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Re: bending of object thrown into pool



What if you shoot the arrow upward from below the water surface? Does
it speed up?

____________________________________________________
Robert Cohen; 570-422-3428; www.esu.edu/~bbq
East Stroudsburg University; E. Stroudsburg, PA 18301


-----Original Message-----
From: Forum for Physics Educators
[mailto:PHYS-L@list1.ucc.nau.edu] On Behalf Of Carl E. Mungan
Sent: Thursday, August 12, 2004 12:42 PM
To: PHYS-L@LISTS.NAU.EDU
Subject: bending of object thrown into pool


If a macroscopic object (say an arrow or a golf ball) is
thrown into a pool at an oblique angle, what will be the
relation between the incident and transmitted angles?

I was perusing the book "What Einstein told his Barber" in
which the author (a retired chemist) claims Snell's law would
be obeyed. I'm finding it hard to see this. It seems to me
that one should start by resolving the incident velocity into
normal and tangential components. The transmitted normal
component would presumably depend on the elastic surface
tension, while the tangential component would only respond to
the viscosity. Once it's in the water, the drag force is of
course oppositely directed to the velocity and so does not
bend the trajectory, although I wonder about the situation
when the arrow is half in and half out of the water?

I have a dim memory that Newton once argued from his
corpuscular view that light particles should bend *opposite*
to the wave prediction of Snell's law. If someone remembers
why that should be so, I'd be grateful for a primer on the subject.

In any case, the standard derivation of Snell's law
(continuity of the electric field crests and troughs,
together with an index-dependent change in velocity) doesn't
seem to me to be readily adaptable to particles. On the other
hand, what about electron microscopy say? How does the size
of the de Broglie wavelength figure into Snell's law? There's
the well-known question about the fastest path to get from
point A on the beach to get to point B in the water, which is
sometimes compared to Feynman's path-interference model of
light propagation: does this mean that coherence is also a factor?

If somebody on the list has a pool, I would be very
interested if they could actually try launching various
objects into the pool and report back on their observations. Carl

ps: Theoretically, it might be best to imagine the object to
be neutrally buoyant, because we're not interested in the
effects of gravity and buoyancy. Experimentally I don't think
these matter too much for dense objects over short distances.

pps: I just tried rolling a ball from a smooth book onto a
rug at the same height and see no obvious bending, although
I'll admit the results appear to depend on whether there's
any remaining lip or crack between them.
--
Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5040
mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/