Date: Fall 2009
Hi. I am writing a 6th-grade science book, and I am
currently working on a chapter on atoms, elements, and compounds. My
question relates to the definitions of matter and mass. In my
research, I have found that matter is defined in terms of mass and
mass is defined in terms of matter. Specifically, matter is defined
as "anything that has mass and takes up space," while mass is
defined as "the amount of matter in an object." If I substitute the
definition of mass into the definition of matter, I get: matter is
anything that has an amount of matter and takes up space. This does
not make sense. Can you please provide me with definitions of matter
and mass that are not mutually dependent on one another and that
will make sense to 6th-grade students? Any clarification that you
can provide will be greatly appreciated.
Operationally, as a chemist I think of ordinary matter as "anything made
although I am hardly an authoritative source.
In "General Chemistry", 9th edition by D.D. Ebbing and S.D. Gammon
(Houghton Mifflin & Co, Boston/NY, 2007), matter is defined as "whatever
space and can be perceived by our senses." I think that is kind of vague, and
I do not like the use of perception in the definition. Still, might be
okay for sixth graders. Also, mass is defined as "the quantity of
matter in a material." I do not love that either because of its lack of
clarity. What is meant by quantity?
In "Chemistry: The Molecular Science", 3rd edition by J.W. Moore et. al.
(Brooks-Cole/Thomson, Belmont CA, 2008) matter is defined as "anything that
has mass and occupies space" while mass is defined as "a measure of an
resistance to acceleration." These definitions are both correct and useful,
but the definition of mass might possibly be a tough one for a sixth
grader because you
have to define acceleration and other Newtonian physics concepts.
Still, it avoids the circular problem that you bought up.
Mass is, in reality, a deeper concept than described here
because of its equivalence with energy (according to Einstein's theory of
However I have ignored this important complication because it is completely
the scope of your question (I am stating this for the benefit of Internet
kibitzers out there
who may be reading this in the future).
We need to emphasize that mass is a *measure of the amount* of
matter, while matter is simply a label, a name, for things that take
up space. So using the substitution you applied, we can say that
mass is a measure of the amount of material in a particular object.
To my mind, rather than having these things defined for the
students, it might be better as an exercise where the students
define it for themselves. There are many little exercises that can
guide students to their own definitions and they do not need to be
hung up on a particular wording.
Greg (Roberto Gregorius)
Matter is the material, the physical "stuff". Mass is the
measurement of the amount of material present. Mass is a number.
It is like seeing cows. The matter is cow. All cows are made up of cow.
A cow's mass is how much cow there is. Not all cows mass the same,
but all are made up of matter called cow.
R. W. "Bob" Avakian
B.S. Earth Sciences; M.S. Geophysics
Oklahoma State Univ. Inst. of Technology
When you get down into these fundamental concepts it is easy to get
trapped in circular definitions -- some would say inevitable. The reference
"Handbook of Mass Measurement" gives a definition attributed to Condon &
Odishaw in "Handbook of Physics": "The property of a body by which it
requires force to change its state of motion is called inertia, and mass is
the numerical measure of this property." In short, it is the resistance to a
change in motion. Paraphrasing Richard Feynman's "Lectures on Physics" Vol.
1, Chapter 9, Section 1: Inertia is how hard it is to change the direction
of motion of an object. Mass is the quantitative measure of inertia.
Surprisingly, the "AIP Physics Desk Reference" 3rd edition does not even
bother to give any definition. The references above also take up the
definition of matter.
One way to define mass is to refer to Newton's Second Law of
Motion. It states that the acceleration produced by a particular
force acting on a body is directly proportional to the magnitude of
the force and inversely proportional to the mass of the body. Mass
is the measure of an object's inertia. Mass is the ratio of an
applied force to the resulting acceleration. That is: mass =
(applied force)/(acceleration). While the weight of an object is
different if you are on the earth or the moon, the mass is the
same. That is, a given force applied to an object will result in
the same acceleration whether on the earth or the moon.
David S. Kupperman
I would define mass as the amount of matter and I would define matter as
anything that is made up of atoms (or protons, neutrons or electrons). I
think these definitions always work but I have always disliked the definition
of mass. It is such a vital concept and yet very difficult to measure directly.
We either have to do through weight or else through inertia in some other way.
I think your question probes one of the basic premises of science.
"Science" is a way of explaining and classifying observations. Science
attempts to observe, describe, and classify what is, but does not
attempt to explain why something is so. So science, and scientific
terms, are fundamentally operational in nature. This is very different
than the more symbolic/axiomatic approach you seem to be implying.
The concept of mass comes from the observation that some objects
require more force to move than others. What is the property that
makes one object require more force to move than another? Science
calls it "mass". Objects that have more "mass" require a greater force
to accelerate at a given rate. "Mass" can be observed by many means,
including how an object responds to a gravitational field. I would shy
away from the definition of mass as "the amount of matter in an
object" because it is the forces that you are observing, not the
matter itself (again, referring back to the operational definition).
We can compare observations and quantify them, but it is important to
be clear about what you are observing, and what you are inferring from
the observation. The more successive inferences you make, the more
risk there is in introducing error.
I also would challenge the common definition "having mass and taking
up space." This is OK in some basic contexts (and is probably just
fine for the vast majority of junior-high subjects), but over the past
several decades, new discoveries in quantum physics have shown this
definition can be inadequate. There is much information on this
subject on the Internet, and various standards organizations have
adopted different strategies on how to address the issue. These are
certainly outside the scope of a 6-8th grade text book, so I will not go
into detail here.
The bottom line is that I think scientific terms are better when
operationally defined. Students should understand what the meaning and
source of these properties/quantities are -- and not rely on
memorizing symbolic definitions. This is partly because operational
definitions tend to avoid the confusions that are concerning you, but
more importantly because science is founded on observation.
Hope this helps,
Oh - I love all this discussion, but let's simplify somewhat for a junior high
or middle school student.
Weight is a measurement in response to gravity for most of us. An object has weight
due to the gravitational pull on it. It would weight a
great deal less on the moon, for example, since the gravitational pull is less.
A spring scale measures weight. The idea of weightlessness comes from the lack of
gravity pulling on an object or gravity being equal on all sides.
The same object can be measured in comparison to known objects by mass. The mass never
changes (well, I have to be somewhat careful here). Using a instrument that compares
the mass of objects to known objects will have the same mass whether on the moon or
the earth. Gravity is not a factor in this measurement.
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