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Re: Are student evaluations useful?




Leigh writes:

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.


Thought experiment: put Leigh in a box and project it vertically upwards
without air resistance. Free fall. At the precise top of the trajectory,
catch the box. No discontinuity in velocity. Inside the box, Leigh will feel
gravity "coming back" as the reaction from the floor is restored. If he had
been in a standing position on a spring balance (a bit like the car's
suspension system) there would have been a distinct movement as the balance
took up his weight.

Now put the box on a horizontal, frictionless plane and attach it via a
large spring to a nearby wall so that it can execute harmonic oscillations
at a comfortable frequency. Leigh certainly feels the oscillations inside as
the is pushed back and forth. But what does he feel if we catch the box at
one of the extremes, when v=0? This time he will have been braced to stay on
his feet at the moment of maximum acceleration, and so would probably topple
slightly as the acceleration goes to zero.

In both cases he feels the jerk because of a redistribution of internal forces.

(Sorry for the indignities, Leigh)

Mark.


*************************************************************
Mark Sylvester
United World College of the Adriatic, Duino, Trieste, Italy.
msylvest@spin.it
tel: +39 40 3739 255
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