In the
physical sciencesPhysics is a natural science; it is the study of matter and its motion through spacetime and all that derives from these, such as energy and force...
,
massIn physics, mass commonly refers to any of three properties of matter, which have been shown experimentally to be equivalent: inertial mass, active gravitational mass and passive gravitational mass...
and
weightIn the physical sciences, the weight of an object is the magnitude, W, of the force that must be applied to an object in order to support it in a gravitational field. The weight of an object in static equilibrium equals the magnitude of the gravitational force acting on the object, less the effect...
are different properties. Mass is a measure of the amount of
matterThe term matter traditionally refers to the substance that all objects are made of. One common way to identify this "substance" is through its physical properties; a common definition of matter is anything that has mass and occupies a volume...
in the body while weight is a measure of the
forceIn physics, a force is any agent that causes a change in the motion of a free body, or that causes stress in a fixed body. It can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a...
on the object caused by a
gravitational fieldGravitation is a natural phenomenon by which objects with mass attract one another. In everyday life, gravitation is most commonly thought of as the agency which lends weight to objects with mass. Gravitation causes dispersed matter to coalesce, thus accounting for the existence of the Earth, the...
.
Thus the mass of an object will remain constant wherever it is on the earth’s surface (assuming it is not traveling at a
relativisticThe term mass in special relativity usually refers to the rest mass of the object, which is the Newtonian mass as measured by an observer moving along with the object. The invariant mass is another name for the rest mass of single particles...
speed with respect to an observer)
,
but if it is moved from the
equatorThe equator is the intersection of the Earth's surface with the plane perpendicular to the Earth's axis of rotation and containing the Earth's center of mass. In simpler language, it is an imaginary line on the Earth's surface equidistant from the North Pole and South Pole that divides the Earth...
to the
North PoleThe North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is, subject to the caveats explained below, defined as the point in the northern hemisphere where the Earth's axis of rotation meets the Earth's surface...
, 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 10kilogram object at the same rate as a 1kilogram 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
Mass corresponds to the general, everyday notion of how “heavy” something is. However, mass is actually an
inertiaInertia is the resistance of any physical object, to a change in its state of motion. It is represented numerically by an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to describe the motion of matter and how it is affected by...
l property; that is, the tendency of an object to remain at constant velocity unless acted upon by an outside
forceIn physics, a force is any agent that causes a change in the motion of a free body, or that causes stress in a fixed body. It can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a...
. Per
Sir Isaac Newton’sSir Isaac Newton FRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian who is perceived and considered by a substantial number of scholars and the general public as one of the most influential men in history...
-year-old
laws of motionNewton's laws of motion are three physical laws that form the basis for classical mechanics. They are:# In the absence of force, a body either is at rest or moves in a straight line with constant speed....
and an important formula that sprang from his work, an object with a mass,
m, of one
kilogramThe kilogram is the base unit of mass in the International System of Units .[The spelling kilogram is the modern spelling used by the International Bureau of Weights and Measures , the U.S...]
will
accelerateIn physics, and more specifically kinematics, acceleration is the change in velocity over time. Because velocity is a vector, it can change in two ways: a change in magnitude and/or a change in direction. In one dimension, i.e. a line, acceleration is the rate at which something speeds up or slows...
,
a, at one
meter per second per secondThe metre per second squared is the SI derived unit of acceleration. It is a measure of magnitude and can be a scalar measure or, when associated with a direction, a vector. The unit is written in symbols as m/s2, m·s−2, or m s−2...
(about one-tenth the acceleration due to
earth’s gravityEarth's gravity, denoted g, refers to the acceleration that the Earth imparts to objects on or near its surface. In SI units this acceleration is measured in m/s
2...
) when acted upon by a force,
F, of one newton.
Inertia is sensed when a
bowling ballA bowling ball is a round ball made from urethane, plastic, reactive resin or a combination of these materials which is used in the sport of bowling. Ten-pin bowling balls generally have a set of three holes drilled in them, one each for the ring and middle finger, and one for the thumb; however,...
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,
inelasticAn inelastic collision is a collision in which kinetic energy is not conserved .In collisions of macroscopic bodies, some kinetic energy is turned into vibrational energy of the atoms, causing a heating effect, and the bodies are deformed.The molecules of a gas or liquid rarely experience perfectly...
and
elastic collisionAn elastic collision is a collision in which the total kinetic energy of the colliding bodies after collision is equal to their total kinetic energy before collision. Elastic collisions occur only if there is no net conversion of kinetic energy into other forms...
s) 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 indexTire code or Tyre code - Automobile tires are described by an alphanumeric code, which is generally molded into the sidewall of the tire. This code specifies the dimensions of the tire, and some of its key limitations, such as load-bearing ability, and maximum speed...
