Re: CAUSATION IN PHYSICS

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

Regarding Ludwik's comments:
>                                 ...                     . John is
> referring to idealizations in which F acts on a particle, or on a rigid
> body. Leigh, on the other hand, was bringing a very persuasive
> argument for "F being a cause of a" in non-ideal situations. The
> center of mass of a real body does not start accelerating at the
> same moment at which the force is applied. What do you think
> about this argument, John? In the last message Leigh wrote:

<SNIP Leigh's comments>

As much as I think Leigh's point was clear, I don't think he meant to
claim (if I'm incorrect here about Leigh's thinking, I hope he would
correct me) that "The center of mass of a real body does not start
accelerating at the same moment at which the force is applied."  I expect
Leigh *would* agree that to the extent that a Newtonian (nonrelativistic)
model of the situation is applicable, the center of mass *does* instantly
respond in concert with the application of the force with F = m*a at each
instant of time, where F is the net applied force and a is the
acceleration of the center of mass of the body.  It is just that when a
stiff (but not perfectly rigid) body is subject to an unbalanced contact
force on its surface the body's motion proceeds inhomogeneously from the
point of contact across the body at a rate determined by a shock wave
typically moving at a speed which is characteristic of the speed of
sound in the body.  As soon as the struck end of the body experiences the
force the motion of that end compresses the body at that end and this
redistribution of the mass of the body at that end relocates the body's
center of mass so that even though the shock wave has not yet reached the
region of the center of mass, and that part of the body does not begin
to respond, the location of the center of mass of the body *does*
instantaneously move according to F=m*a because just which part of the
body happens to *be* at the center of mass changes (before that part
begins to respond to the force from the propagating shock front).

David Bowman
David_Bowman@georgetowncollege.edu