Re: positive and negative work

["John S. Denker" <jsd@MONMOUTH.COM>]

kowalskil wrote:

> "John S. Denker" wrote (in part):
>
> > ... I'm not assuming that work is a useful concept.
> > Sometimes it is useful, but sometimes it isn't. ...
>
> Would you say the same about the concept of force?

1) Well, in a nit-picky philosophical way, yes, there are plenty of
cases where force is not a useful concept.  For instance, when
calculating the entropy of a deck of cards, there is no need to talk
about force, and a student who wrote down F=ma as a starting point would
not receive partial credit.

2) But to speak more to the spirit of Ludwik's question:  In cases where
force "seems like" an appropriate concept, it probably is.  In this
thread I've repeatedly said energy is primary and fundamental.  Let me
hasten to say that momentum is also primary and fundamental.  Force is
intimately related to momentum.  Talking about the momentum associated
with the CM motion of a complex system makes sense.  We get a gift from
Mother Nature here because the momentum/force relationship is linear, so
we don't need to be too fussy about what forces are applied where.

OTOH, trying to connect the CM motion with work = F dot ds for a complex
system is usually hopeless, because the complex system doesn't have a
"ds" of its own that means anything.  The energy/force relationship
isn't linear in the way that the momentum/force relationship is, so we
have to be very fussy about what forces are applied when and where.