In the context of FCI....
On 06/24/2013 08:11 AM, Philip Keller wrote:
As for #17/18, the elevator: it looks like 1st law to me, not 3rd.
OK, you're right about that. I was mistaken.
It was a mistake, and I'm not going to pretend otherwise ... but I
would like to suggest that it was an "interesting" mistake. The
physics was right, even if my terminology was wrong.
The overarching point is that when expressed in terms of momentum,
the first, second, and third laws are all so similar that I have
trouble telling them apart.
It was an understatement when I said that a number of FCI problems
become much simpler if you reformulate the third law in terms of
conservation of momentum. What I "should" have said is that a whole
bunch of problems -- FCI and otherwise -- become much simpler if you
think about the first, second, *and* third laws in terms of momentum.
As a starting point, let's write the second law as
dp / dt = F [2]
Then the first law is a corollary of the second law, in the special
case where the applied force is zero. Therefore any first-law
question also counts as a second-law question.
The third law says that momentum is conserved. This is the most
general and most powerful result. As always, conservation is to
be understood as follows:
change in momentum = net flow of momentum [3]
(inside boundary) (inward minus outward across boundary)
Therefore the second law can be seen as a corollary to the third
law, in the special case where the only flow in momentum is due
to the net force.
This is not the only possibility; advection is another possibility.
As yet another interesting point: the first law says momentum is
constant, while the third law says momentum is conserved. These
are not the same, but there is only a fine line between them,
especially in a closed system ... so you can see how it would be
easy to get the terminology wrong ... even while *not* getting the
physics wrong.
In the particular case of the FCI elevator question (#17 or #18),
the net force is zero, so the distinction between first, second,
and third laws is purely a matter of conventional terminology;
the physics is the same no matter what terminology you hang on
it.
This is yet another example of what I call the unity, grandeur,
and simplicity of physics: Fundamentally Newton's three laws of
motion are really only one law, plus a couple of corollaries.