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Re: [Phys-L] determine k



It's interesting to see the difference in point of view between (at least)
some mathematicians and some physicists on how to determine the spring
constant k. Nowadays, having retired from adjunct teaching of physics at
the local community college and finding substituting in the physics
department not enough consistent effort to satisfy me, I do a little weekly
volunteer math tutoring in the college's math lab. One young lady, taking a
calculus course intended for science and engineering majors, came in with
following problem. Determine k and the relaxed spring length (L_0) for a
spring which requires 3 J of work to stretch from 12 to 18 cm and 8 J of
work to stretch from 18 to 24 cm (with L_0, of course, less than 12 cm).
The students were expected to use Hooke's law to get the force required for
a spring elongation x = L - L_0 and then the work done by integrating x for
each case between integration limits which involve L_0. This yields two
equations in the two unknowns (k, L_0) which are easy to solve, since the
quadratic terms in L_0 cancel out of each equation. I got k = 0.1389 N/cm
and L_0 = 11.40 cm.

At the time, it struck me as interesting (and somewhat amusing) that the
mathematics course approach was to first state the work done (with no
mention of how it was determined or the difficulty involved) and then
compute k and L_0, while the physics course approach would have been to
first measure k and L_0 and then compute the work done.

Don

Dr. Donald G. Polvani
Adjunct Faculty, Physics (retired)
Anne Arundel Community College
Arnold, MD 21012