I've been following the energy discussion with interest. I found Carl
Mungan's contribution particularly interesting in that it is something I
have been mulling over for some time.
On Mon, 18 Feb 2008 14:29:32 -0500 (EST), Carl Mungan wrote:
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I've become somewhat leery of the idea on an object "storing" KE.
It doesn't seem to me be a property intrinsic to an object at all.
Rather it is a property of a system of the object PLUS some external
reference system (probably the earth, for ordinary lab experiments).
After all, the object's speed must be measured relative to something
external. So in this sense of being associated with a system and not an
individual object, KE is like PE.
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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. In this
model, all energy is internal energy. In this model, the definition of
energy is simple--energy is mass. In this model, John Denker's example
(see https://carnot.physics.buffalo.edu/archives/2008/2_2008/msg00157.html
and https://carnot.physics.buffalo.edu/archives/2008/2_2008/msg00163.html )
of the total energy U+K of a system increasing as a result of work done
on the system by a gradial force (where a GRADIAL force is a force that
can be expressed as the GRADient of a potentIAL) doesn't work because if
the system under consideration is a particle, no part of the system can
ever make any kinetic energy contribution to the energy of the system
because the energy of the system is the energy calculated in the center
of mass frame of the system and a single particle never has any kinetic
energy in its own center of mass frame. The system consisting only of
the particle in John's example always has one and the same amount of
energy--the mass of the particle. An example that would work in this
model would be one that involves two non-rotating dust particles
identical in all respects except that their charges, while equal in
magnitude are opposite in sign. The charge-to-mass ratio of each
particle is miniscule compared to that of a proton. At the start of
observations, the particles are slowly drifting apart from each other
along the line containing both of them, at a decreasing rate. The rate
of separation is decreasing because at the start of observations, the
only force acting on either one of them is the Coulomb force exerted
upon it by the electric field of the other. The system is the two
particles and the electric field of the two particles. The entire system
is slowly drifting toward the capacitor depicted by John Denker at: http://www.av8n.com/physics/img48/accelerator.png
The axis of symmetry of the capacitor is collinear with the line passing
through the two particles and with the velocity of the center of mass of
the system of two particles and their fields. The super-system that
includes the capacitor and the particles is in a weightless, vacuum
environment. As the charged particles approach the capacitor, the
positively-charged particle is in the lead and the electric field in
between the capacitor plates is in the same direction as the velocity of
the center of mass of the particles relative to the capacitor. After
they pass through the capacitor, both particles are moving away from the
capacitor in the same direction as before, but relative to the
capacitor, the positively-charged particle is moving faster and the
negatively charged particle is moving slower such that, in the center of
mass frame of the system of two particles plus their fields, the two
particles are farther apart and drifting away from each other faster
than they were at the start of observations. As such, both the kinetic
energy and the potential energy of the system of two particles and their
field have increased. The mass of the system has increased.