Re: car acceleration

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Wed, 6 Feb 2002, John S. Denker wrote:

> Are people shocked by the notion that there can be a large
> momentum transfer without a large energy transfer?  They'd
> better get used to it!

I'll second that emotion.  I might tout the paper, "Stopping
Objects with Zero External Work: Mechanics meets Thermodynamics",
Am. J. Phys. 61, 121-127, (1993) in which Harvey Leff and I
treated the case of two mirror image putty wads smacking each
other head on at the plane of symmetry.  In this case it is nearly
trivial to see that

1 the symmetry of the situation requires

  "real work" of 1 on 2 = "real work" of 2 on 1

and

2 the points (planes really) of contact may move, but remain at
all times within the plane of symmetry and the contact forces are
equal and opposite which requires

  "real work" of 1 on 2 = -"real work" of 2 on 1

The only way of satisfying these requirements is for

  "real work" of 1 on 2 = "real work" of 2 on 1 = 0

It is even clearer that the momentum change of each putty wad is
NOT equal to zero.

A little thought about this situation should make it crystal
clear that momentum change need not be accompanied by "real work"
and certainly not by any change in the total energy of the
interacting systems.

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm