Re: Theories, models, and simplifications.

From: EKurtz99 (EKurtz99_at_TwilightZone.com)
Date: 01/31/05 

Date: Sun, 30 Jan 2005 22:17:18 -0500 (EST)

"Perplexed in Peoria" <jimmenegay@sbcglobal.net> wrote
>
> Newton's rule f=ma contains the symbol m. This "m" is
> constant in a different way than G is, but it is still
> a constant. We need to measure m once for each situation
> that we study using f=ma. But in any particular situation,
> we only need to measure it once - it remains constant
> through time as the situation continues to be studied.
> (There may seem to be exceptions to this (in rockets for
> example), but these supposed exceptions involve
> progressively ignoring part of the mass (the rocket exhaust).
> Proper understanding of how to use f=ma would consider
> that exhaust mass to still be part of the system being
> modeled.

Actually, the opposite is true. Read on.

> (Mr. Kurtz, are you reading this? He is not
> as confused as you think!)

Oh yes he is, and I am beginning to think you are.

If you are considering the behavior of an object under a force F using F =
ma, then you are de facto neglecting the change in momentum of the object
that generated the force. The object of mass m in the equation is subject to
an acceleration a, and thus experiences an increase of momentum in the
direction of F, but the equation does not prescribe a change in the velocity
of any other object to conserve momentum overall, ie F = ma ignores
conservation of momentum (though no one denies that such a compenatory
change takes place).

If you wish to consider a dynamical system such as a rocket in empty space
(assuming that the thrust of the rocket and rate of mass loss are known),
you use the full form of the equation, F = d(mv)/dt ("force equals rate of
change of momentum"), ie F = vdm/dt + mdv/dt
In the rocket case you neglect *both* the conservation of momentum *and* the
conservation of mass.

We use F = d(mv)/dt in both cases because we are interested in the dynamics
of only a part of a system to which, in its entirety, the conservation laws
apply.

Proper understanding of how to use of F = ma involves recognizing that it is
*not* an expression of the conservation laws; if you are interested in
conserved quantites, the system would have to be analyzed differently. F =
ma with a disembodied F would not apply. (Of course, you could argue that
the only system to which conservation of momentum *really* applies is the
entire universe; it applies only approximately to local systems;
interestingly, this is not true of mass, which is locally conserved (in
classical physics)).

> Furthermore, both G in gravitation and m in mechanics
> have similar epistemological roles:
> 1. They must be measured.
> 2. They remain constant through time.
> 3. Any attempt to remove them from consideration in a
> model of the theory is inevitably going to result in
> a model that is pathologically inferior to the
> parent theory.
> Non-refutability is one possible
> such pathology. John and I may remain in dispute as
> to whether it is an inevitable pathology, but it is
> certainly a possible pathology. And we agree that
> some kind of pathology, some loss of something, IS
> inevitable.

But as you so astutely observed, with the inverse square law expressed as a
relationship of proportionality without G it is still possible to verify
Kepler's laws. That doesn't seem like pathological inferiority to me. (or
did you mean remove both of them?)

Relevant Pages

  • Re: Theories, models, and simplifications.
    ... then you are de facto neglecting the change in momentum of the object ... The object of mass m in the equation is subject to ... > conservation of momentum (though no one denies that such a compenatory ... >> to whether it is an inevitable pathology, ...
    (sci.bio.evolution)
  • Re: Uh Oh, Discrepancy Alert
    ... that inertia doesn't exist, ... I said that time is one & mass might be. ... That seems to be about the conservation of momentum. ...
    (alt.machines.cnc)
  • Re: Conservation of angular momentum
    ... conserved if no net external force acts on it; ... shows that the puck stops with a lever of 6x the mass of the puck and ... and transfers all its momentum to it, ...
    (sci.physics)
  • E = mc^2
    ... In the first place that was a loose derivation since the details required ... a definition of momentum. ... That can't be given without defining mass first. ... Due to the principle of the conservation ...
    (sci.physics.relativity)
  • Re: .Re: Why all the fascination with E = mc^2 ??
    ... >> Conservation of Momentum, which, in Newtonian mechanics, is a direct ... >> consequence of Newton's Third Law of Motion. ... >> and the kinetic energy of a body is given by ...
    (sci.physics)
Quantcast