> From: [EMAIL PROTECTED] (Joseph B. Reid)
> Subject: [USMA:9044] Energy
>
> Isaac Newton called mv "quantity of motion", which is now known a momentum.
> Leibnitz argued that quantity of motion would be lost in collisions, but
> that mv^2, which he called "vis viva", would be preserved. I think that in
> modern language we would say that mv is a vector quantity, whereas mv^2 is
> a scalar.
Both Newton and Leibnitz, as well as others, were trying to decide what was
the "best" way to measure "motion". They all realized that it was more than
just velocity (the "v" in the above equations) and that it somehow involved
the mass as well (the m in the above equations).
The disagreement arose because there were some experimental results that
seemed to show that the quantity mv was conserved in certain interactions
while mv^2 was not. At the same time, other experiments in other
circumstances showed that the quantity mv^2 was conserved while mv^2 was
not. What we now realize is that it is not one or the other, but both.
Both mv (now called momentum) is conserved and another quantity (now called
energy) is ALSO conserved. It turns out that (1/2)mv^2 is only one of the
kinds of energy and that it is total energy, not just (1/2)mv^2 that is
conserved. The experiments that seemed to prove that (1/2)mv^2 was not
conserved were mistakenly omitting the other forms of energy that we now
know are involved. The experiments that seemd to show that mv was not
conserved were failing to take into account the fact that momentum includes
the direction of motion and that, for example, two momenta in opposite
direction needed to be subtracted instead of added (and could even "add" up
to zero if the two were equal).
(The switch from measuring mv^2 to measuring (1/2)mv^2 was a technicality
that doen't affect whether the quantity is conserved or not.)
Regards,
Bill Hooper
