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example of alternate form of 1st law



Dadgum it, it turned out to be easier than I expected to come up with
a problem that doesn't lend itself to Q+W=delta(E). Gene Mosca
provided me with it.

Drop a block. The earth does work on the block. But the block does no
work on the earth (because the earth's motion is negligible). Oops!
The resolution of this situation is of course to include the energy
of the gravitational field. But unless one is willing to talk about
work done on a field (and I don't think I am), there's no way to
include this term on the LHS of the 1st law as stated above.

The only way out, I must concede, is to admit that Q+W=delta(E) is
not useful anytime field forces (which are external to the system)
are involved. Unfortunately this includes large numbers of problems.

ps: If you want to try balancing energies in the above problem, I
suggest the following geometry. Take the earth to be spherical and
uniform in density. Instead of a block, consider a shell of mass dm.
Let this shell fall inwards spherically starting from infinity. It
works out nicely: the gain in field energy between the surface of the
earth and infinity equals the loss in potential energy of the mass
shell. You may be more comfortable doing this problem using electric
rather than gravitational fields.
--
Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu http://physics.usna.edu/physics/faculty/mungan/