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-----Original Message-----
From: Forum for Physics Educators
[mailto:PHYS-L@list1.ucc.nau.edu] On Behalf Of rlamont
Sent: Tuesday, December 14, 2004 10:09 AM
I thought I'd bring up a slightly different aspect of using
springs in lab.
Textbooks emphasize Hooke's Law in the form F = -kx. This is
fine for springs that are manufactured such that their
unloaded configuration is such that the coils are not
touching. However, most springs - and specifically the ones
we have been using in our simple harmonic motion lab - have a
relaxed configuration where the coils are touching. This
requires hanging a small but significant weight from the
spring before any displacement occurs.
We have found that the differential form of Hooke's Law, dF =
-k dx, is a better starting place. In the lab, one has to use
a weight hanger (50 g) plus some small additional mass to
extend the spring to a comfortable position to start
reasonably sized oscillations. Students get suspicious if you
apply the traditional form of Hooke's Law to this situation.
They have been conditioned by the textbooks to view x as the
displacement from the "relaxed" position - when in fact it
can be from any initial position (loaded or unloaded). Their
suspicions are somewhat justified by the appearance of x^2 in
the energy term - which is non-linear.
If the loaded equilibrium position is xo, and the spring is
then pulled down to a new position x before being released to
oscillate, is the increase in the spring potential energy
(1/2 kx^2 - 1/2 k xo^2), or is it 1/2 k(x-xo)^2? This leads
to two different values of kinetic energy at the center of
oscillation - which obviously cannot be.
Bob at PC