I guess I'd better explain that I was commenting on (what I believe to be)
Mike's treatment:
1) linear CM acceleration follows from: mu*N = m*dv/dt
2) the energy dissipated is calculated as: Integral {mu*N*dx}
Combining these leads to a dissipated energy of (1/2) m * v ^ 2; simply
the change in kinetic energy forced by equation 1) !
The error is in not distinguishing mu in eq1) from the different mu in eq
2).
PS. The parenthetical remark in my post:
" (which I would re-word as: the energy dissipated cannot quantitatively
be accounted for as the line integral of a CONSTANT frictional force)"
is withdrawn as irrelevant and wrong - the result of a mistaken twist in
my thought. In Mike's treatment, the mu's cancel, so that it is moot
whether or not they are constant.
Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net http://www.velocity.net/~trebor
----- Original Message -----
From: "John S. Denker" <jsd@MONMOUTH.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Saturday, November 02, 2002 1:26 PM
Subject: Re: When Physical Intuition Fails
| . . .
| Thanks for the clarification.
|
| I'm a little mystified by the notion of MU*N as "the"
| force which affects dissipation. The usual model of
| dissipation involves ultra-high-speed fluctuations in
| the force. So the actual force cannot be described by
| MU*N... even though its time-average can be described
| by mu*N. The time-average suffices for accounting for
| the momentum tranfer, but the detailed, unaveraged
| force is required to explain the dissipation.
|
| Or have I completely missed the point?
| . . .|
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