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Re: Kraft



Jim Green wrote on Tue, 04 Mar 1997 01:39:07 -0700 :

Now can someone tell me what Helmholtz meant in the title of his famous =
paper:

"Die Erhaltung der Kraft"

In this article Helmholtz uses the old notation, where "Kraft"
means sometimes 'force' but mostly 'energy' - derived from
Leibniz's "vis viva" =3D "lebendige Kraft" for (m*v^2)(Leibniz
1695) or (m*v^2)/2(Coriolis)

Citing Ernst Mach: "Die Mechanik in ihrer Entwicklung", 7.
Auflage, Wien 1912, (engl:"The Science of Mechanics...",Open
Court), p. 283 ff:=20
m*v =3D p*t (m,v,t as usual, p as the Newtonian force)
...
Coriolis also used the name WORK (Arbeit) for p*s. Poncelet=20
enforced this usage and took the KILOGRAMMETER,=20
that is the pressure-effect ("Druckwirkung") of a=20
kilogramm-weight on the distance of one meter, as unit of
work.

p. 292: dimensions

..., length l, time t, mass m, ...
Geschwindigkeit...v......l*t^(-1)
Beschleunigung....phi....l*t^(-2)
Kraft.............p......m*l*t^(-2)
Bewegungsgroesse..m*v....m*l*t^(-1)
Antrieb...........p*t....m*l*t^(-1)
So Mach doesn't use p for momentum, nor does he use that name at
all, and he distinguishes between m*v and p*t (We use
"Kraftstoss" for F*t)
Arbeit............p*s....m*l^2*t^(-2)
lebendige Kraft...(m*v^2)/2

So we see: the development of our actual definitions took a long
time and rests of the old ambiguities are still remaining among
us.
Bye, bye
Guntbert
-----------------------------------------------------
+please correct me, if I misuse some technical terms+
-----------------------------------------------------
Mag. Guntbert Reiter, Graz, Austria
teacher for physics and mathematics
e-mail : guntbert@cut.big.ac.at