Re: (d/dt) ACCELERATION

[brian whatcott <inet@INTELLISYS.NET>]

> At 10:14 AM 9/14/00 -0500, Jack Uretsky asserted:
> > Sudden change of velocity implies infinite acceleration, which is infinitely
> > destructive and therefore unphysical.  Sudden change of acceleration
> > does not violate any physical principle, although it may be difficult
> > to achieve in particular cirmumstances.  So the displacement-time graph
> > need be only twice differentiable.
At 21:30 9/16/00 -0400, John Denker responded in a reasoned voice:

> I'm skeptical of this argument, for dimensional reasons among others.
>
> Preliminary remark:  One must always be careful with the meaning of
> "infinity".  In situations like this, the only safe procedure I know of is
> to use it to denote the result of a limiting process, where something grows
> without bound as we pass to the limit.
>
> In this way I take Jack's statement to mean that there are physical
> processes which in some limit can be extrapolated to give an unboundedly
> sudden change in acceleration, i.e. an infinite jerk.
/snip/

I fear that I am acting in the role of the enthusiast who insists there
 is always another construction possible, when one reminds him there
are no perpetual motions whatsoever.
   All the same, I ask you to consider a plausible step change in
acceleration:

One arranges a wire that will yield at 30 newtons secured to the floor
at one end, and to the test mass of 2 kg at its other end.
One arranges a second wire that will break at 25 newton force, attached
to the test mass and pulled upwards by a tension spring of constant
5 newton per cm. This  spring is pulled upwards with great deliberation,
so that no inertial effects supervene.

One expects the spring to stretch by about 5 cm before the upper wire
breaks. The motion of the test mass is a small slow upward motion
(with the straining of the lower wire) followed by a steady downward
acceleration due to gravity.
brian whatcott <inet@intellisys.net>  Altus OK
                Eureka!