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Re: Name that force

On 10/28/2003 10:12 AM, Bob Sciamanda wrote:
These are totally inelastic collisions (interactions) between the
car and the water. Ie., interactions between two objects resulting
in a common final velocity. This can only happen if the interaction
includes a dissipative mechanism. Conservation of momentum mandates
the dissipation of kinetic energy.

That is a good approximation and correctly (for all
practical purpose) describes *what* happens, but the
result holds more generally -- momentum is conserved
even if there is no common velocity; momentum is
conserved even if there is negligible dissipation.

Imagine an empty boxcar with initial velocity V
that picks up an initially-stationary ping-pong ball,
and imagine that the interactions are sufficiently
elastic that no dissipation occurs for a long time.
The ball will bounce back and forth with lab-frame
velocity alternating between (approximately) +2V and
zero, i.e. boxcar-frame velocity alternating between
(approximately) +V and -V. The *average* velocity of
the combined system will be just what you expect, i.e.
P/(M+m), even though the instantaneous velocity will
alternately be more and less than that.

Of course we expect that over some longer timescale
dissipation will eventually occur and the velocity
will settle down to the average velocity, but this
is not *necessary* for conservation of momentum.

=====================

Let me take this opportunity to chime in with another
word that could be used to "name that force" ...
hydrostatic pressure (in addition to the previously-
mentioned viscosity). If we make the steady-state
approximation, and a few other approximations, there
will be a pool of water on the bottom of the boxcar,
and the surface of the water will have a slope. The
steady addition of new water will, via viscosity etc.,
maintain this slope. The hydrostatic pressure will
push on all the walls, but because of the slope
there will will be greater force on the back wall,
resulting in deceleration.