ISEN-ASTC-L is a service of the Association of Science-Technology Centers
Incorporated, a worldwide network of science museums and related institutions.
*****************************************************************************

Imagine a simple version - one track is the hypotenuse of a right
triangle, the other track goes straight down one side, then has a sharp
curve and goes across the base.  On the hypotenuse track, acceleration
is a fraction of g controlled by trigonometry (force down ramp =
g*sin(angle of ramp from horizontal)) On the vertical track the
acceleration is g, so the ball on the vertical track accelerates more
quickly, then shoots around the corner and onto the flat track.  It is
no longer accelerating, but assuming a smooth track and a relatively
massive ball for its size, it should not decelerate much, either, so it
travels the horizontal leg at a constant, relatively high velocity.
Meanwhile, the ball on the hypotenuse continues to accelerate, but only
a little at a time  If the geometry of the triangle is correct, the
higher average velocity of the longer track will more than compensate
for its greater length.  At some geometry, there is likely to be a trade
off, but that's too much math for Monday afternoon.  Your track is more
complex, but the basic principle is the same.  You could easily design a
track where the longer track came in second, but where's the surprise in
that?

Now, since it is your young kids area, you do indeed need to give a lot
of thought to the point of the exhibit, but even if it was in an adult
area, you might need to be more careful than you would think.  The
average person has a very tenuous grasp of the concepts of acceleration
and velocity and an especially tenuous concept of integration, which is
really what this is all about.  People will leave long before they have
read enough text to explain all the concepts.  You need a scaffolded set
of exhibits to teach all the physics if your goal is for them to really
understand.

Instead, perhaps the concept goals are something like:
1.  The speed of objects can change along their path
2.  Complex paths consist of "legs" with different behavior on different
legs
3.  The shortest path is not always the most favored path (true in lots
of areas other than physics)

Or, maybe, the goal is for them to be really puzzled.  So puzzled that
they are annoyed that you won't just tell them.  So annoyed that they go
home and work on it at home.  How do you scaffold this so that people
can construct understanding, not read it off a sign, soon to be
forgotten?  Maybe, ubiquity notwithstanding, it's a bad exhibit because
you cannot scaffold understanding and so it never produces much
learning.

Dave Smith, Da Vinci Discovery Center, recovering physics professor

***********************************************************************
More information about the Informal Science Education Network and the
Association of Science-Technology Centers may be found at http://www.astc.org.
To remove your e-mail address from the ISEN-ASTC-L list, send the
message  SIGNOFF ISEN-ASTC-L in the BODY of a message to
[log in to unmask]