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Re: oscillations test question



At 14:16 -0500 11/20/02, Carl E. Mungan wrote:

I'm interested in hearing what folks think of the following question
in the test bank for Giancoli:

Chap 14 #11. Two hundred grams hung on a spring stretches it 8.4 cm.
How much energy is stored when stretched 8.4 cm?

This is a typically poorly thought out question. The answer they give
may be correct, depending on how one defines the zero of potential
energy. I had just worked out the general form of this problem for
other purposes and here is what one gets. If the zero of potential
energy is defined as the original equilibrium point. the new energy
of the new equilibrium point is -(kx^2)/2 (not hard to work out), and
except for the minus sign, that is the answer you report from them.
So I would say that their answer is not correct, since what the
result I quote above is the new total energy of the system *relative
to the original zero point.* Since it is less than zero, the energy,
which is numerically equal to their value, does *not* represent an
amount stored. After all, it was given up, and to recover the
original conditions, one has to put that amount of energy back into
the system, not remove it.

But the zero of potential energy is arbitrary, and so you could as
easily take the new equilibrium position to be zero, except that that
doesn't address the energy difference between the two chosen zero
points. Had the question asked been phrased "Relative to the original
state of the system (unstretched spring with the mass attached but
not released to extend the spring), what is the new total energy of
the system," and had their answer been -82 mJ. I don't think anyone
could have quibbled with their result. Or they could have preserved
their original answer had they specified that they were interested in
how much energy was stored *in the spring.* The fact that that energy
came from the gravitational field now becomes irrelevant, and the
question becomes essentially a worthless P&C. I like my first
rephrasing of the question much better.

Hugh
--

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

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This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.