” rating on automobile tires, which specifies the maximum
structural loadStructural loads are forces applied to a component of a structure or to the structure as a unit.In structural design, assumed loads are specified in national and local design codes for types of structures, geographic locations, and usage. In addition to the load magnitude, its frequency of...
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 massThe molecular mass of a substance, frequently referred to by the older term molecular weight and abbreviated as MW, is the mass of one molecule of that substance, relative to the unified atomic mass unit u...
) are still seen.
Because mass and weight are separate quantities, they have different units of measure. In the
International System of UnitsThe International System of Units is the modern form of the metric system and is generally a system devised around the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science.The older metric system included several groups...
(SI), the
kilogramThe kilogram is the base unit of mass in the International System of Units .[The spelling kilogram is the modern spelling used by the International Bureau of Weights and Measures , the U.S...]
is the unit of mass, and the newton is the unit of force. The non-SI
kilogram-forceThe unit kilogram-force or kilopond is defined as the magnitude of the force exerted on one kilogram of mass by a gravitational field . So one kilogram-force is by definition equal to newtons...
is also a unit of force typically used in the measure of weight. Similarly, the
avoirdupoisThe avoirdupois system is a system of weights based on a pound of sixteen ounces. It is the everyday system of weight used in the United States, and is still widely used to varying degrees by many people in Canada, the United Kingdom, and some other former British colonies despite the official...
poundThe pound or pound-mass is a unit of mass used in the imperial, United States customary and other systems of measurement...
, used in both the Imperial system and
U.S. customary unitsThe United States customary system, or American system and sometimes "English units", of units of measurement is the most commonly used system of measurement in the United States. It is similar but not identical to the British Imperial units. The U.S...
, is a unit of mass and its related unit of force is the
pound-forceThe pound-force or simply pound is a unit of force.- Definitions :The pound-force is approximately equal to the gravitational force exerted on a mass of one avoirdupois pound on the surface of Earth...
.
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-forceThe unit kilogram-force or kilopond is defined as the magnitude of the force exerted on one kilogram of mass by a gravitational field . So one kilogram-force is by definition equal to newtons...
(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/s
2. The
CGPMThe General Conference on Weights and Measures is the English name of the Conférence générale des poids et mesures . It is one of the three organizations established to maintain the International System of Units under the terms of the Convention du Mètre of 1875...
(also known as the “General Conference on Weights and Measures”) fixed the value of
standard gravityStandard gravity, usually denoted by g0 or gn, is the nominal acceleration due to gravity at the Earth's surface at sea level, defined to be precisely 9.80665 m/s2 . This value was established by the 3rd CGPM...
at precisely 9.80665 m/s
2 so that disciplines such as
metrologyMetrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement.-Introduction:...
would have a standard value for converting units of defined mass into defined forces and
pressurePressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
s. In fact, the kilogram-force is defined as precisely 9.80665 newtons. As a practical matter, gravitational acceleration (symbol:
g) varies slightly with
latitudeLatitude, usually denoted by the Greek letter phi gives the location of a place on Earth north or south of the equator. Lines of Latitude are the imaginary horizontal lines shown running east-to-west on maps that run either north or south of the equator...
,
elevationThe elevation of a geographic location is its height above a fixed reference point, often the mean sea level. Elevation, or geometric height, is mainly used when referring to points on the Earth's surface, while altitude or geopotential height is used for points above the surface, such as an...
and subsurface density; these variations are typically only a few tenths of a percent. See also
GravimetryGravimetry is the measurement of the strength of a gravitational field. Gravimetry may be used when either the magnitude of gravitational field or the properties of matter responsible for its creation are of interest...
.
Professionals in engineering and scientific disciplines involving accelerations and
kinetic energiesThe kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its...
rigorously maintain the distinctions between mass, force, and weight, as well as their respective units of measure. Engineers in disciplines involving
weightIn the physical sciences, the weight of an object is the magnitude, W, of the force that must be applied to an object in order to support it in a gravitational field. The weight of an object in static equilibrium equals the magnitude of the gravitational force acting on the object, less the effect...
loadingStructural loads are forces applied to a component of a structure or to the structure as a unit.In structural design, assumed loads are specified in national and local design codes for types of structures, geographic locations, and usage. In addition to the load magnitude, its frequency of...
(force on a structure due to gravity), such as
structural engineeringStructural engineering is a field of engineering dealing with the analysis and design of structures that support or resist loads. Structural engineering is usually considered a specialty within civil engineering, but it can also be studied in its own right....
, 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 modulusAn elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically when a force is applied to it...
are measured and published in terms of the newton and
pascalThe pascal is the SI derived unit of pressure, stress, Young's modulus and tensile strength. It is a measure of force per unit area, defined as one newton per square metre...
