Thank you all for the contributions above. I didn't bother to quote everyone, but I think the general conclusions I have drawn from this discussion are these:
Assuming that we are dealing with an isolated system and that all interactions are two-body, Newton's Third Law and the Conservation of...
I think what Jano is trying to say is that, in a truly axiomatic system, if some claim about nature is derivable from some other claim about nature, they should not both be considered laws (i.e. axioms or postulates). However, in practice they often are because the choice of which is a law and...
So then can it be said that mechanical energy conservation (when it applies) is a direct consequence of Newton's Laws, whereas total energy conservation is a more fundamental and independent postulate?
Thanks for the suggestion! I will definitely take a look at the videos when I get a little bit of time. Is there perhaps a "short answer" to my momentum and energy independence question, or does it maybe depend upon the system under consideration?
Yes, but in the traditional derivation of the...
Everything you said is right, of course. Sure it may not be "worth it" to consider energy conservation in an elastic collision, but that is not a purely mechanical process (energy is dissipated as heat).
I'm really asking this as an exercise in mathematical physics than in application. You are...
Thanks for the replies!
Well, if both are a direct consequence of Newton's Laws, then both should be applicable at least whenever Newton's Laws are. I don't see how, in the consideration of only classical "slow-moving" point particles undergoing solely mechanical interactions, one can be more...
Suppose we take the three Newton’s Laws as axioms.
Existence of inertial reference frames
F = ma
F(A on B) = -F(B on A)
Also suppose also we are considering purely classical mechanical processes on point particles (no heat transfer, etc.).
It is clear to me that the conservation of momentum...
Ozgen and DivergentSpectrum, thanks for the replies.
What exactly is meant by "unit density flow?" I cannot find a reference to this anywhere else.
The resource I was using is this: http://tutorial.math.lamar.edu/Classes/CalcIII/CurlDivergence.aspx
The discussion on divergence is copied almost...
I'm trying to figure out what the physical meaning of divergence is for a vector field.
My textbook offered the following example: if v = <u, v, w> represents the velocity field of a fluid flow, then div(v) evaluated at P = (x, y, z) represents the net rate of the change of mass of the fluid...
If someone asked me to differentiate x^2cos(x) (with respect to x implied because it's the only variable in the expression), I would do what you did in (2).
So, differentiation = the act or process of taking a derivative.
Now, whether "finding the differential" can be referred to as...
Chet,
Of course it hasn’t limited your ability to get correct answers - we’re only discussing definitions and not some behavior of the universe after all!
These terms seem to be very ambiguous, even in standard thermodynamic texts. Smith, Van Ness, and Abbott (which I know you are fond of)...
Chet,
I'm a little confused by your definition of quasi-static.
From the definition that Useful nucleus gave in the first post, it would seem that the "contact with a succession of thermal reservoirs" case would be a quasi-static process whereas the "contact with finite temperature difference"...
It's rigorous because it's impossible to contradict! Forget the Zeroth Law for a minute and consider just arbitrary functions.
Let f1 = f1(x1, x2, x3, x4) = 0 and f2 = f2(x1, x2, x3, x4) = 0.
Furthermore, suppose that we know whenever f1 and f2 are 0, so is some third function f3 = f3(x1, x2...
Say you made it a point to prove every theorem and concept in physics before you every apply it yourself. Ultimately, you'd find that you'd gone far from the realm of science into the realm of theoretical math and eventually into the realm of philosophy.
Imagine your burden of proof! Not only...
This last post of yours very elegantly clarified my confusion.
My mistake, as I can see now, was to calculate change in entropy for a fall + perfectly elastic collision process and then erroneously accredit gravity for this entropy change.
Thank you very much for sticking with me through this...