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Re: Refraction at Constant Speed



It's an interesting idea, but I'm not sure what physical systems it
could be used to model. Other may be more creative than I. What it
cannot model is optical refraction, because, although it shows a
direction change at the interface, the change does not behave like
that at an optical interface. For instance, if the vehicle arrives at
the moving sheet perpendicular to the motion of the sheet, it's
motion will still be "bent" in the direction of the sheet's motion.
In fact, the motion of the vehicle will always be bent in the
direction of the moving sheet, which means that it will behave
similar to light only if it has a component of its initial velocity
which is opposite to the direction of the motion of the sheet. And,
of course, the speed of the bulldozer relative to the floor or the
sheet doesn't change when it moves from one to the other, only the
direction of motion. In the case of light, the direction of
propagation changes *because* the speed changes in the new medium.

An airplane encountering a wind shift, or a boat entering a region of
different current will display some of the same effects as you
describe, although the heading of the craft will not likely be
altered in most cases since the condition existing with the bulldozer
and the sheet is usually not present--that is, that the gradient of
the wind or current shift needs to be large over the size of the
craft in order to produce a significant turning couple. That clearly
exists in the case of the bulldozer and seldom in the case of an
aircraft or boat.

I have a whole catalog of neat demonstrations that I have thought up
over the years, but had to abandon because they didn't demonstrate
what I wanted them to. This may be another of that category. I hope
that someone cleverer than I on this list can find something for the
idea to demonstrate.

Hugh

From early PSSC days, the "constant speed vehicle" has been portrayed as a
track-laying bulldozer of some sort. If the expected congruences apply, it
is a constant velocity vehicle as well. Relative motion in two dimensions
is often undertaken by having one dozer pull a large flat sheet on which a
second dozer is moving to be examined in the room's frame of reference.

But if the second dozer is started from off the large sheet, on the carpet
let's say, and made to intercept the moving sheet, an interesting
refraction occurs at the interface. The reason is simple. One track is
getting traction on the moving sheet before the other. Depending on the
angle of incidence, refraction can be observed either towards the normal or
away from it. This behavior can be predicted by noticing which track would
enter the moving sheet first or leave it last since this is what produces
the couple that turns the vehicle.

If the towed sheet has parallel edges, it is observed that the refracted
dozer makes parallel paths on the carpet before and after being transported
by the sheet. One presumes the shape of a prism or lens section could be
towed.

The question for the list is:

What physical systems could be usefully modeled with such an arrangement?
It is typical, but not necessary for both dozers to have the same speed.
The dozer blade might be regarded as an element of a wavefront or the path
of the dozer, a ray, e.g.

Tom Ford
The Science Source
Manufacturer of Science Educational
and Design Technology Equipment
P. O. Box 727
299 Atlantic Highway
Waldoboro, ME 04572-0727
(207) 832-6344
1-800-299-5469
FAX (207) 832-7281
e-mail: tomford@thesciencesource.com
http://www.thesciencesource.com

--

Hugh Haskell
<mailto://haskell@ncssm.edu>
<mailto://hhaskell@mindspring.com>

(919) 467-7610

Let's face it. People use a Mac because they want to, Windows because they
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