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Re: bouncing ball or car acceleration



On Wed, 6 Feb 2002, John Barrer wrote:

... The key (I think?) as JD pointed out is that a system with
internal structure changes the analysis (W-E theorem no longer
applies).

Please don't say that. There are many theorems that might be (and
often are interchangeably) called "the" work energy theorem. ALL
of them are ALWAYS true as long as you don't mix them up and try
to take the work-like quantity from one and equate it to the
change in the energy quantity from another.

For instance, within the realm of Newtonian mechanics it is ALWAYS
true that the sum of the line integrals of all *external* forces
dotted into the infinitesimal displacements of the *points of
application* is equal to the change in the *total energy* of the
system. This is probably (but not certainly) the most common
proper choice for what people call "the" work-energy theorem.

Similarly, it is also ALWAYS true that the line integral of the
*net external* force dotted into the infinitesimal displacement of
the *center of mass* is equal to the change in the *bulk
translational kinetic energy* of the system. I won't even suggest
a name for this very useful and commonly used theorem here except
to note that many people call *it* *the* work-energy theorem.

There are many more such relationships and, again, within the
realm of Newtonian mechanics, ALL of them are ALWAYS true. Whether
or not they are useful is a competely different question as is
whether or not you *care* to use them.

All I ask is that we recognize that, within the realm of Newtonian
mechanics, they NEVER stop applying.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm