Mass versus weight


In common usage, the mass of an object is often referred to as its weight, though these are in fact different concepts and quantities. In scientific contexts, mass is the amount of "matter" in an object, whereas weight is the force exerted on an object by gravity. In other words, an object with a mass of 1.0 kilogram weighs approximately 9.81 newtons on the surface of the Earth, which is its mass multiplied by the gravitational field strength. The object's weight is less on Mars, where gravity is weaker, and more on Saturn, and very small in space when far from any significant source of gravity, but it always has the same mass.
Objects on the surface of the Earth have weight, although sometimes the weight is difficult to measure. An example is a small object floating in water, which does not appear to have weight since it is buoyed by the water; but it is found to have its usual weight when it is added to water in a container which is entirely supported by and weighed on a scale. Thus, the "weightless object" floating in water actually transfers its weight to the bottom of the container. Similarly, a balloon has mass but may appear to have no weight or even negative weight, due to buoyancy in air. However the weight of the balloon and the gas inside it has merely been transferred to a large area of the Earth's surface, making the weight difficult to measure. The weight of a flying airplane is similarly distributed to the ground, but does not disappear. If the airplane is in level flight, the same weight-force is distributed to the surface of the Earth as when the plane was on the runway, but spread over a larger area.
A better scientific definition of mass is its description as being composed of inertia, which is the resistance of an object being accelerated when acted on by an external force. Gravitational "weight" is the force created when a mass is acted upon by a gravitational field and the object is not allowed to free-fall, but is supported or retarded by a mechanical force, such as the surface of a planet. Such a force constitutes weight. This force can be added to by any other kind of force.
While the weight of an object varies in proportion to the strength of the gravitational field, its mass is constant, as long as no energy or matter is added to the object. For example, although a satellite in orbit is "weightless", it still retains its mass and inertia. Accordingly, even in orbit, an astronaut trying to accelerate the satellite in any direction is still required to exert force, and needs to exert ten times as much force to accelerate a 10ton satellite at the same rate as one with a mass of only 1 ton.

Overview

Mass is an inertial property; that is, the tendency of an object to remain at constant velocity unless acted upon by an outside force. Under 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 accelerates, a, at one meter per second per second when acted upon by a force, F, of one newton.
Inertia is seen when a bowling ball is pushed horizontally on a level, smooth surface, and continues in horizontal motion. This is quite distinct from its weight, which is the downwards gravitational force of the bowling ball one must counter when holding it off the floor. The weight of the bowling ball on the Moon would be one-sixth of that on the Earth, although its mass remains unchanged. Consequently, whenever the physics of recoil kinetics 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 billiard 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, as they are different physical properties. In everyday use, as all everyday objects have both mass and weight and one is almost exactly proportional to the other, "weight" often serves to describe both properties, its meaning being dependent upon context. For example, in retail commerce, the "net weight" of products actually refers to mass, and is expressed in mass units such as grams or ounces ''. 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 20th century, the distinction between the two was not strictly applied in technical writing, so that expressions such as "molecular weight" are still seen.
Because mass and weight are separate quantities, they have different units of measure. In the International System of Units, the kilogram is the basic unit of mass, and the newton is the basic 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 is expressed in "kilograms", this actually refers to the kilogram-force, also known as the kilopond, which is a non-SI unit of force. All objects on the Earth's surface are subject to a gravitational acceleration of approximately 9.8 m/s2. 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. Thus the kilogram-force is defined as precisely 9.80665 newtons. In reality, gravitational acceleration varies slightly with latitude, elevation and subsurface density; these variations are typically only a few tenths of a percent. See also Gravimetry.
Engineers and scientists understand the distinctions between mass, force, and weight. Engineers in disciplines involving weight loading, such as structural engineering, convert the mass of objects like concrete and automobiles to a force in newtons to derive the load of the object. Material properties like elastic modulus are measured and published in terms of the newton and pascal.

