phenomenon is called inertia. 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 or is affected by a gravitational field. If a first body of mass m_A is placed at a distance r (center of mass to center of mass) from a second body of mass m_B, each body experiences an attractive force F_g = Gm_Am_B/r², where G = Template:Val is the "universal gravitational constant”. This is sometimes referred to as gravitational mass. Repeated experiments since the 17th century have demonstrated that inertial and gravitational mass are identical; since 1915, this observation has been entailed a priori in the equivalence principle of general relativity.

2005

• (Hyperphysics Encyclopedia, 2005) ⇒ http://hyperphysics.phy-astr.gsu.edu/hbase/mass.html
  • The mass of an object is a fundamental property of the object; a numerical measure of its inertia; a fundamental measure of the amount of matter in the object. Definitions of mass often seem circular because it is such a fundamental quantity that it is hard to define in terms of something else. All mechanical quantities can be defined in terms of mass, length, and time. The usual symbol for mass is m and its SI unit is the kilogram. While the mass is normally considered to be an unchanging property of an object, at speeds approaching the speed of light one must consider the increase in the relativistic mass.

1996

• (Wolfram Science World, 2005) ⇒ http://scienceworld.wolfram.com/physics/Mass.html
  • The quantity of "matter" contained in an object, given by [math]\displaystyle{ m=\int\rho\;dV }[/math] where [math]\displaystyle{ \rho }[/math] is the density. The cgs unit of mass is the gram, the MKS unit the kilogram, and the foot-pound-second unit is the slug. Note that the pound is not a unit of mass, but rather one of weight. While no less an authority than the National Institute of Standards and Technology notes that "in commercial and everyday one, and especially in common parlance, weight is usually used as a synonym for mass" (Taylor 1995, p. 24), this extremely confusing practice should be universally discouraged.

The term "mass" is commonly confused with weight. However, whereas mass is an inherent property of a body, weight [math]\displaystyle{ w=mg }[/math] is the product of mass m by the gravitational acceleration g (this formula is a special case of Newton's second law), and therefore depends on the strength of gravitational acceleration to which a body is subjected. The weight of a body would therefore be less at the top of a mountain than at the mountain's foot.

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