Chronology | Current Month | Current Thread | Current Date |
[Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
Model 2a --> a little more realistic world with nonconservative forces, but
no dissipation (no entropy production). Example: Charged particle in
time-varying magnetic field.
2) If OTOH we are talking about work in terms of F dot dx, and if we are
willing to impose a number of restrictions and assumptions, and if we don't
mind some slightly circular arguments, then we can make some
pedagogically-useful connections to potential energy.
4) There is an intimate connection between force and momentum. IF (big if)
you know the relationship between momentum and kinetic energy, you can
connect work to kinetic energy. (Note we are calculating kinetic energy,
not potential energy. Also note we are calculating the KE, not defining
it.) Then if you want to connect this with potential energy, you have to
make several major assumptions:
a) You need to _assume_ that KE+PE=constant.
b) You need to _assume_ that the force field is conservative, so that it
is possible for there to be a PE function that depends only on position.
c) We are still assuming we know the KE as a function of momentum.
Let us discuss each of these assumptions:
A) I've seen way too many textbooks that claim they have "proved"
conservation of energy, when in fact they just assumed it, as assumption
(1a). The alleged proof is blatantly circular.
If you are going to _assume_ KE+PE=constant, why not be up front about it?
B) Introductory texts typically restrict the discussion to conservative
force-fields. But this (like the previous item) seems circular to
me. Circles within circles. Assuming the force-field is conservative is
more-or-less tantamount to assuming it is the gradient of some
potential. So defining the potential in terms of a conservative force
doesn't tell us anything beyond what we just assumed.