Re: That jerk again!

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

As I have followed this discussion unfolding I think that Brian has come
closest to unraveling the mystery so far.  Now that I have a few moments of
time I thought that I would contribute my take on the situation.

As, I think, Brian noted, the suspension system of the car is somewhat
loosely coupled to the rigid car frame by springs, struts, and shock
absorbers that all have a significant range of motion. In different states of
motion and acceleration the equilibrium position of these springs differs.
When the car is in a freely accelerating roll (due to the road surface not
being perpendicular to the Earth's gravitational field) the equilibrium set
point of the suspension system is different than its equilibrium point when
the car is at fixed rest on the same tilted hill.  From a frame in which the
car remains at rest the direction of the effective gravitational field is
different when the car is in a free roll than the direction of this field
when the car is at rest on the tilted slope.  The discontinuous change in the
direction of this force field when the brakes are applied at the 'stop point'
causes a reequilibrating response of the suspension system which causes a
temporary motion of the rigid car compartment.

Leigh wrote:
> If my car is in neutral and I roll slowly up a slight grade I
> eventually reverse my direction and roll back down. The
> turnaround is very smooth; I feel no sudden discontinuity. I
> have tried to apply my brake at the instant of the turnaround
> many times in this situation, and whenever I do I feel a
> discontinuity in the motion. I'm convinced that I've hit the
> instant dead on more than once, but still the discontinuity
> is always present, and not noticeably varying in magnitude.
>
> What's happening here? There is no discontinuity in velocity,
> but when I apply the brake there is a discontinuity in the
> acceleration. Of course the car is in equilibrium in an
> accelerated frame while it slows, but I can't believe that is
> the cause (the rapid change to a nonaccelerating frame)
> because the acceleration can vary a great deal and the
> subjective discontinuity does not seem to do so.

David Bowman
dbowman@gtc.georgetown.ky.us