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Re: [Phys-l] energy is well defined



-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
Sent: Saturday, February 23, 2008 4:49 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] energy is well defined

On 02/23/2008 08:08 AM, Jeffrey Schnick wrote:

You make good points here.

:-)



Some additional supporting points:

In the context of a batted ball:

Insofar as we can neglect Oscillation and rotation of the ball,

In general the rotation of the ball is not negligible.
And the rotation of the bat is not at all negligible; it
is expected that the bat is /swung/ not pushed.

Hmmm. I think we are miscommunicating here. You said "In the frame of the ball, the ball has zero KE." I was stating the conditions under which I would agree with you. (The conditions are those in which the ball can be treated as a particle.) Indeed there are many kinetic energy contributions to the total energy of the ball system in the inertial reference frame in which the center of mass of the ball is at rest, including the kinetic energy associated with the motion of the constituent particles of the ball characterized by the rotation of the ball. That energy is part of the total energy of the ball. It is my understanding that most of the mass of the ball is due to the motion of the quarks in the nuclei of the atoms making up the ball.


A heretical reformulation of physics that can't handle
rotation is not ready for prime time.

Of course. Although I don't think we're talking about a reformulation here--just a point of view. There is no problem with rotation.

Which of the following statements is or are heretical?
Mass is energy.
Some energy is mass.
All energy is mass.


=======

In the context of fluid dynamics, with N parcels of fluid:

There is no reason to choose N different reference frames.

Agreed!

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,

Well, then, if it is OK to have N parcels with nonzero CM
motion, because the reference frame is not attached to the
parcel, why not go the last step and drop the requirement
that the reference frame be attached to the "entire system"???

If it isn't attached to the system then what you get when you sum up the internal energies of all the parcels and the energy due to the configuration of the parcels relative to each other and the (1/2)mv^2 for each parcel with v being the speed of the particle relative to the reference frame in question (call it O), is not the energy of the system. It includes a (1/2)MV^2 part (where the M is the total energy of the system and the V is the speed of the center of mass of the system relative in O. That part represents energy that might be a contribution to some supersystem whose center of mass is at rest in frame O, but it is not energy of the system. I don't think that that energy is going to be useful in predicting how the parcels of the system interact with each other.

BTW, in the case of flow of an infinite fluid, the CM of
the "entire system" is undefined. In conventional physics,
this is not a problem. It would be a step in the wrong
direction to reformulate physics in such a way that this
becomes a problem.

In aeronautical engineering, it is convenient to attach
the reference frame to the airframe, not to the fluid.
In principle you could do it the other way, but the
result would be a mess of epic proportions.

Conventional physics allows the reference frame to be
attached to anything, or to nothing in particular. This is
Galileo's principle of relativity. You are free to choose
whatever frame you like, but others may choose differently.
Any theory that restricts this choice is a Bad Idea.

Of course. In the model/viewpoint under consideration, everybody would agree on the value of the energy of the system. This seems to argue (weakly) in support of the model/viewpoint under consideration rather than against it. The conventional kinetic energy of the system associated with the motion of the system relative to an abstract (not attached to the center of mass of any system) inertial reference frame in which the center of mass of the system is not at rest is irrelevant to any interaction of the constituents of the system with each other.


Also, more importantly: As soon as you allow a parcel to have
nonzero KE,

I don't. The KE associated with the motion of the parcel relative to the center of mass of the system is energy of the system, not of the parcel.

the previous assertion that "energy is mass" goes
out the window.

This argument is based on a false premise so the assertion that "energy is mass" remains on the table.

The quantity mc^2 is equal to the rest energy,

We are in strong agreement here.

not the total energy. For details, see
http://www.av8n.com/physics/mass.htm
and references therein (especially Oas).

I've read at least some of that, and I'll probably read it again. I enjoy reading your work and I find it informative. Wish I had the time right now.

For a system consisting of a bunch of particles, the total energy of the system in the system's center of mass frame *is* the rest energy of the system. Consider two protons moving toward each other. Let's view the situation in the center of mass of the system. The energy of each proton (in the model under discussion) is m_p, the mass of a proton. But the energy of the system is 2m_p plus two times the energy associated with the motion of either particle relative to the center of mass of the system. There is a kinetic energy contribution to the total energy of the system for each proton. The total energy of the system is the rest energy of the system and it is the mass of the system.


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.

That's fine. There is good physics to justify that approach.
The justification is nontrivial, because the fundamental
equation
Φ = G M m / r
is symmetric under the interchange of M and m, so in some superficial
sense it might seem OK to assign the energy to the earth rather than
to the particle. But I wouldn't recommend it.

The rationale for the recommended assignment goes like this:
a) The energy "really" belongs to the system (or to the field).
b) We make a negligible mistake in assigning the energy to the
particle, in the limit that the particle is verrry small compared
to the earth. We can transfer momentum to/from the earth, but
we cannot transfer significant KE. A glance at the formula
p^2/2M explains why.

Going through this rationale is important, for some audiences,
because it communicates something about the _limits of validity_.
For a gravitating system where the two masses are comparable,
such as the earth/moon system, it is not generally valid to
assign the gravitational energy to one mass or the other.

If you want additional counterexamples, the idea of assigning
gravitational energy to "the" particle is DoA when there are
multiple sources of the gravitational field.

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.

I agree with both parts there:
-- Most students can handle the idea that "mgh" is exceedingly
accurate over laboratory length scales but not cosmological
length scales.
-- They do need to be "reminded" now and then.

Thanks.

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