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Re: da/dt = jerk?



Aron must have never replaced his own brake shoes. Had he done so, he
would have been aware that there is a considerable difference between
the way a car's shoe brakes work in the forward direction and the way
that they work going backwards. One of the artifacts of most brake
systems is that after the brakes have once been used in the forward
direction, there is some slack that must be taken up before the brakes
will even make a pretext at breaking after the car has changed its
direction of travel by 180 degrees. This slack is greatly reduced in the
disk brake system but is still evident.

Therefore, once a car has rolled up hill to a stop and the brakes
applied at the moment of zero forward motion, it must roll backward a
slight amount before the backlash in the system will be used up, at
which time a very solid stopping action will suddenly be felt
throughout the vehicle.

With the spongy suspensions that are fashionable these days, after the
backlash is used up and the wheels finally become locked (brakes on
hard) and further rotation of the wheels is impossible, the down hill
torque on the wheels produces a torque on the suspension structures
which are composed of rubber bushings and fairly thin (thinner than I
think they should be) pressed metal . This slight rotation of the
suspension members will also allow some additional down hill motion
before their combined spring tension will be enough to offset the force
down the hill that is due to the "diluted" gravity plus any slight
momentum that the car has acquired. The suspension system and the
rubber tires that are mounted on the now rigidly attached wheels, will
form a spring system. The impulse that is produced by the backlash being
"used up" and the wheels suddenly being solidly locked, combined with
the springiness of the system, produces a damped oscillation that
probably makes the whole event seem much more impressive than it
actually is. It is even possible that the vehicle will cycle several
times between the limits of the brake system's backlash, adding some
interesting sounds to an already interesting event.

It is my opinion, if that at the moment of zero forward motion, wheel
chocks were placed behind each incompressible wheel and those wheels
were mounted on solidly attached axles, there would be no backward
motion, no "jerk" and no settling of the passenger in his seat.
Everything would simply remain just as "stopped" as it was at the
instant of "zero" forward motion.

Bill