Weight is a measure of force that is equal to the gravitational pull on an object. The weight of an object is dependent on its location. On the moon, the force due to gravity is about one-sixth that of the gravitational force on earth.

- Weight, gravitational force of attraction on an object, caused by the presence of a massive second object, such as the Earth or Moon.
- Weight is a consequence of the universal law of gravitation: any two objects. Because of their masses, attract each other with force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
- Thus, more massive objects weigh more in the exact location; the farther an object is from the Earth, the smaller its weight. The weight of an object at the Earth’s South Pole is slightly more than its weight at the Equator. Because the Earth’s polar radius is slightly less than the equatorial radius. Though the mass of an object remains constant, its weight varies according to its location. The smaller mass and radius of the Moon compared with those of the Earth combine to make the same object on the Moon’s surface weigh one-sixth the value of its weight on Earth.
- Because of all the mass in the universe, each point of space has a property called the gravitational field, numerically equal to the acceleration of gravity at that point. Alternatively, weight is the product of an object’s mass and either the gravitational field or the acceleration of gravity at the point where the object is located. Weight is the product of mass multiplied by acceleration acting on that mass. Usually, it’s an object’s mass multiplied by the acceleration due to gravity.

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## Units of Weight

On Earth, mass and weight have the same value and units. However, weight has a magnitude, like mass, plus a direction. In other words, mass is a scalar quantity, while weight is a vector quantity.

In the United States, a pound is a unit of mass or weight. The SI unit of weight is the newton. The cgs unit of weight is the dyne.

Most of the time, physical quantities are measured in SI units to make things easier.

Therefore, the SI unit of weight can be measured in kg⋅m/s^{2} (kilograms times meters per second squared) equal to a newton (N).

Since weight is the force extended by the gravitational force on a mass, it is represented by the formula W=m*g, where weight can be kg * m/s^{2} equal to N.

### Table with the SI unit, CGS unit, and the dimension of weight:

SI Unit | N |

SI Base Unit | kg.m.s^{-2} |

cgs | dyne |

Dimension | MLT^{-2} |

In the United States, the units of mass and weight are the same. The most common unit of weight is the pound (lb).

However, sometimes the poundal and slug are used. The poundal is the force needed to accelerate a 1-lb mass at 1 ft/s^{2}. The slug is the mass accelerated at 1 ft/s^{2} when a 1 pound-force is exerted.

One slug is the equivalent of 32.2 pounds. In the metric system, units of mass and weight are separate.

The SI unit of weight is the newton (N), which is 1-kilogram meter per second squared. It is the force required to accelerate a 1-kg mass 1 m/s^{2}.

The cgs unit of weight is the dyne. The dyne is the force needed to accelerate a mass of one gram at the rate of one centimeter per second squared. One dyne equals exactly 10^{-5} newtons.

## History

Discussion of the heaviness (weight) concepts and lightness (levity) dates back to the ancient Greek philosophers. These were typically viewed as inherent properties of objects.

Plato described weight as the natural tendency of objects to seek their kin. To Aristotle, weight and levity represented the tendency to restore the natural order of the basic elements: air, earth, fire, and water. He ascribed absolute weight to earth and absolute levity to fire.

Archimedes saw weight as quality as opposed to buoyancy, with the conflict between the two determining if an object sinks or floats.

The first operational definition of weight was given by Euclid, who defined weight as: “the heaviness or lightness of one thing, compared to another, as measured by a balance”. Operational balances (rather than definitions) had, however, been around much longer.

According to Aristotle, weight was the direct cause of the falling motion of an object. The speed of the falling object was supposed to be directly proportionate to the weight of the object.

As medieval scholars discovered that in practice, the speed of a falling object increased with time. This prompted a change to the concept of weight to maintain this cause-effect relationship.

Weight was split into a “still weight” or pondus, which remained constant. And the actual gravity or gravitas changed as the object fell.

The concept of gravitas was eventually replaced by Jean Buridan’s impetus, a precursor to momentum.

The rise of the Copernican view of the world led to the Platonic idea that objects attract but in the context of heavenly bodies.

In the 17th century, Galileo made significant advances in the concept of weight. He proposed a way to measure the difference between the weight of a moving object and an object at rest.

## Other Definitions

There are multiple definition of weight list below :

### According to Newton

The introduction of Newton’s laws of motion and the development of Newton’s law of universal gravitation led to the considerable further development of the concept of weight. Weight became fundamentally separate from the mass.

Mass was identified as a fundamental property of objects connected to their inertia. At the same time, weight became identified with the force of gravity on an object and, therefore, dependent on the object’s context.

In particular, Newton considered weight to be relative to another object causing the gravitational pull, e.g., the weight of the Earth towards the Sun.

Newton considered time and space to be absolute. This allowed him to consider concepts as true position and true velocity.