(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”
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
volumeThe volume of any solid, liquid, gas, plasma, theoretical object, or vacuum is how much three-dimensional space it occupies, often quantified numerically. One-dimensional figures and two-dimensional shapes are assigned zero volume in the three-dimensional space...
and therefore have a
buoyantIn physics, buoyancy is the upward force that keeps things afloat. The net upward buoyancy force is equal to the magnitude of the weight of fluid displaced by the body. This force enables the object to float or at least seem lighter....
effect in air. Buoyancy—a force that opposes gravity—reduces the weight of all objects immersed in
fluidA fluid is a substance that continually deforms under an applied shear stress. All gases are fluids, but not all liquids are fluids. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
s. This means that objects with precisely the same mass but with different
densitiesThe density of a material is defined as its mass per unit volume. The symbol of density is ρ .- Formula :Mathematically:where: is the density, is the mass, is the volume....
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. In
metrologyMetrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement.-Introduction:...
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
platinumPlatinum is a chemical element with the chemical symbol Pt and an atomic number of 78. Its name is derived from the Spanish term platina del Pinto, which is literally translated into "little silver of the Pinto River." It is in Group 10 of the periodic table of elements...
-
iridiumIridium is the chemical element with atomic number 77, and is represented by the symbol Ir. A very hard, brittle, silvery-white transition metal of the platinum family, iridium is the second densest element and is the most corrosion-resistant metal, even at temperatures as high as 2000 °C...
mass standards like the International Prototype Kilogram (IPK), high-quality “working” standards are made of special
stainless steelIn metallurgy, stainless steel, also known as inox steel or inox, is defined as a steel alloy with a minimum of 11% chromium content by mass. Stainless steel does not stain, corrode, or rust as easily as ordinary steel...
alloys that occupy greater volume than those made of platinum-iridium, which have a density of about 21,550 kg/m
3. 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/m
3 which it balances in air with a density of 1.2 kg/m
3.” The effect is a small one, 150
ppmParts-per notation is used, especially in science and engineering, to denote relative proportions in measured quantities; particularly in low-value proportions at the parts-per-million , parts-per-billion , and parts-per-trillion level...
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
Technically, whenever someone stands on a balance-beam-type
scaleA weighing scale is a measuring instrument for determining the weight or mass of an object. A spring scale measures weight by the distance a spring deflects under its load. A balance compares the unknown weight to a standard weight using a horizontal lever...
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 cellA load cell is an electronic device that is used to convert a force into an electrical signal. This conversion is indirect and happens in two stages. Through a mechanical arrangement, the force being sensed deforms a strain gauge. The strain gauge converts the deformation to electrical signals...
-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.
See also
- Apparent weight
An object's weight, henceforth called "actual weight", is the force exerted upon it by a gravitational field. By contrast, an object's apparent weight is the normal force exerted on it by a body with which it is in contact. This will only equal the object's actual weight if it holds the object at...
- Gravimetry
Gravimetry is the measurement of the strength of a gravitational field. Gravimetry may be used when either the magnitude of gravitational field or the properties of matter responsible for its creation are of interest...
- Inertia
Inertia is the resistance of any physical object, to a change in its state of motion. It is represented numerically by an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to describe the motion of matter and how it is affected by...
- International System of Units
The International System of Units is the modern form of the metric system and is generally a system devised around the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science.The older metric system included several groups...
(SI)
- Kilogram
The kilogram is the base unit of mass in the International System of Units .[The spelling kilogram is the modern spelling used by the International Bureau of Weights and Measures , the U.S...]
- Kilogram-force
The unit kilogram-force or kilopond is defined as the magnitude of the force exerted on one kilogram of mass by a gravitational field . So one kilogram-force is by definition equal to newtons...
- Mass
In physics, mass commonly refers to any of three properties of matter, which have been shown experimentally to be equivalent: inertial mass, active gravitational mass and passive gravitational mass...
- Newton (unit)
- Pound (mass)
The pound or pound-mass is a unit of mass used in the imperial, United States customary and other systems of measurement...
- Pound-force
The pound-force or simply pound is a unit of force.- Definitions :The pound-force is approximately equal to the gravitational force exerted on a mass of one avoirdupois pound on the surface of Earth...
- Standard gravity
Standard gravity, usually denoted by g0 or gn, is the nominal acceleration due to gravity at the Earth's surface at sea level, defined to be precisely 9.80665 m/s2 . This value was established by the 3rd CGPM...
- Weight
In the physical sciences, the weight of an object is the magnitude, W, of the force that must be applied to an object in order to support it in a gravitational field. The weight of an object in static equilibrium equals the magnitude of the gravitational force acting on the object, less the effect...
External links