[Phys-L] Re: stretch it a bit

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

> All other factors remaining the same, why are shorter springs stiffer
> (higher k) than longer ones? If you cut a spring in half, the spring
> constant of either half is twice that of the original spring. What is the
> easiest way to analyze this?

One way is to stretch a spring and notice that each half applies the
SAME force on its ends as the whole spring does, but each half is
being stretched only HALF as much.

Another (equivalent) way is to consider the generic behavior of
elastic materials where strain is proportional to stress.  Keeping
the stress constant, keeps the strain constant, but don't forget that
longitudinal strains are properly measured as FRACTIONAL changes in
length.  SAME strain in HALF the length yields HALF the change in
length.
--
John "Slo" Mallinckrodt

Professor of Physics, Cal Poly Pomona
<http://www.csupomona.edu/~ajm>

and

Lead Guitarist, Out-Laws of Physics
<http://www.csupomona.edu/~hsleff/OoPs.html>
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