Buoyancy and weight

Usually, the relationship between mass and weight on Earth is highly proportional; objects that are a hundred times more massive than a one-liter bottle of soda almost always weigh a hundred times more—approximately 1,000 newtons, which is the weight one would expect on Earth from an object with a mass slightly greater than 100 kilograms. Yet, this is not always the case and there are familiar objects that violate this proportionality.
A common helium-filled toy balloon is something familiar to many. When such a balloon is fully filled with helium, it has buoyancy—a force that opposes gravity. When a toy balloon becomes partially deflated, it often becomes neutrally buoyant and can float about the house a meter or two off the floor. In such a state, there are moments when the balloon is neither rising nor falling and—in the sense that a scale placed under it has no force applied to it—is, in a sense perfectly weightless. Though the rubber comprising the balloon has a mass of only a few grams, which might be almost unnoticeable, the rubber still retains all its mass when inflated.
Again, unlike the effect that low-gravity environments have on weight, buoyancy does not make a portion of an object's weight vanish; the missing weight is instead being borne by the ground, which leaves less force being applied to any scale theoretically placed underneath the object in question. If one were however to weigh a small wading pool that someone then entered and began floating in, they would find that the full weight of the person was being borne by the pool and, ultimately, the scale underneath the pool. Whereas a buoyant object would weigh less, the object/fluid system becomes heavier by the value of object's full mass once the object is added. Since air is a fluid, this principle applies to object/air systems as well; large volumes of air—and ultimately the ground—supports the weight a body loses through mid-air buoyancy.
The effects of buoyancy do not just affect balloons; both liquids and gases are fluids in the physical sciences, and when all macrosize objects larger than dust particles are immersed in fluids on Earth, they have some degree of buoyancy. In the case of either a swimmer floating in a pool or a balloon floating in air, buoyancy can fully counter the gravitational weight of the object being weighed, for a weighing device in the pool. However, as noted, an object supported by a fluid is fundamentally no different from an object supported by a sling or cable—the weight has merely been transferred to another location, not made to disappear.
The mass of "weightless" balloons can be better appreciated with much larger hot air balloons. Although no effort is required to counter their weight when they are hovering over the ground, the inertia associated with their appreciable mass of several hundred kilograms or more can knock fully grown men off their feet when the balloon's basket is moving horizontally over the ground.
Buoyancy and the resultant reduction in the downward force of objects being weighed underlies Archimedes' principle, which states that the buoyancy force is equal to the weight of the fluid that the object displaces. If this fluid is air, the force may be small.

Buoyancy effects of air on measurement

Normally, the effect of air buoyancy on objects of normal density is too small to be of any consequence in day-to-day activities. For instance, buoyancy's diminishing effect upon one's body weight is that of gravity. Furthermore, variations in barometric pressure rarely affect a person's weight more than ±1 part in 30,000. However, in metrology, the precision mass standards for calibrating laboratory scales and balances are manufactured with such accuracy that air density is accounted for to compensate for buoyancy effects. Given the extremely high cost of platinum-iridium mass standards like the international prototype of the kilogram, high-quality "working" standards are made of special stainless steel alloys with densities of about 8,000 kg/m3, which 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 8,000 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 manufacture of all precision mass standards so they have the true labeled mass.
Whenever a high-precision scale in routine laboratory use is calibrated using stainless steel standards, the scale is actually being calibrated to conventional mass; that is, true mass minus 150 ppm of buoyancy. Since objects with precisely the same mass but with different densities displace different volumes and therefore have different buoyancies and weights, any object measured on this scale has its conventional mass measured; that is, its true mass minus an unknown degree of buoyancy. In high-accuracy work, the volume of the article can be measured to mathematically null the effect of buoyancy.

Types of scales and what they measure

When one stands on a balance-beam-type scale at a doctor’s office, they are having their mass measured directly. This is because balances compare the gravitational force exerted on the person on the platform with that on the sliding counterweights on the beams; gravity is the force-generating mechanism that allows the needle to diverge from the "balanced" point. These balances could be moved from Earth's equator to the poles and give exactly the same measurement, i.e. they would not spuriously indicate that the doctor's patient became 0.3% heavier; they are immune to the gravity-countering centrifugal force due to Earth's rotation about its axis. But if you step onto spring-based or digital load cell-based scales, you are having your weight measured; and variations in the strength of the gravitational field affect the reading. In practice, when such scales are used in commerce or hospitals, they are often adjusted on-site and certified on that basis, so that the mass they measure, expressed in pounds or kilograms, is at the desired level of accuracy.

Use in commerce

In the United States of America the United States Department of Commerce, the Technology Administration, and the National Institute of Standards and Technology have defined the use of mass and weight in the exchange of goods under the Uniform Laws and Regulations in the areas of legal metrology and engine fuel quality in NIST Handbook 130.
NIST Handbook 130 states:


U.S. federal law, which supersedes this handbook, also defines weight, particularly Net Weight, in terms of the avoirdupois pound or mass pound. From :


See also 21CFR201 Part 201.51 – "Declaration of net quantity of contents" for general labeling and prescription labeling requirements.