Table of Contents

## Definition of Mass

- Mass is a property of a physical object that quantifies the amount of matter it contains.
- Mass is a measure of the amount of matter that an object contains.

The mass of an object is made in comparison to the standard mass of 1 kilogram. The kilogram was originally defined as the mass of 1L of liquid water at 4oC (the volume of a liquid changes slightly with temperature). Unlike weight, the mass of something stays the same regardless of location.

Mass is a central concept of classical mechanics and related subjects, and there are several forms of mass within the framework of relativistic kinematics.

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.

Mass, is quantitative measure of inertia, a fundamental property of all matter. It is, in effect, the resistance that a body of matter offers to a change in its speed or position upon the application of a force.

The greater the mass of a body, the smaller the change produced by an applied force.

### Definition on the Basis of Conservation of Mass

According to the principle of conservation of mass, the mass of an object or collection of objects never changes, no matter how the constituent parts rearrange themselves.

If a body is split into pieces, the mass divides with the pieces so that the sum of the masses of the individual pieces is equal to the original mass. Or, if particles are joined together, the mass of the composite is equal to the sum of the masses of the constituent particles.

However, this principle is not always correct. With the advent of Einstein’s special theory of relativity in 1905, the notion of mass underwent a radical revision. The mass lost its absoluteness. The mass of an object was seen to be equivalent to energy, to be interconvertible with energy, and to increase significantly at exceedingly high speeds near that of light (about 3 × 108 meters per second, or 186,000 miles per second).

The total energy of an object was understood to comprise its rest mass and its increase of mass caused by high speed. The rest mass of an atomic nucleus was discovered to be measurably smaller than the sum of the rest masses of its constituent neutrons and protons.

Mass was no longer considered constant or unchangeable. In both chemical and nuclear reactions, some conversion between mass and energy occurs so that the products generally have smaller or greater mass than the reactants.

The difference in mass is so slight for ordinary chemical reactions that mass conservation may be invoked as a practical principle for predicting the mass of products.

However, mass conservation is invalid for the behavior of masses actively involved in nuclear reactors, particle accelerators, and the thermo nuclear reactions in the Sun and stars. The new conservation principle is the conservation of mass energy.

## Units of Mass

The unit of mass in the International System of Units (SI) is the kilogram, which is defined in terms of Planck’s constant, which is defined as equal to 6.62607015×10^{-34} joule second.

One joule is equal to one kilogram times metre squared per second squared. With the second and the metre already defined in terms of other physical constants, the kilogram is determined by accurate measurements of Planck’s constant. (Until 2019 the kilogram was defined by a platinum-iridium cylinder called the International Prototype Kilogram kept at the International Bureau of Weights and Measures in Sevres, France.)

In the English system of measurement, the unit of mass is the slug, a mass whose weight at sea level is 32.17 pounds.

**Following are the most commonly used units for the measurement of mass :**

- Gram(g)
- Kilogram(kg)

### Other Units of Mass

Other units that are accepted for use in SI are gram (g) and its multiples and submultiples, a tonne (t) (or “metric ton”), electronvolt (eV), the atomic mass unit (u) which is most convenient for expressing the masses of atoms and molecules.

## How Weight Related to Mass?

Weight, though related to mass, nonetheless differs from the latter. Weight essentially constitutes the force exerted on the matter by Earth’s gravitational attraction, so it varies slightly from place to place.

In contrast, mass remains constant regardless of its location under ordinary circumstances. A satellite launched into space, for example, weighs increasingly less the farther it travels away from Earth. Its mass, however, stays the same.

## Origin of Mass

In theoretical physics, a mass generation mechanism is a theory which attempts to explain the origin of mass from the most fundamental laws of physics.

A number of different models have been proposed that advocate different views of the origin of mass. The problem is complicated because the notion of mass is strongly related to the gravitational interaction.

Still, a theory of the latter has not been reconciled with the currently popular model of particle physics, known as the Standard Model.

## Phenomena of Mass

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 F = ma).
- 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 the first body of mass m
_{A}is placed at a distance r (center of mass to center of mass) from the second body of mass m_{B}, each body is subject to an attractive force F_{g}= Gm_{A}m_{B}/r^{2}, where G = 6.67×10^{-11}N⋅kg^{-2}⋅m^{2}is the “universal gravitational constant.” This is sometimes referred to as gravitational mass. Repeated experiments since the 17^{th}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.

## Other Definitions of Mass

### Definition-1

Inertial mass is a measure of an object’s resistance to acceleration when a force is applied. It is determined by applying a force to an object and measuring the acceleration that results from that force.

An object with small inertial mass will accelerate more than an object with large inertial mass when acted upon by the same force. One says the body of greater mass has greater inertia.

### Definition-2

Active gravitational mass measures the strength of an object’s gravitational flux (gravitational flux is equal to the surface integral of the gravitational field over an enclosing surface). Gravitational field can be measured by allowing a small “test object” to fall freely and measuring its free-fall acceleration.

**For example**, an object in free-fall near the Moon is subject to a smaller gravitational field and accelerates more slowly than the same object would if it were in free-fall near the Earth. The gravitational field near the Moon is weaker because the Moon has less active gravitational mass.

