Re: [Phys-l] energy is well defined

["Jeffrey Schnick" <JSchnick@Anselm.Edu>]

See comments inserted below.

> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
> bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
> Sent: Friday, February 22, 2008 10:58 PM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] energy is well defined
>
> On 02/22/2008 08:08 PM, Jeffrey Schnick wrote:
>
> > I think that KE being energy of a system in the way PE is energy of
> a
> > system and not an individual particle is reasonable model.  In this
> > model, what is typically referred to as the kinetic energy of a
> system
> > due to the motion of the center of mass of a system through space in
> > reference frame O is always just one part of the energy of a larger
> > system whose center of mass is at rest in reference frame O.
>
> I'm skeptical that such a model is "reasonable".
>
> There are many applications (such as baseball) where it is
> quite impossible to restrict attention to "the" system.
> Instead, it is necessary to pay attention to various subsystems.
> In the frame of the ball, the ball has zero KE.  In the frame
> of the bat, the bat has zero KE.  But those zeros do not well
> describe the physics of a batted ball.

Insofar as we can neglect Oscillation and rotation of the ball, as well
as the motion of the electrons, quarks, etc. of which the ball consists,
I agree that for a system consisting exclusively of the ball, the system
has no kinetic energy contributions to the total energy of the ball.
Study of that system would not be helpful in answering the usual
questions one would like to know the answers to in the case of a batted
ball.  However, insofar as one can neglect energy of deformation, and
the potential energy of the various electromagnetic and nuclear
interactions going on inside the ball, the system consisting of only the
ball has no potential energy either so the ball as the entire system
would not be a good choice anyway.  The fact that the zeroes in question
"do not well describe the physics of a batted ball" does not shoot down
the model, it just means that the ball alone is not a good choice of
system for investigating the physics of a batted ball.  (Actually it
might be a good choice for a researcher working for the manufacturer--it
all depends on what part of the physics you are interested in--but that
is beside the point.)  The ball and the earth together would be a better
system to choose if you want to find out things like, given the velocity
of the ball just after it leaves the bat, in a reference frame in which
the center of mass of the ball-plus-earth is at rest, how high above the
surface of the earth does the ball go and how fast is it going at the
last instant before it touches the ground.  The total energy of that
system includes kinetic energy associated with the motion of the ball
relative to the center of mass of the system.

In this model, the energy of a system is all about the masses of the
constituent particles and the configuration.  The potential energy has
to do with what the configuration is, and the kinetic energy has to do
with how fast the configuration is changing.

In the system consisting of two charged particles (and their fields but
I'm going to stop saying that part) that I discussed in my previous
post, there is no rule in this model against discussing the contribution
to the total energy of the system of the kinetic energy associated with,
for instance, the positively charged particle relative to the center of
mass of the system.  The point is, that that energy is energy of the
system, it is not energy of the particle.  It does not contribute to the
mass of the particle, it contributes to the mass of the system.

There are those that argue that energy isn't real because you can make
the kinetic energy of a particle anything you want just by viewing that
particle from the right reference frame.  To test whether the kinetic
energy of the particle has any observable consequences you need at least
another particle for the first particle to interact with.  And isnsofar
as the energy associated with the first particle can be used to predict
what happens in the case of an isolated pair of particles, it is the
kinetic energy associated with the motion of the first particle relative
to the center of mass of the system of two particles that matters.  This
kinetic energy, which in the model under discussion is one contribution
to the total energy of the system of two particles, is the only kinetic
energy associated with the motion of the first particle, from among the
infinite set of values you could calculate for the kinetic energy
associated with the motion of that particle (in the infinite set of
inertial reference frames), that is useful in predicting the outcome of
the interaction.

> As a fancier example, consider fluid dynamics.  It is quite
> impossible to restrict attention to "the" system.  Instead,
> it is necessary to pay attention to a great many subsystems
> (such a N different parcels of fluid).  It is necessary that
> the conservation laws apply to each subsystem separately.
> Using N different reference frames for the N different
> subsystems is actually possible, but it is fiendishly
> complex, far more complex than the usual formulation that
> allows subsystems to be moving relative to a given reference
> frame.

There is no reason to choose N different reference frames.  Pick the
center of mass frame for the entire system and stick with it.  There is
no problem with focusing your attention on one "blob" of the fluid, and
a value obtained by multiplying half the mass of that blob times the
square of the speed of the center of mass of the blob relative to the
center of mass of the system may very well be a very useful quantity.
In the model under consideration, that quantity would be one (kinetic
energy) contribution to the total energy of the system--but it would not
make any contribution to the total energy of the blob.  In other words,
it would be one contribution to the mass of the system, but it would not
be a contribution to the mass of the blob.

> To say the same thing more formally:  The choice of reference
> frame is a free choice the *first* time you choose, but
> thereafter it is not free at all.  There is a steep price
> to be paid if different subsystems are using different
> reference frames.
>
> =============
>
> It is important for students to be able to use models in which
> the KE is nonzero.  It is important for students to be able to
> handle situations where there are multiple subsystems.
>
> In simple cases it may be convenient to choose a frame where
> "the" KE is zero, but this is definitely not the general case.

You make good points here.  As usual, your wisdom is showing.

At some point, I have to admit that I am not a purist.  If I were to
incorporate this model into my teaching, or in other words to adopt the
viewpoint represented by what I have been calling a model into my
teaching, I'm sure that I would keep on using expressions like "the
kinetic energy of the baseball" when what I meant was the contribution
to the total energy of the earth plus baseball system associated with
the velocity of the baseball relative to the center of mass of that
system.  I'd use the tactic I use with gravitational potential energy.
I tell the students that the gravitational potential energy associated
with the configuration of the earth plus ball system is energy of the
system as a whole and is not energy of the ball itself, but for
accounting purposes, I am going to assign that energy to the ball and
call it the gravitational potential energy of the ball because it is
easier to talk about it that way.  Then, for case after case I use the
expression "the gravitational potential mgh of the object," every once
in a while earnestly reminding the students that the energy is really
the energy of the earth-plus-object system--not the object.

> _______________________________________________
> Forum for Physics Educators
> Phys-l@carnot.physics.buffalo.edu
> https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l