User:Gene Nygaard/·

The distinction between the two
Image:8ball_break.jpg|thumb|257px|Matter’s mass strongly influences many familiar kinetic properties.

As stated above in The nature of mass, the kilogram is a unit of mass, which is an inertial property. Inertia is the property that is sensed when pushing horizontally to accelerate a bowling ball that is resting 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. Unless relativistic effects apply, mass is an unchanging, universal property of matter that is unaffected by gravity. Weight on the other hand, is a property of matter that is entirely dependent upon the strength gravity. 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, the “net weight” of retail products, which may be given in pounds (U.S.) and kilograms, refers to mass (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, actually refers to weight; that is, the force due to gravity.

The unit of force: kilogram-force
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.

Since masses are rarely measured to an uncertainty of better than one percent, it is technically just as valid to state that a one-kilogram object on Earth has a weight of one kilogram-force as it is to state that it has a mass of one kilogram. Accordingly, it may correctly be assumed that when someone speaks or writes of a “weight” in kilograms, they are referring to the gravitational load of the kilogram and the proper “kilogram-force” is implied.

Converting mass to weight loads in engineering
Unlike laypeople, professionals in virtually all 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 quite properly measured and published in terms of newtons and pascals (which is a unit of pressure derived from the newton). Mass in kilograms is converted to weight in newtons by multiplying by gravitational acceleration (see The unit of force: kilogram-force, above).

Buoyancy and “conventional mass”
Image:Submerged-and-Displacing.png|thumb|right|174px|Regardless of the fluid in which an object is immersed (gas or liquid), the buoyancy of an object is proportional to the mass 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 counters gravity’s—reduces the weight of all objects immersed in fluids. Further, 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. In metrology however, where mass standards are calibrated with extreme accuracy, buoyancy is a significant effect so air density is accurately accounted for during calibration.

Given the extremely high cost of platinum-iridium prototypes, high-quality “working” standards are made of special stainless steel alloys, which occupy greater volume than those made of platinum-iridium. 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 they have the true mass indicated on them. In routine laboratory use however, 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 some (usually unknown) degree of buoyancy.

The effect of buoyancy invalidates the standard answer to the childhood riddle of “Which weighs more, a ton of lead or a ton of feathers (or aluminum)?” The standard answer is that they both weigh the same, but the correct answer is “Lead weighs more than aluminum, by 327 grams-force or 3.21 newtons (a difference of 0.0327%).” This is because the density of lead is greater and displaces less air.

Types of scales and what they measure
It’s notable at a purely technical level, that whenever someone stands on a balance-beam scale at a doctor’s office, they are really and truly having their mass measured. Excluding buoyancy, which affects all types of scales in fluids, balance-beam scales compare the mass on the platform with those 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. On scales such as these, gravity can vary in strength without affecting the reading. Conversely, whenever someone steps onto a spring-based or digital load cell-based scale, they are technically having their weight measured notwithstanding that the displayed units of measure are in kilograms. On force-measuring instruments such as these, variations in gravity will 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.