Re: CONSERVATION OF ENERGY

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

Gene Mosca asks:

> Below are two alternative descriptions of the system's energics.  Does
> either of these descriptions use the term internal energy in an orthodox
> manner? 
>
> 1.  The system's total energy is the kinetic energy of the block plus the
> internal energy of the system (the block's internal energy plus the
> plate's internal energy).  As friction slows the block its kinetic energy
> decreases and the system's internal energy increases, with the sum of
> these remaining constant. 
>
> 2. The system's internal energy excludes the system's translational
> kinetic energy which is (1/2) (mass of block + mass of plate) (velocity of
> the block-plate's center of mass)^2.  The system's total energy is then
> this translational kinetic energy plus the system's internal energy.  As
> friction slows the block, the sum of system's translational kinetic energy
> and its internal energy remain constant. 

I think we already know that there is disagreement about this; some want 
"internal energy" and "total energy" to be synonymous.   Nevertheless, 
the above is precisely what I would say with one important clarification 
(which is, I suspect, what you *meant*):  In 1, when you speak of the 
"system's internal energy," you should say "the sum of the internal 
energies of the components of the system."  This is different from how 
you (properly, in my view) define "system internal energy" in 2.

To be concrete, in the given case, with m = 1 kg, M = 99 kg, v = 10 m/s, 
V = 0, we have (initially, in the reference frame of the plate),

SYSTEM     INTERNAL ENERGY     KINETIC ENERGY      TOTAL ENERGY   
Block           U_b                 50 J            50 J + U_b
Plate           U_p                  0 J               U_p
Both      U_b + U_p + 49.5 J       0.5 J         50 J + U_b + U_p

So, while the total energies are additive, the internal energies are 
not.  The internal energies would all be the same regardless of the 
chosen reference frame.  The total energies would all be different, but 
they would always be additive.

> Further thoughts:  Consider as a system a billiard ball initially sliding
> without rotation on a billiard table.  The system, the ball and the table,
> now contains rotational as well as translational kinetic energy.  Would
> this system's internal energy include the rotational kinetic energy? 

My taste is to consider rotational kinetic energy internal because 
it is frame independent as long as we work in Newtonian 
inertial, or at worst, translationally accelerating frames.

John
-----------------------------------------------------------------
 A. John Mallinckrodt      http://www.intranet.csupomona.edu/~ajm
 Professor of Physics    mailto:ajmallinckro@csupomona.edu
 Physics Department       voice:909-869-4054
 Cal Poly Pomona            fax:909-869-5090
 Pomona, CA 91768-4031   office:Building 8, Room 223