Re: That jerk again!

[Jim Riley <jriley@lib.drury.edu>]

Let us compare three situations. 

First, the car is at rest, not moving, has never been moving, and I apply
the brakes.  Obviously I will feel nothing.

Second, the car has been moving but under the influence of gravity the car
and its contents have come instantaneously at rest.  Call this time t=0.   I
apply the brakes at this instant.  Is there any physical difference between
the objects involved at this instant and the previously mentioned condition?
Answer-No.  Therefore I should feel nothing at this time either..  

Third the car has been moving under the influence of gravity, I do not apply
the brakes, the car and contents at some instant have a zero velocity and
then begin rolling backward, having at all time a constant acceleration, and
no jerk.
 
How do we explain Leigh' sensation of a "jerk"?  Possible answers:

1)  Leigh is not skillful enough to apply brakes at the correct instant.
(But Leigh has practiced this and still notices the "jerk")

2)  Assuming the brakes have been applied at the precise instant that
everything has come to rest there will be no "jerk".  The "jerk" occurs at a
later instant.  Although the car and contents are at rest at t=0 there is
still a gravitational force on all objects involved.  The wheels are in
contact with the ground and prevented from moving by the friction with the
road.  They do not move.  The auto and contents however will now continue to
accelerate backward under the influence of gravity as it was doing just
prior to time t = 0.  But the suspension of the auto will now become
progressively more and more stressed.  Eventually the stress is great enough
to stop them as well.  The influence of the auto suspension builds up over a
finite amount of time so that the acceleration is not a constant.  It
changes from an acceleration directed down the hill (a constant up to and
including time t=0) to one directed up the hill as the suspension is
stressed and finally back to zero again as the car and contents reaches its
second stopping point.

It might help to visualize the velocity vs time graph of the three
situations above.

Situation one.  The velocity vs time graph is a constant, its slope is also
a constant = zero, constant acceleration means no "jerk" 

Situation three.  The car is just allowed to roll backwards.  Velocity vs
time  will be a straight line crossing the time axis at the point t=0 as
above.  The slope of the line, and thus the acceleration, will be a
constant.   No " jerk" is felt.  

Situation two.  Velocity vs time will be a straight line until it reaches
the axes at time t=0. As it crosses the axis it will have a slope equal to
the value it has had during the time it was rolling to a stop.  At time t=
epsilon, a small time after 0,  the wheels remain at rest but the rest of
the car and contents move backward until the suspension system, which until
time t=0 were unstressed, becomes stressed enough to bring everything to a
stop.  The velocity vs time graph of the driver becomes negative and then
returns to zero.  The slope goes from negative to positive to zero.  The
acceleration obviously does the same.  Non-constant acceleration = "jerk"

At 06:10 AM 11/19/97 -0800, you wrote:
> Others have already discussed the role of the suspension in insuring that
> no sudden application of the brakes can successfully halt the motion of
> the car on an incline.  Nevertheless, even sans suspension you'd feel a
> jerk--and I'm *not* talking about Leigh.  This, even if the brakes were
> applied at the precise instant that v = 0.
>
> One *can*, of course, bring a car to rest on level ground without any
> noticeable jerk or subsequent oscillations by carefully, speed-dependently
> applying the brakes.  I've gotten pretty good at this as have others I
> suspect without, perhaps, even knowing they are trying.  It simply
> requires easing off the brakes as the car comes to a stop so that the
> acceleration smoothly approaches and reaches zero at the same time as the
> velocity.  Doing this works perfectly in theory in a suspensionless car. 
> It works well enough in a car with suspension as long as Leigh, er, I mean
> the rate of change of the acceleration isn't too large and the shock
> absorbers are doing their job adequately.
>
> John
> -----------------------------------------------------------------
> A. John Mallinckrodt      http://www.intranet.csupomona.edu/~ajm
> Professor of Physics    mailto:ajmallinckro@csupomona.edu
> Physics Department       voice:909-869-4054
> Cal Poly Pomona            fax:909-869-5090
> Pomona, CA 91768-4031   office:Building 8, Room 223
Jim Riley
Department of Physics
Drury College
Springfield Missouri  65802
(417) 873 7233
e-mail:  jriley@lib.drury.edu
fax: (417) 873 7432