Re: [Phys-L] Internal Energy of Wood Taking a Bullet

[John Denker <jsd@av8n.com>]

On 02/02/2018 08:21 AM, Jeffrey Schnick wrote:
> When you fire a bullet into a block of wood, while the bullet is 
> embedding itself in the wood, it is clear that the internal kinetic 
> energy of the wood is increasing.

OK.

> How about the internal potential energy of the wood?  Is it 
> increasing because chemical bonds are broken,

Yes.

> increasing for other reasons,

See below.

> decreasing because the wood is being compacted bringing the molecules
> closer together where they find themselves more strongly bound,

That's a tricky question.

The purely electrostatic part of the PE decreases when
something is compacted.  However.....

Everybody agrees that the chemical bond energy (CBE) is
a function of position, and it is at a minimum at the
equilibrium bond-length.  So moving things in /either/
direction -- compaction as well as expansion -- increases
the CBE.

One conventional and reasonable way of looking it is to say
that since it is a function of position, CBE is a form of
internal potential energy.  OTOH if you look more closely,
you find that CBE involves both electrostatic potential
energy and submicroscopic /kinetic/ energy.  The equilibrium
bond-length balances these two contributions.

This terminological snafu shows up in many other situations.
Many trucks are supported on "air springs".  
 -- If you look closely, you discover that the air-spring
  energy is embodied in the KE of the molecules.
 ++ OTOH it is 100% conventional to label the energy
  in a spring, even an air spring, as PE.  You could
  replace the air spring with a metal coil spring and
  get the same macroscopic black-box behavior, so this
  convention make sense.
 -- On the third hand, the energy in the metal spring
  depends on chemical bonds, which depend on KE as well
  as PE, so again we get into trouble if we look too
  closely.
 ++ Physics is a collection of tools for getting the
  right answers to important questions.  Classical
  mechanics says you should write down the Lagrangian
  in terms of KE and PE and then turn the crank to
  derive the equations of motion.  For a mass on a
  spring, you get the right answer if you treat the
  spring as a black box that provides potential energy.
 -- OTOH a typical thermometer responds to the translational
  KE (not the total E nor even the total KE) so if your
  spring is part of a heat engine you care about more
  than just the E-versus-position behavior;  there is
  larger set of properties you care about, even at the
  black-box level.

====

Even more generally, beware that distinguishing (a)
"internal and microscopic" versus (b) "external and
macroscopic" depends on how closely you look.

==================

Returning to the aforementioned classical canonical
mechanics:  In a mass-on-a-spring oscillator, it
might seem obvious what's PE and what's KE ... but
for an electrical LC oscillator, does the L play the
role of mass, or does the C?  It turns out it doesn't
matter!  You can do it either way.  Pick a coordinate,
and then let the Lagrangian tell you what is the momentum
conjugate thereto.  It even turns out that for the
mechanical oscillator it doesn't matter!!  You can
choose coordinates such that the spring provides the
KE and the mass provides the PE.  The Lagrangian does
not care, so long as you are consistent about it.
Google "canonical transformation" or "contact
transformation".

Bottom line:  The meaning of energy (plain old total
energy) in this context is clear-cut and not seriously
open to dispute ... but the partition into KE and PE
is open to various interpretations.  The answer to
the PE/KE question depends on what you intend to do
with the answer.

In situations where we have different physical concepts
masquerading behind the same name, it is usually very
helpful to distinguish them, perhaps by attaching
adjectives, or perhaps by coining entirely new names.
In this case I don't have a fully-complete set of
suggestions for how to do that, but it's something
to think about.  As a start:
 *) If you are primarily concerned with chemical bond
  energy, you can call it CBE and not worry too much
  about how it is partitioned into submicroscopic PE
  and KE.
 *) If you are primarily interested in the thermal
  translational KE, you can call it that, or (better)
  just refer to temperature, recognizing that there
  is a world of difference between temperature and
  energy.
 *) If you are primarily interested in the purely
  electrostatic part of the submicroscopic potential
  energy, you can call it that.
 +) et cetera.