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Re: car acceleration



-----Original Message-----
From: John S. Denker [mailto:jsd@MONMOUTH.COM]
Sent: Wednesday, February 06, 2002 1:31 PM

[snip]

Specifically: The physics changes when the compliance of the
wall becomes small compared to the compliance of the ball.

[snip]

I suppose we can just model the ball as a spring of spring constant k_1 and
the wall as a spring of spring constant k_2 so that the ratio of the elastic
energy in each is:

PE_1 0.5*k_1 x_1 x_1
---- = ---------------
PE_2 0.5*k_2 x_2 x_2

where x_1 and x_2 is the compression of each during contact. Since k_1 x_1
= k_2 x_2 (N3), we get

PE_1 x_1
---- = ---
PE_2 x_2

which shows that the PE of the wall spring, while present, is negligible
compared to that in the ball when the ball is more springy.

Does RT or JB see something to the argument below that JD (and I) don't see?

--- Rick Tarara <rtarara@SAINTMARYS.EDU> wrote:
The 'reasoning' goes like this (I
believe). During the push
there MUST be some deformation of the wall. That
deformation may be very
small, but then the forces are very large. Energy
is stored in the deformed
wall BUT came from the person. As the wall rebounds
there is a force
(perhaps quite large) that acts through a
displacement (perhaps quite small)
that will account for the change in KE of the
person. In the end analysis,
the energy does come from the person, but was
temporarily stored in the
wall. There will also be dissipative losses, but we
can imagine those being
minimized.
____________________________________________
Robert Cohen; rcohen@po-box.esu.edu; http://www.esu.edu/~bbq
Physics, East Stroudsburg Univ, E. Stroudsburg, PA 18301