Weight

Scale

Weight is a vital concept in physics and daily life. Its definition and understanding have evolved over the years and can be examined from various perspectives, including gravitational, operational, and international standards. This article provides a thorough examination of the concept of weight, its measurements, and its implications in various situations.

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Definitions of Weight

Gravitational Definition

The gravitational definition of weight is the most commonly taught in introductory physics textbooks. It posits that weight is the force exerted on a body due to gravity. Mathematically, this force is represented as W W=mg, where: W = Weight m = Mass of the object g = Gravitational acceleration This definition was formalized in 1901 by the 3rd General Conference on Weights and Measures (CGPM) in their resolution. They highlighted weight as a vector quantity, akin to force. Some references, however, describe weight as a scalar, noting its magnitude from gravitational force.

Given the variability of gravitational acceleration in different locations, sometimes it's standardized to 9.80665 m/s^2, termed as the standard weight. A force having a magnitude equivalent to mg newtons is also labeled as the m kilogram weight (abbreviated as kg-wt).

Operational Definition

In the operational definition, weight is gauged by the force it exerts on its support when being weighed. This means that an object in free fall, which exerts minimal force on its support, is said to be weightless. However, its weight as defined gravitationally remains unchanged. This operational perspective is sometimes refined to consider an object at rest, usually relative to the Earth. This definition can differ from the gravitational definition in specific scenarios, such as the centrifugal effects from Earth's rotation.

The operational definition might not always factor in buoyancy effects, which can reduce an object's measured weight when submerged in a fluid.

ISO Definition

ISO 80000-4(2006) provides another perspective on weight. This definition is rooted in the chosen frame of reference. If the chosen frame moves alongside the object, it aligns seamlessly with the operational definition. For a frame set to Earth's surface, the difference between ISO and gravitational definitions arises from the Earth's rotational centrifugal effects.

Apparent Weight

Main article: Apparent weight The measured weight in practical scenarios can sometimes deviate from the idealized definitions due to various factors, leading to the concept of apparent weight. Factors like buoyancy can make objects seem lighter when submerged. Other effects, such as levitation and mechanical suspension, can also influence apparent weight. When using the gravitational definition of weight, the weight measured by an accelerating scale might also be termed as the apparent weight.

Weight vs. Mass

Main article: Mass versus weight Weight and mass are distinct yet often interchangeably used in colloquial language. While mass is an intrinsic property of matter, weight arises from the gravitational force acting on that matter. On Earth, due to relatively uniform gravitational strength, an object's weight is directly proportional to its mass.

However, this direct relationship doesn't hold true everywhere. For instance, the Moon's surface gravity is only about one-sixth of Earth's, affecting the weight of objects but not their mass.

Measurement of Weight

Main article: Weighing scale Weight can be ascertained using two primary methodologies:

Spring, Hydraulic, or Pneumatic Scales: These devices measure local weight, i.e., the local gravitational force on an object. Given the variable nature of Earth's gravitational force in different locations, spring scales can sometimes give different readings for the same object. For commercial legality and high precision, these scales need to be calibrated at their specific location of use. Balances: Balances compare the weight of an unknown object to a set of standard masses. They provide consistent readings across different locations on Earth because they rely on the consistent effect of gravity on both the unknown and known weights.

Units of Weight

Weight can be expressed in various units, with the SI unit being the newton (N), defined as kg·m/s^2. In daily and commercial usage, the term "weight" often implies "mass," and the kilogram (kg) is used as the standard unit.

Non-SI units like the pound, kilogram-force, dyne, poundal, and slug also find usage in specific contexts.

Sensation of Weight

Our perception of weight is influenced by the force exerted by fluids in the vestibular system located in the inner ear. This sensation reflects the experience of g-force, be it due to gravity or other external forces, such as acceleration or centrifugal forces.

Conclusion

The concept of weight has been pivotal in shaping our understanding of physics and the world around us. Through various definitions and perspectives, we appreciate the intricacies and nuances that weight presents in different scenarios. The manner in which weight is measured, perceived, and defined plays a fundamental role in various scientific, commercial, and everyday contexts.

See Also

• Gravity
• Mass
• Force
• Acceleration
• International System of Units (SI)

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