Re: [Phys-l] energy is well defined

[John Denker <jsd@av8n.com>]

On 02/18/2008 11:40 AM, Jeff Weitz wrote:

> Why define "energy"?  Look at the linguistic knots we get stuck in.

That's a reasonable question.

There are lots of people who can _count_ just fine, using the
concept of integer, without being able to give a concise 
definition of "integer".

Students like definitions, but this is not always a good thing.

> How about defining "kinetic energy" as the work done to accelerate an object
> from rest to a given speed?

That doesn't work too well for photons.

In my experience, it is relatively easier to understand energy as 
a whole -- plain old energy -- and relatively harder to understand
the various categories and subtypes.

In particular, it is easier to know the energy of a photon than to
know what part of it is kinetic and what part is potential.


> Then, how about defining "change in potential energy" as the negative of the
> work done by a conservative force on an object that moves from one point to
> another?
>
> "Potential energy" as an absolute value remains undefined since the
> reference point is arbitrary.  But, in practice, we speak of "potential
> energy" as the change in PE from a specified reference.  The two definitions
> insure that the sum of KE and PE remains constant as long as there are no
> non-conservative forces acting, which helps to motivate the odd-looking
> definition of (delta)PE.
>
> An advantage of these definitions is that it puts the work in the past, not
> in the future, 

That's clever.

> as in "ability to do work," 

So now (if you'll pardon my awkward phrasing) it's "ability to have been 
done by work".  That's clever.  That puts us on the correct side of the
inequality in the 2nd law of thermodynamics.  I will need some time to
think about this.

   All this is predicated on students having a robust pre-existing notion
   of "work" ... which is not always the case.  There is a school of
   thought that starts with energy and derives work from there.  There
   are some applications, such as piloting an airplane, where it is
   important to think about energy, but incomparably less important to
   think about force dot displacement.


======

Once you adopt the work-in-the-past idea, can't you drop the restriction
about "conservative" forces?

There's lots of non-conservative force fields in the world.  Don't they
do work, too?  

   In particular, the "electric power" sold by the electric company is
   almost always traceable to non-conservative fields in a dynamo
   somewhere.