### Definition-3

Passive gravitational mass is a measure of the strength of an object’s interaction with a gravitational field. Passive gravitational mass is determined by dividing an object’s weight by its free-fall acceleration. Two objects within the same gravitational field will experience the same acceleration.

However, the object with a smaller passive gravitational mass will experience a smaller force (less weight) than the object with a larger passive gravitational mass.

### Definition-4

Energy also has mass according to the principle of mass-energy equivalence. This equivalence is exemplified in many physical processes, including pair production, nuclear fusion, and the gravitational bending of light.

Pair production and nuclear fusion are processes in which measurable amounts of mass are converted to energy or vice versa. In the gravitational bending of light, photons of pure energy are shown to exhibit a behavior similar to passive gravitational mass.

### Definiton-5

The curvature of spacetime is a relativistic manifestation of the existence of mass. Such curvature is extremely weak and difficult to measure. For this reason, curvature was not discovered until after Einstein’s theory of general relativity predicted it.

Same atomic clocks on the surface of the Earth. For example, are found to measure less time (run slower) when compared to similar clocks in space. This difference in elapsed time is a form of curvature called gravitational time dilation. Other forms of curvature have been measured using the Gravity Probe B satellite.

### Definition-6

Quantum mass manifests itself as a difference between an object’s quantum frequency and its wave number. The quantum mass of a particle is proportional to the inverse Compton wavelength and can be determined through various forms of spectroscopy.

In relativistic quantum mechanics, mass is one of the irreducible representation labels of the Poincare group.

## Types of Mass Properties

In classical mechanics, there are three types of mass or properties called mass: Inertial mass; passive gravitational mass; and active gravitational mass.

Although inertial mass, passive gravitational mass and active gravitational mass are conceptually distinct, no experiment hasever unambiguously demonstrated any difference between them.

- Inertial mass is a mass parameter giving the inertial resistance to the acceleration of the body when responding to all types of force. Gravitational mass is determined by the strength of the gravitational force experienced by the body when in the gravitational field g.
- Passive gravitational mass is a measure of the strength of an object’s interaction with a gravitational field. Passive gravitational mass is determined by dividing an object’s weight by its free-fall acceleration. Energy also has mass according to the mass-energy equivalence principle.
- Active gravitational mass measures the strength of an object’s gravitational flux (gravitational flux is equal to the surface integral of the gravitational field over an enclosing surface). Gravitational field can be measured by allowing a small “test object” to fall freely and measuring its free-fall acceleration.

## Calculation of Mass

The mass of an object can be calculated in a number of different ways :

**mass=density × volume (m=ρV)**. Density is a measure of mass per unit of volume, so the mass of an object can be determined by multiplying density by volume.**mass=force ÷ acceleration (m=F/a)**. According to Newton’s second law (F=ma), the acceleration of an object is directly proportional to the force applied to it. Consequently, the amount of acceleration accompanying the application of a constant force is inversely proportional to the mass.**mass=weight÷ gravitational acceleration (m=W/g)**. Weight is the product of the acceleration of mass in a gravitational field. Depending on the strength of gravitational acceleration, the weight will be different.

All three of these formulae are a way of determining the mass of an object. Since mass is a fundamental property, It is not defined in other units, like the joule (J) of newton (N) are.

There are other ways to calculate the mass of an object, but these three formulae are the most common ones.

m=ρV

m=W/g

m=F/a

### From Density And Volume

For example, water has a density of 977 kg/m^{3} at standard temperatures and pressures. That is, one cubic meter of water has a mass of 977 kg. If we know the density and volume of a substance, we can also figure out the mass. Say we have a 0.7m^{3} sample of water. How much mass does that sample have?

Solving for mass gives us:

m=ρV

m=(0.7m^{3})(977kg/m^{3}) = 683 kg

0.5 cubic meters of water at standard temperature and pressure would have a mass of 683 kg.

Some objects are incredibly dense. A neutron star, for example, has an average density of 1.1 x 1018 kg/m^{3}. A single teaspoon of a neutron star would weigh about 100 million tons on Earth.

### From Force And Acceleration

For example, say that we apply a 748 N force to a metal cube, and we measure its acceleration as 21m/s2. What is the mass of the metal cube?

We can figure calculate the mass by dividing the magnitude of the force by the magnitude of acceleration so:

m=F/a

m=(748N)/(21m/s^{2}) ≈ 35.62 kg

So we know that the metal cube must have a mass of 35.62 kg.

### From Weight

For example, on the surface of the Earth where g=9.81 m/s2, a 50 kg object would have a weight in pounds of:

W=(50kg)(9.81m/s^{2})=490.5N

Converting newtons to pounds gives us:

490.5N(.22lbs/1N)≈108 pounds

Conversely, on the moon where g has a value of 1.6m/s^{2}, a 50 kg object would weigh:

W=50(kg)(1.6m/s^{2})(0.22lbs/1N)≈18 pounds

The same 50 kg object weights 108 lbs on Earth and 18 lbs on the moon.

Likewise, if we know the weight of an object, we can work backward to figure out its mass. Say an object weighs 160 pounds ofEarth. we can calculate the mass of the object as:

180lbs(1N/0.22lbs)=818.18N

818.18N=m(9.81m/s2)

m=818.18N/(9.81m/s2)≈83.4 kg

So a 180 lb body on Earth has a mass of about 84.3 kg.

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