# Mass versus weight: Map

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In the physical sciences, mass and weight are different properties. Mass is a measure of the amount of matter in the body while weight is a measure of the force on the object caused by a gravitational field.

Thus the mass of an object will remain constant wherever it is on the earth’s surface (assuming it is not traveling at a relativistic speed with respect to an observer),but if it is moved from the equator to the North Pole, its weight will increase by about 0.5% due to the increase in the earth’s gravitational field.

Accordingly, for astronauts in microgravity, no effort is required to hold objects off the cabin floor; they are “weightless”. However, since objects in microgravity still retain their mass and inertia, an astronaut must exert ten times as much force to accelerate a 10 kilogram object at the same rate as a 1 kilogram object.

On earth, a common swing set can demonstrate the relationship of force, mass, and acceleration without being appreciably influenced by weight (downward force). If one were to stand behind a large adult sitting stationary in a swing and give him a strong push, the adult would accelerate relatively slowly and swing only a limited distance forwards before beginning to swing backwards. Exerting that same effort while pushing on a small child would produce much greater acceleration.

## Overview

Matter’s mass strongly influences many familiar kinetic properties.

Mass corresponds to the general, everyday notion of how “heavy” something is. However, mass is actually an inertial property; that is, the tendency of an object to remain at constant velocity unless acted upon by an outside force. Per Sir Isaac Newton’s -year-old laws of motion and an important formula that sprang from his work, an object with a mass, m, of one kilogram will accelerate, a, at one meter per second per second (about one-tenth the acceleration due to earth’s gravity)In professional metrology (the science of measurement), the acceleration of earth’s gravity is taken as standard gravity (symbol: gn), which is defined as precisely meters per square second (m/s2). The expression means that for every second that elapses, velocity changes an additional 1 meter per second. In more familiar terms: an acceleration of 1 m/s2 can also be expressed as a rate of change in velocity of precisely 3.6 km/h per second (≈2.2 mph per second). when acted upon by a force, F, of one newton.

Inertia is sensed when a bowling ball is pushed horizontally on a level, smooth surface. This is quite distinct from “weight”, which is the downwards gravitational force of the bowling ball that one must counter when holding it off the floor. For instance, an astronaut’s weight on the Moon is one-sixth of that on the Earth, whereas his mass has changed little during the trip. Consequently, wherever the physics of recoil kinetics (mass, velocity, inertia, inelastic and elastic collisions) dominate and the influence of gravity is a negligible factor, the behavior of objects remains consistent even where gravity is relatively weak. For instance, billiard balls on a billiards table would scatter and recoil with the same speeds and energies after a break shot on the Moon as on Earth; they would however, drop into the pockets much more slowly.

In the physical sciences, the terms “mass” and “weight” are rigidly defined as separate measures in order to enforce clarity and precision. In everyday use, given that all masses on Earth have weight and this relationship is usually highly proportional, “weight” often serves to describe both properties, its meaning being dependent upon context. For example, in commerce, the “net weight” of retail products actually refers to mass and is properly expressed in pounds (U.S.) or kilograms (see also Pound: Use in commerce). Conversely, the “load index” rating on automobile tires, which specifies the maximum structural load for a tire in kilograms, refers to weight; that is, the force due to gravity. Before the late twentieth century, this distinction was not as strictly applied, even in technical writing, so that expressions such as “molecular weight” (for molecular mass) are still seen.

Because mass and weight are separate quantities, they have different units of measure. In the International System of Units (SI), the kilogram is the unit of mass, and the newton is the unit of force. The non-SI kilogram-force is also a unit of force typically used in the measure of weight. Similarly, the avoirdupois pound, used in both the Imperial system and U.S. customary units, is a unit of mass and its related unit of force is the pound-force.

## Converting units of mass to equivalent forces on Earth

When an object’s weight (its gravitational force) is expressed in kilograms, the unit of measure is not a true kilogram; it is the kilogram-force (kgf or kg-f), also known as the kilopond (kp), which is a non-SI unit of force. All objects on Earth are subject to a gravitational acceleration of approximately 9.8 m/s2. The CGPM (also known as the “General Conference on Weights and Measures”) fixed the value of standard gravity at precisely 9.80665 m/s2 so that disciplines such as metrology would have a standard value for converting units of defined mass into defined forces and pressures. In fact, the kilogram-force is defined as precisely 9.80665 newtons. As a practical matter, gravitational acceleration (symbol: g) varies slightly with latitude, elevation and subsurface density; these variations are typically only a few tenths of a percent. See also Gravimetry.

