Mass, Weight, Force, Load:
SI is an absolute system (see
Unit Systems
on page
142
), and consequently it is necessary
to make a clear distinction between mass and weight. The
mass
of a body is a measure of its
inertia, whereas the weight of a body is the
force
exerted on it by gravity. In a fixed gravitational field, weight
is directly proportional to mass, and the distinction between the two can be
easily overlooked. However, if a body is moved to a different gravitational
field, for example, that of the moon, its weight alters, but its mass remains
unchanged. Since the gravitational field on earth varies from place to place by
only a small amount, and weight is proportional to mass, it is practical to use
the weight of unit mass as a unit of force, and this procedure is adopted in
both the English and older metric systems of measurement. In common usage, they
are given the same names, and we say that a mass of 1 pound has a weight of 1
pound. In the former case the pound is being used as a unit of mass, and in the
latter case, as a unit of force. This procedure is convenient in some branches
of engineering, but leads to confusion in others.
As mentioned earlier, Newton's second law of motion states that
force is proportional to mass times acceleration. Because an unsupported body
on the earth's surface falls with acceleration
g
(32 ft/s2 approximately),
the pound (force) is that force which will impart an acceleration of
g
ft/s2 to a pound (mass).
Similarly, the kilogram (force) is that force which will impart an acceleration
of
g
(9.8 meters per second2 approximately),
to a mass of one kilogram. In the SI, the
newton
is that force which will impart unit acceleration (1 m/s2)
to a mass of one kilogram. It is therefore smaller than the kilogram (force) in
the ratio 1:
g
(about 1:9.8). This fact has
important consequences in engineering calculations. The factor
g
now disappears from a wide range of
formulas in dynamics, but appears in many formulas in statics where it was
formerly absent. It is however not quite the same
g
, for reasons which will now be
explained.
In the article on page
171
,
the mass of a body is referred to as
M
,
but it is immediately replaced in subsequent formulas by
W
/
g
, where
W
is
the weight in pounds (force), which leads to familiar expressions such as
WV
2
/ 2
g
for kinetic energy. In this
treatment, the
M
which appears briefly is really
expressed in terms of the slug (page
142
), a
unit normally used only in aeronautical engineering. In everyday engineers’
language, weight and mass are regarded as synonymous and expressions such as
WV
2
/ 2
g
are used without pondering the
distinction. Nevertheless, on reflection it seems odd that
g
should appear in a formula which
has nothing to do with gravity at all. In fact the
g
used here is not the true, local
value of the acceleration due to gravity, but an arbitrary standard value which
has been chosen as part of the definition of the pound (force) and is more
properly designated
g
o (page
142
). Its function is not to indicate
the strength of the local gravitational field, but to convert from one unit to
another.
In the SI the unit of mass is the
kilogram
, and the unit of force (and
therefore weight) is the
newton
.
The following are typical statements in dynamics expressed in SI
units:
A force of
R
newtons
acting on a mass of
M
kilograms produces
an acceleration of
R
/
M
meters per second2. The kinetic energy of a mass of
M
kg moving with velocity
V
m/s is 1
⁄
2
MV
2
kg (m/s)2 or 1
⁄
2
MV
2
joules. The work done by a force
of
R
newtons moving a distance
L
meters is
RL
Nm, or
RL
joules. If this work were converted
entirely into kinetic energy we could write
RL
= 1
⁄
2
MV
2
and
it is instructive to consider the units. Remembering that the N is the same as
the kg · m/s2, we have (kg · m/s)2
×
m = kg (m/s)2, which is obviously correct. It
will be noted that
g
does not appear
anywhere in these statements.
In contrast, in many branches of engineering where the weight of a
body is important, rather than its mass, using SI units,
g
does appear where formerly it was
absent. Thus, if a rope hangs vertically supporting a mass of
M
kilograms the tension in the rope
is
Mg
N. Here
g
is the acceleration due to gravity,
and its units are m/s2. The ordinary numerical value of 9.81 will be
sufficiently accurate for most purposes on earth. The expression is still valid
elsewhere, for example, on the moon, provided the proper value of
g
is used. The maximum tension the
rope can safely withstand (and other similar properties) will also be specified
in terms of the newton, so that direct comparison may be made with the tension predicted.
Words like load and weight have to be used with greater care. In
everyday language we might say “a lift carries a load of five people of average
weight 70 kg,” but in precise technical language we say that if the average
mass is 70 kg, then the average weight is 70
g
N, and the total load (that is force) on the lift is 350
g
N.
If the lift starts to rise with acceleration
a
· m/s2, the load becomes
350 (
g
+
a
) N; both
g
and
a
have units of m/s2, the
mass is in kg, so the load is in terms of kg · m/s2, which is the same
as the newton.
Pressure and stress:
These quantities are expressed in
terms of force per unit area. In the SI the unit is the pascal (Pa), which
expressed in terms of SI derived and base units is the newton per meter squared
(N/m2). The pascal is very small—it is only equivalent to 0.15
×
10
−
3
lb/in2
— hence the kilopascal (kPa = 1000 pascals), and the megapascal (MPa = 106
pascals) may be more
convenient multiples in practice. Thus, note: 1 newton per millimeter squared =
1 meganewton per meter squared = 1 megapascal.
In
addition to the pascal, the bar, a non-SI unit, is in use in the field of
pressure measurement in some countries, including England. Thus, in view of
existing practice, the International Committee of Weights and Measures (CIPM)
decided in 1969 to retain this unit for a limited time for use with those of
SI. The bar = 105 pascals and the hectobar = 107 pascals.
Copyright 2004,
Industrial Press, Inc., New York, NY