The situation is actually more complex in that there is also no such =
thing
as a rigid body! This means that an applied force has to propagate th=
rough
objects as a compressional wave (speed of sound ?) before a steady st=
ate
is obtained. The bottom line is that you can't expect the simple beha=
vior
we describe in elementary problems to withstand scrutiny in the limit=
of
t -> 0 .
Sorry for the =3D3D infection.
Al Bachman
----- Original Message -----=20
From: ALVIN BACHMAN<mailto:bachman_28@MSN.COM>=20
To: PHYS-L@LISTS.NAU.EDU<mailto:PHYS-L@LISTS.NAU.EDU>=20
Sent: Saturday, November 05, 2005 3:53 PM
Subject: Re: A problem of motion and derivatives
The situations requiring a discontinuous force or acceleration are =
ex=3D
actly what appears in most textbook problems, and what leads to the=
f=3D
irst question in the original post.
My point was that this does not really occur, but the situation cou=
ld=3D
be modeled with a continuous transition.
For example, f =3D3D (Fo/2)( 1 + Sine((2 pi/T)(t-T/4))) between =
t=3D
=3D3D0 and t=3D3DT/2, with a value of T << duration of the problem,=
eg ~=3D
1 msec. f =3D3D Fo for t>=3D3DT/2 .
John, I can't think of examples of discontinuous forces aside fro=
m
situations where force is exerted as a series of pulses -- for in=
st=3D
ance force exerted
by a jackhammer or by antilock brakes. However, each individual p=
ul=3D
se would
be continuous.
>For an object with v=3D3D0 and a=3D3D0 at t < 0, the imposition=
of a =3D
constant force
>or acceleration at t=3D3D0 is a discontinuous event. (This inclu=
des =3D
dropping an
>object, where the holding force has to go to zero instanteously=
.)
I think it might be the case that the force on a particle (or th=
e =3D
net
force on a system of particles--i.e., an "object") rarely if eve=
r
really changes discontinuously. I can't think of one. Can anyo=
ne
else?