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[Phys-L] Re: E vs. KE/PE



Robert Cohen wrote:

Anyway, I've gone back and forth on using E vs. KE/PE. I'd use E_p and
E_k but then I start to distinguish between E_{p,spring} and
E_{p,gravity} for and then all of a sudden I'm using E_{p,spring,i} and
E_{p,spring,f} and my subscripts are getting unwieldy.

For starters, a painless simplification is
E_{gravity} instead of E_{p,gravity}
E_{spring,f} instead of E_{p,spring,f}

Is there a pedagogical problem with using a lot of subscripts?

-- That's one horn of a dilemma. Simplicity is good; clutter is bad.
-- The other horn is that being explicit is good.

=====================

For my $2e-2, assuming i and f above stand for initial and final, in
the canonical bob-on-a-spring system, I would probably prefer something
like
E_spring(t_i) (1)
E_spring(t_f) (2)
and
E_bob(t_i) (3)
E_bob(t_f) (4)

making E() a function of time using the () notation for functions,
which is standard in math and computer science. [This also answers
the question posed in today's other thread.]

The fact that E_spring is "potential" and E_bob is "kinetic" is
interesting, but not very tricky, and does not require the notation
to remind me of it every time E_spring or E_bob is mentioned.

Energy _per se_ is primary and fundamental. The partition of E into
potential and kinetic is incomparably less fundamental.