Weight

In modern physics, weight is a measure of the gravitational force acting on an object. Weight is the force exerted by a body on a point of support, caused by the action of the local gravitational field on the mass of the body. Because it is a force, weight is represented as a vector, defined by its magnitude, direction and sense, applied to the center of gravity of the mass and directed approximately towards the center of the Earth. By extension of this definition, we can also refer to the weight of a body on any other star (Moon, Mars, among others) in whose vicinity it is located.

The magnitude of the weight of an object, from the operational definition of weight, depends only on the intensity of the local gravitational field and the mass of the body, in a strict sense. However, from a legal and practical point of view, it is established that the weight, when the reference system is the Earth, comprises not only the local gravitational force, but also the local centrifugal force due to the rotation of the Earth; conversely, atmospheric buoyancy is not included, nor are any other external forces.

Difference in weight and mass

The dynamometer serves to measure the weight of the bodies

Weight and mass are two very different concepts and physical magnitudes, although even today, in everyday speech, the term “weight” is often mistakenly used as a synonym for mass. The Academy recognizes this confusion in the definition of "weigh": "To determine the weight, or more properly, the mass of something by means of a balance or other equivalent instrument."

The mass of a body is an intrinsic property of it, the amount of matter, independent of the intensity of the gravitational field and of any other effect. It represents the inertia or resistance of the body to changes in the state of motion (acceleration, inertial mass), in addition to making it sensitive to the effects of gravitational fields (gravitational mass).

The weight of a body, on the other hand, is not an intrinsic property of the same, since it depends on the intensity of the gravitational field in the place of space occupied by the body. The scientific distinction between "mass" and "weight" is not important for many practical purposes because the gravitational force does not change greatly near the Earth's surface. In a constant gravitational field, the force exerted by gravity on a body (its weight) is directly proportional to its mass. But in reality the terrestrial gravitational field is not constant; It can vary by up to 0.5% between the different places on Earth, which means that the "mass-weight" relationship is altered with the variation in the force of gravity.

On the contrary, the weight of the same body undergoes very significant changes when changing the massive object that creates the gravitational field. Thus, for example, a person of mass 60 kg (6.118 UTM) weighs 588.60 N (60 kgf) on the Earth's surface. The same person, on the surface of the Moon, would weigh only about 98.05 N (10 kgf); however, his mass will still be 60 kg (6.118 UTM). Note: In italics, International System; (between parentheses), Technical System of Units.

Under the denomination of apparent weight, other effects are included, in addition to the gravitational force and the centrifugal effect, such as buoyancy, the non-inertial nature of the reference system (eg, an accelerated elevator), etc. The weight that the dynamometer measures is actually the apparent weight; the real weight would be the one that would measure in a vacuum in an inertial reference system.

Weight units

Since weight is a force, it is measured in units of force. However, the units of weight and mass have a long shared history, in part because their difference was not well understood when those units came into use.

International Unit System

This system is the priority or the only legal one in most of the nations (excluding Burma and the United States), so in scientific publications, in technical projects, in machine specifications, etc., the Physical quantities are expressed in units of the International System of Units (SI). Thus, weight is expressed in SI units of force, that is, in newtons (N):

• 1 N = 1 kg · 1 m/s2

Technical Unit System

In the Technical System of Units, weight is measured in kilogram-force (kgf) or kilopond (kp), defined as the force exerted on one kilogram of mass by the acceleration in free fall (g = 9.80665 m /s²)

• 1 kgf = 9,80665 N = 9,80665 kg·m/s2

Other systems

Weight is also usually indicated in force units of other systems, such as the dyne, the pound-force, the ounce-force, etc.

The dyne is the CGS unit of force and is not part of the SI. Some English units, such as the pound, can be for force or mass. Related units, like the slug, are part of unit sub-systems.

Weight calculation

Contribution of gravitational and centrifugal accelerations in weight

The calculation of the weight of a body from its mass can be expressed by the second law of dynamics:

where the value of g{textstyle g} is the acceleration of gravity in the place where the body is located. In the first approach, if we consider Earth as a homogeneous sphere, it can be expressed with the following formula:

g=Fm=GMTRT2{displaystyle g={frac {F}{m}}}={frac {GM_{T}{R_{T}}}{{2}}}}}}}{

according to the law of universal gravitation.

In reality, the value of the acceleration of gravity on Earth, at sea level, varies between 9,789 m/s² at the equator and 9,832 m/s² at the poles. It was conventionally set at 9.80665 m/s² at the third General Conference on Weights and Measures convened in 1901 by the International Bureau of Weights and Measures (Bureau International des Poids et Mesures). As a consequence, the weight varies in the same proportion.

Comparison of weight in the solar system

Anomalies of the terrestrial gravitational field (expressed in miligal) regarding the estimated value, considering the variation of the terrestrial radius.

The following list describes the weight of a "unit mass" body on the surface of some Solar System bodies, compared to its weight on Earth:

The weight of a human being

Correlation between mass (kg) and height (m) of a human being

On average, a newborn has a mass of 3 to 4 kilograms (colloquially it is said to weigh 3 to 4 kilograms), and at twelve months it has a mass of 9 to 12 kilograms.

Already in adulthood, men generally weigh more than women, due to the difference in height that is usually greater in men. An average adult male weighs between 70 and 90 kg (with a height of 1.75 m); While the average adult woman weighs between 50 and 70 kg (with a height of 1.60 m). Example of weight:

The body mass index establishes the relationship between the mass and the height of the person. The equation to calculate the BMI is: body mass (“weight”, expressed in kilograms) divided by the square of the height (expressed in meters).

• BMI of less than 18,0 is considered Low Weight
• BMI 18.5-24.9 is considered a healthy weight.
• BMI of 25,0-29,9 is considered overweight.
• IMC of 30.0-39.9 is considered obesity.
• BMI of 40,0 or more is considered severe obesity (or morbid obesity).

There have been extreme cases in which the difference between a person's weight and the average weight exceeded hundreds of kilograms. To date, Jon Brower Minnoch is the person who has weighed the most for which data is available.

Sensation of weight

The sensation of weight is due to the force exerted by the fluids of the vestibular system, a three-dimensional set of cavities of the inner ear. Actually, the sensation of "G-Force", regardless of whether the presence of gravity is stationary, or, if the body is in motion, the result of other forces acting on it, such as acceleration or deceleration of an elevator, or the force we feel when riding a roller coaster.

The weight and its teaching

Newtonian concepts of gravity were challenged by the Theory of Relativity in the 20th century. Einstein's equivalence principle places all observers in the same plane. This led to ambiguity as to what exactly is meant by “gravitational force” and consequently “weight”. The ambiguities introduced by relativity led, starting in the 1960s, to a wide debate in the educational community on how to define weight for their students. The choice was a Newtonian definition of weight as the force on an object at rest on the ground due to gravity, or an operational definition defined by the act of weighing.^{[citation needed]} In the operational definition, weight becomes zero, under weightless conditions such as in Earth orbit or free fall in a vacuum. In such situations, the Newtonian view is that there continues to be a force due to gravity that is not measured (thus causing an apparent weight of zero), while the Einsteinian view is that there is never a measurable force due to gravity (even in the ground), but, in free fall, no force can be measured because the ground does not exert the mechanical force ordinarily observed as "weight."