Re: momentum before force (was: friction)

["Eugene P. Mosca" <mosca@nadn.navy.mil>]

Daniel L. MacIsaac wrote

> > Newton worked in dP/dt -- the change in momentum (he was too cagey to
> > assume constant mass like the statement F = ma is often misinterpreted).
> > From IMPETUS or the better-differentiated MOMENTUM that followed, he
> > defined force.
>
> ...by this murky writing I was trying to bring up the fact that
> dP/dt = m dv/dt + v dm/dt; with which Newton was intimately aware and
> which is often overlooked in our more modern treatments of F= ma in
> beginning dynamics.  We tend to leap at F = m dv/dt right away.  .  .

I have a problem with the statement F = dP/dt = m dv/dt + v dm/dt.  If F,
m, and dv/dt are Galilean invarients and v is not, then this equation
cannot be correct.  In fact, the rocket equation -m dv/dt = u dm/dt cannot
be derived from this statement.  Note that in the rocket equation m, dv/dt
and u are Galilean invarients.  For the original statement F = dP/dt = m
dv/dt + v dm/dt to be correct requires that the mass not be a scalar, as
is the case with the so called relativistic mass m/(1 - (v/c)^2)^1/2. 

I realize that Dan admitted to murky writing, but it seems to me that his 
following remarks failed to clear the waters.

Gene

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