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From: gwyn@brl-tgr.ARPA (Doug Gwyn )
Newsgroups: net.physics
Subject: Re: Newton's Second Law
Message-ID: <11382@brl-tgr.ARPA>
Date: Thu, 4-Jul-85 21:04:04 EDT
Article-I.D.: brl-tgr.11382
Posted: Thu Jul  4 21:04:04 1985
Date-Received: Thu, 11-Jul-85 05:36:34 EDT
References: <9255@Glacier.ARPA>
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> What is mass? Mass is force divided by acceleration.
> 
> What is force? Force is mass multiplied by acceleration.
> 
> Something is definitely not right here. So exactly what are force and mass?
> What is the content of Newton's Second Law? Is it a definition? Can definitions
> be called physical laws?

You should read "Concepts of Mass" and "Concepts of Force" by Max
Jammer (also author of "Concepts of Space") if you want to see
various attempts through history to nail down these concepts.

Before discussing physics, I want to object to the implicit idea
that a "definition" is an arbitrary setting of a term equal to some
combination of other terms.  A proper definition must capture the
ESSENCE of a concept.  This may, indeed, amount to a physical
statement.

Sticking strictly to Newtonian physics for purposes of discussion,
force would be better defined as the gradient of energy, i.e. how
much work per unit distance has to be exerted to change position.
(Since energy is a conserved quantity in Newtonian physics, it is
"more fundamental" than force.)

Mass has two meanings.  It is the amount of "inertia" a body has,
and it is also the amount of a source of gravitation.  The equality
of these two characteristics is unexplained in Newtonian physics.
Your question is about the inertial aspect of mass.  The amount of
mass in an object can be obtained by adding the masses of its
constituent pieces, all the way down to the atomic level (there is
a very small discrepancy due to mass associated with binding energy,
but this is a relativistic detail).  The preceding sentence states
a fundamental physical property of what is called "mass", such that
mass appears to be a measure of the "amount" of material in an
object.  This is the intuitive meaning that people used all along;
Newton provided a mathematical theory relating mass to other things.

Newton's First Law is a special case of his Second; the reason it
was separately stated was probably to emphasize that the "natural"
state of things (free motion) is different from what was previously
believed (e.g. Aristotle claimed that an object would stop moving
if not continually subjected to a force).  A better statement of
the Second law would be
	A body's momentum (mass * velocity) changes at a rate
	equal to the applied force (gradient of work).
This is really a vector (3-D) statement.  The reason that this is
a better statement of the law is that an object's mass can change
under some circumstances (e.g., a rocket in flight loses mass as
it consumes fuel).

In general, a physical theory consists of a number of properties
(mass, energy, position, force, charge, etc.) and a number of
formulas that give quantitative relationships among the primitive
properties.  Besides these purely formal aspects, there must also
be a method of relating the elements of the theory to what is
actually observed in the physical world.  Sometimes there are
implicit assumptions that are not considered (due to lack of
omniscience), as the Euclidean nature of 3-D space in Newtonian
physics.  The whole package making up a complete physical theory
normally takes considerable study to comprehend, especially since
most of the primitive quantities can only be measured by applying
some consequences of the theory itself.  This does not necessarily
indicate a "vicious circle" of self-reference, but perhaps just an
internal self-consistency.  This helps show why alternative theories
are possible, though.

To feel better about the relationship between mass and force,
practice working Newtonian mechanics problems and eventually
gravitational and electromagnetic particle problems.  The concepts
work out pretty well, although if pressed too hard one has to give
up Newtonian physics for relativistic or quantum theories.