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:
g_{n}),
which is defined as precisely
meters per square second
(m/s
^{2}). 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/s
^{2} 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/s
^{2}. The
CGPM
(also known as the “General Conference on Weights and Measures”)
fixed the value of
standard gravity
at precisely 9.80665 m/s
^{2} 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/m
^{3}, 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/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
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.
See also
Notes
External links