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Re: Atwood's machine problem



What about a demo based on this item, for
somebody thinking about an AAPT apparatus
competition project. A self-winding cylinder,
with a small battery-operated motor, could
be placed inside the monkey. The rest is
obvious. A great teaching tool to show who
is right and who is wrong.

Unless somebody has already built such
demo you might win the first prize for it.
Many years ago I was the first prize winner,
together with a colleague, and our item was
only slightly different from existing items of
the same kind. A small dose of originality
was sufficient. Go for it.
Ludwik Kowalski

On Sunday, Oct 3, 2004, at 18:00 America/New_York, Ken Caviness wrote:

Quoting Herb Schulz <herbs@WIDEOPENWEST.COM>:

On 10/1/04 2:27 PM, "Peter Schoch" <pschoch@NAC.NET> wrote:

Hello all,

I just got a question I can't answer, and could use some help.

A student got this problem out of a book (didn't tell which one) and
asked
me, and I 'clutched':

An Atwood's machine is in perfect balance, with equal weights on both
sides. One of the weights is a monkey, and the other is a stack of
bananas. The monkey begins to climb at a constant speed. What
happens to
the bananas; ie, do they rise, fall, or stay stationary.

My first inclination was to use CM and say that if the monkey climbs
the
bananas must fall to keep the CM stationary. However, the book he
Xeroxed
this from, said the bananas rise with the monkey.

Maybe it's just because it's Friday, but I don't see the 'mechanism'
for
that explanation. Can somebody help?

Thanks,
Peter Schoch
(sleep deprived with a 15 month at home)


Howdy,

Consider the system to be the Monkey, Bananas, Rope (assumed
massless) and
Pulley (assumed massless and frictionless and rigidly attached to a
wall).
When the monky pulls down on the rope there ends up being anet
externaL
force on the system through the pivot of the Pulley (i.e., P-2mg not
= 0) so
the CM of the system is free to move. However, the net external
torque on
the system measured about the pivot is zero so the Angular Momentum
of the
System ABOUT THE PIVOT must be conserved and it was zero before.
Therefore
the Bananas must have the same velocity (m and r are the same) at any
given
instant as the monkey so the two Angular Momentum Vectors add to give
zero.

Good Luck,

Herb Schulz
(herbs@wideopenwest.com)

I once put this question on a General Physics test, and regretted it
afterwards
because such a large percentage of the class got it wrong, yet I had
difficulty
coming up with a reasonable explanation for the correct answer (which
is that
both monkey and bananas rise together).

Herb, I'm not sure that I like your explanation either. Perhaps I've
misunderstood you, but:

Isn't the angular momentum about the pulley equal to zero? L-vector =
r-vector
cross p-vector, so the |L| = mrv sin(angle between r and v). Looks
like zero
to me, since r & v are parallel (or anti-parallel). What have I
missed?

Ken Caviness
Physics @ Southern