Professionals in engineering and scientific disciplines involving accelerations and kinetic energies rigorously maintain the distinctions between mass, force, and weight, as well as their respective units of measure. Engineers in disciplines involving weight loading (force on a structure due to gravity), such as structural engineering, first convert loads due to objects like concrete and automobiles—which are always tallied in kilograms—to newtons before continuing with their calculations. Primarily, this is because material properties like elastic modulus are measured and published in terms of the newton and pascal (a unit of pressure derived from the newton). For all practical engineering purposes on Earth, mass in kilograms is converted to weight in newtons by multiplying by 9.80665 (standard gravity).

## Buoyancy and “conventional mass”

Regardless of the fluid in which an object is immersed (gas or liquid), the buoyant force on an object is equal to the weight of the fluid it displaces.

The masses of objects are relatively invariant whereas their weights vary slightly with changes in barometric pressure, such as with changes in weather and altitude. This is because objects have volume and therefore have a buoyant effect in air. Buoyancy—a force that opposes gravity—reduces the weight of all objects immersed in fluids. This means that objects with precisely the same mass but with different densities displace different volumes and therefore have different buoyancies and weights.

Normally, the effect of air buoyancy is too small to be of any consequence in normal day-to-day activities. For instance, buoyancy’s diminishing effect upon one’s body weight (a relatively low-density object) is 1/860 that of gravity and variations in barometric pressure rarely affect one’s weight more than ±1 part in 30,000.Assumptqerqerions: An air density of 1160 g/m3, an average density of a human body (with collapsed lungs) equal to that of water, and variations in barometric pressure rarely exceeding ±22 torr. Assumptions primary variables: An altitude of 194 meters above mean sea level (the worldwide median altitude of human habitation), an indoor temperature of 23 °C, a dewpoint of 9 °C, and 760 mmHg sea level–corrected barometric pressure. In metrology however, mass standards are calibrated with extreme accuracy, so air density must be taken into account to allow for buoyancy effects.

Given the extremely high cost of platinum-iridium mass standards like the International Prototype Kilogram (IPK), high-quality “working” standards are made of special stainless steel alloys that occupy greater volume than those made of platinum-iridium, which have a density of about 21,550 kg/m3. For convenience, a standard value of buoyancy relative to stainless steel was developed for metrology work and this results in the term “conventional mass”. Conventional mass is defined as follows: “For a mass at 20 °C, ‘conventional mass’ is the mass of a reference standard of density 8000 kg/m3 which it balances in air with a density of 1.2 kg/m3.” The effect is a small one, 150 ppm for stainless steel mass standards, but the appropriate corrections are made during the calibration of all precision mass standards so that they have the true mass indicated on them.

In routine laboratory use, the reading on a precision scale when a stainless steel standard is placed upon it is actually its conventional mass; that is, its true mass minus buoyancy. Also, any object compared to a stainless steel mass standard has its conventional mass measured; that is, its true mass minus an unknown degree of buoyancy. For certain high-precision disciplines, the density of a sample is sometimes known or can be closely estimated (such as when weighing aqueous solutions) and the effect of buoyancy is compensated for mathematically.

## Types of scales and what they measure

A balance-type weighing scale: Unaffected by the strength of gravity.
Load-cell based bathroom scale: Affected by the strength of gravity.

Technically, whenever someone stands on a balance-beam-type scale at a doctor’s office, they are truly having their mass measured. This is because balances (“dual-pan” mass comparators) compare the weight of the mass on the platform with that of the sliding counterweights on the beams; gravity serves only as the force-generating mechanism that allows the needle to diverge from the “balanced” (null) point. Balances can be moved from Earth’s equator to the poles without spuriously indicating that objects gain over 0.3% more weight; they are immune to the gravity-countering centrifugal force due to Earth’s rotation about its axis. Conversely, whenever someone steps onto spring-based or digital load cell-based scales (single-pan devices), they are technically having their weight (force due to strength of gravity) measured. On force-measuring instruments such as these, variations in the strength of gravity affect the reading. As a practical matter, when force-measuring scales are used in commerce or hospitals, they are calibrated on-site and certified on that basis so the measure is mass, expressed in pounds or kilograms, to the desired level of accuracy.