Newton also recognized that weight, as measured by weighing, was affected by environmental factors such as buoyancy.

He considered this a false weight induced by imperfect measurement conditions, for which he introduced the term apparent weight as compared to the true weight defined by gravity.

Although Newtonian physics distinguished weight and mass, the term weight continued to be commonly used when people meant mass.

This led the 3rd General Conference on Weights and Measures (CGPM) of 1901 to officially declare, “The word weight denotes a quantity of the same nature as a force: the weight of a body is the product of its mass and the acceleration due to gravity,” thus distinguishing it from the mass for official usage.

### According to Relativity

In the 20th century, the Newtonian concepts of absolute time and space were challenged by relativity.

Einstein’s equivalence principle put all observers, moving or accelerating, on the same footing. This led to an ambiguity as to what exactly is meant by the force of gravity and weight. A scale in an accelerating elevator cannot be distinguished from a scale in a gravitational field.

Gravitational force and weight there by became essentially frame-dependent quantities. This prompted the abandonment of the concept as superfluous in the fundamental sciences such as physics and chemistry. The concept remained important in the teaching of physics.

The ambiguities introduced by relativity led, starting in the 1960s, to considerable debate in the teaching community as to how to define weight for their students, choosing between a nominal definition of weight as the force due to gravity or an operational definition defined by the act of weighing.

### Gravitational Definition

The most common definition of weight found in introductory physics textbooks defines weight as the force exerted on a body by gravity.

This is often expressed in the formula **W = mg**, where W is the weight, m the mass of the object, and g gravitational acceleration.

In 1901, the 3rd General Conference on Weights and Measures (CGPM) established this as their official definition of weight:

“The word weight denotes a quantity of the same nature as a force: the weight of a body is the product of its mass and the ac celeration due to gravity.”

— Resolution 2 of the 3rd General Conference on Weights and Measures. This resolution defines weight as a vector, since force is a vector quantity. However, some textbooks also take weight to be a scalar by defining:

“The weight W of a body is equal to the magnitude Fg of the gravitational force on the body.”

The gravitational acceleration varies from place to place. Sometimes, it is simply taken to have a standard value of 9.80665 m/s^{2}, which gives the standard weight.

The force whose magnitude is equal to mg newtons is also known as the m kilogram weight (which term is abbreviated to kg-wt.).

### Operational Definition

In the operational definition, the weight of an object is the force measured by the operation of weighing it, which is the force it exerts on its support.

Since W is the downward force on the body by the center of the Earth and there is no acceleration in the body. There exists an opposite and equal force by the support on the body.

Also, it is equal to the force exerted by the body on its support. Because action and reaction have the same numerical value and opposite direction.

This can make a considerable difference, depending on the details; **for example**, an object in free fall exerts little if any force on its support, a situation that is commonly referred to as weightlessness.

However, being in free fall does not affect the weight according to the gravitational definition. Therefore, the operational definition is sometimes refined by requiring that the object is at rest.

However, this raises the issue of defining “at rest” (usually, being at rest with respect to the Earth is implied using standard gravity).

In the operational definition, the weight of an object at rest on the surface of the Earth is lessened by the effect of the centrifugal force from the Earth’s rotation.

The operational definition, as usually given, does not explicitly exclude the effects of buoyancy. Which reduces the measured weight of an object when it is immersed in a fluid such as air or water.

As a result, a floating balloon or an object floating in water might be said to hav e zero weight.

### ISO Definition

F_{g} = mg

where m is mass and g is local acceleration of free fall.

#### Remarks

- When the reference frame is Earth, this quantity comprises the local gravitational force and the local centrifugal force due to the rotation of the Earth, a force that varies with latitude.
- The effect of atmospheric buoyancy is excluded in the weight.
- In common parlance, the name “weight” continues to be used where “mass” is meant, but this practice is deprecated.

The definition is dependent on the chosen frame of reference. When the chosen frame is co-moving with the object in question, this definition precisely agrees with the operational definition.

Suppose the specified frame is the surface of the Earth. In that case, the weight according to the ISO and gravitational definitions differ only by the centrifugal effects due to the rotation of the Earth.

## Types of Weight

**Formula weight**– In chemistry, the sum of the atomic weights of all atoms appearing in a given chemical formula. It is generally applied to a substance that does not consist of individual molecules, such as the ionic compound sodium chloride. Such a substance is customarily represented by a chemical formula that describes the simplest ratio of the number of atoms of the constituent elements, i.e., an empirical formula.**Molecular weight**, also called molecular mass. The mass of a molecule of a substance, based on 12 as the atomic weight of carbon-12. It is calculated in practice by summing the atomic weights of the atoms making up the substance’s molecular formula. The molecular weight of a hydrogen molecule (chemical formula H2) is 2 (after rounding off); for many complex organic molecules (e.g., proteins, polymers) it may be in the millions.

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