Re: A problem (displacement of contact force)

["John S. Denker" <jsd@MONMOUTH.COM>]

At 10:44 AM 8/6/01 +0200, Savinainen Antti wrote:

> >But during the deceleration, the weight and the contact
> >force are not colinear, resulting in a torque.
>
> ... in case of a decelerating car I see why the contact force and the
> weight cannot be colinear: otherwise the torque exerted by the friction
> would not be balanced. But why does  this "displacement" of the contact
> force take place?

Good question;  see below.

> I am not totally satisfied with the answer "to keep the net torque zero".
> The contact force may not have intentions :-).

Indeed you should not be satisfied with such an answer.  That would be
tantamount to assuming the answer -- and assuming the wrong answer!

The proper way of attacking such problems is to *not* assume anything about
the net torque.  It might or might not be zero.  So.... What happens if it
is nonzero?  Answer:  When you initially apply the brakes, the car will
pitch forward, i.e. pitch nose down.  This will compress the springs in the
front-wheel suspension and decompress the springs in the rear-wheel
suspension.  That means the "weighted average" force on the wheels moves
forward.

The point is that it is unphysical to imagine zero pitch angle.  The
physics would be an indeterminate form (zero over zero), or worse, if you
did that.  You have to imagine that it pitches a little bit... which gives
rise to forces that keep it from pitching more.

What we are doing is a stability analysis, and all such analyses start the
same way:  consider a small change in the coordinate of interest......

Formulating the problem in terms of a perfect cube (as opposed to a car
with springs with finite compressibility) is NOT a helpful
simplification.  It suckers people into thinking that the system is
infinitely stiff and infinitely stable.  Such infinities are unphysical.

The only sensible way to analyze the cube would be to analyze the car and
then consider a sequence of cars with stiffer and stiffer (but not
infinitely stiff) suspensions.

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

Pedagogical / philosophical remark:  It's really hard to answer a question
if the question itself embodies unphysical assumptions.  The temptation is
to not answer the question at all, and just change the subject.  But you
can't always get away with that.  Sometimes "the boss" or some such is
really demanding an answer.  The recommended approach is to rephrase the
question, and then answer the question that should have been asked.

The hard part, as often as not, is to figure out how to modify the
question.  This typically requires more psychology than physics, to figure
out where the other guy is coming from.