NOVEMBER 2000
M A S S A N D W E I G H T: E X P L A I N I N G T H E D I F F E R E N C E
We teachers are responsible for
some of the ideas students have. We
must exercise that responsibility by
being clear in our use of words, especially those that have different meanings in common speech, and by being as technically specific as possible.
Two of the most commonly confused
words in science class are mass and
weight. The terms weight, mass, and
weighing are systematically used in
inappropriate ways. Students need
to know that there is a difference and
that it is important to maintain the
distinction.
Weight is a force. Forces are the
manifestation of interactions between two bodies. We define a force
as the interaction’s effect on one of
the two objects that can cause that object to change its motion. When something about the motion changes, it is
evidence for the existence of a force.
You may have heard the joke
that asks: “What are the three top
issues in real estate?” The answers:
location, location, location. The same
is true of weight—location determines weight. An object near Earth
has a gravitational force exerted on it
by Earth [its weight—measured in
newtons in the International System
of Units (SI)]. An object on the Moon
has a gravitational force on it due to
the Moon, not Earth, and so its weight
is different. The object’s weight on
the Moon would be about one-sixth
what would be measured on Earth.
Because weight is a force, we
could measure weight by observing
the amount of stretching of a spring,
for example. That’s why a bathroom
scale, a spring scale, actually measures weight. Many businesses use
10
spring scales to measure the weights
of objects for sale.
If weight is caused by nearness
to Earth, why do astronauts experience “weightlessness” on orbital
flights, even though orbital flights are
within the pull of Earth’s gravity? The
answer is—location and motion. Astronauts standing on Earth would be
stopped by the Earth’s surface and
would feel their weight. On the shuttle,
the astronauts are changing their
motion because of the gravitational
pull of Earth, but they are changing in
the exact same way the shuttle does,
so they do not feel the change in
motion because the shuttle does not
prevent the change from happening.
Mass is not a force. The mass of
an object is a measure of how much
matter it has. It would be easier to
change the motion of an elephant
than a locomotive, and easier to change
the motion of a person than an elephant, even if we used a spring calibrated to exert the same force on
these objects. Something about them
is different. We say that a locomotive
has more inertia than an elephant,
which has more inertia than a person.
We can define something to
measure the amount of inertia and
call it mass. Our fundamental measure of mass is obtained by observing
how rapidly the motion of the object
is changed when we apply a force to
it. If we use a stretched rubber band
to change the motion of two objects,
we can verify that (given the same
amount of stretch) 1 cm3 of aluminum would experience twice the
change of 2 cm3 of aluminum. If two
objects, say a stone and a ball, change
in the same way as the result of a
T H E
S C I E N C E
T E A C H E R
given force, we say that their masses
are equal. If one changes three times
as much as the other, we deduce that
it has one-third the mass.
We now make use of the remarkable property that if two objects
have equal masses they also have equal
weights at a given location, regardless
of what they are made of (weight = mg,
where m is the mass and g is the acceleration due to gravity, about 10 N/kg).
By comparing the effect of a specified
object to the effect of a standard object or set of objects on an equal arm
balance, we can define the mass of an
object as the number of standard
masses it takes to balance that object.
The SI unit of mass is the kilogram.
Using this inertia property, we can
compare masses of different kinds of
objects.
The results of this measurement
are independent of the location
where the measurement is made—at
the poles, at the equator, or on the
Moon. So mass is a constant property
of an object, no matter where it may
be—on Earth, on the Moon, wherever.
Most human activities take place
on Earth, near sea level, so if one
knows a mass, one can give the weight,
and if one knows the weight, one can
give the mass. Nevertheless, they are
quite distinct properties. Mass—what
we are usually interested in—is the
quantity of material, measured in kilograms; weight is just a gravitational
force, measured in newtons.
I am grateful for the advice and
help of my colleagues A.P. French
and M. Iona in preparing this note.
Gordon J. Aubrecht, II
Department of Physics
Ohio State University, Marion, OH