## PSN-L Email List Message

Subject: Re: Technical Lesson Please
From: John Lahr johnjan@........
Date: Tue, 31 Jul 2007 21:27:35 -0700

```Hi Jerry,

Physicists like to think of things in an ideal world, where a mass
can be concentrated at a point and where a relaxed spring will take
little force to expand.  Visualize a spring lying on a table, with
one end fixed to the other table and the other free to move when
pulled by a spring scale.  Consider the location of the free end to
be at X = 0.  The spring scale is attached, but reads zero
force.  The distance from the fixed end to the free end is L, the
spring length.  As the spring scale is pulled in the +X direction the
spring will pull back in the -X direction.  If the free end is pulled
to X, the distorted length will be L+X.  The Force = -k(L+X - L),
where k is the spring constant.  Of course L+X-L just equals X, the
amount that the spring was stretched beyond its relaxed length.

The reason for the minus sign is that the direction of the force is
in the opposite direction to the extension.

As the measurements are taken, it is noted that applying even a very
small force will slightly extend the spring.  Therefore, the "length"
of this spring would just as it appears to be.

Springs can be wound so that when undisturbed they are prevented from
getting any shorter due to the thickness of their own coil wire.  In
that case some measurements are necessary to determine their
"length," which is what their unstressed length would be had not
their own coils gotten in the way.

I made some spring constant measurements recently that are summarized
on this page:
http://jclahr.com/science/psn/as1/springs/

In each case I hung the spring from a nail and measured the length
with nothing attached, as well as with two different weights
attached.  Look at the EQ1 spring, for example.

Weight (kg)             Length of Spring (cm)
0                       27.72
0.93                    33.75
1.13                    38.66
k (kg/cm) 0.041
Effective L (cm) 10.92

At first glance one might think that the length of the spring was
27.7 cm, but the computed length actually turned out to be only 10.9
cm.  If you look at the graph on the web site above, you can see that
the value 10.9 is determined by extrapolation.  38.66 cm with 1.13 kg
and 33.75 cm with 0.93 km   Based on those two observations, what
would be the length with zero kg?  Turns out to be 10.92 cm.

Hope this helps!
John

At 04:36 PM 7/31/2007, you wrote:
>Not being a physics student and rather dense (yes, I admit it), will
>someone please explain what a "zero length spring" is?  I have
>searched on the net and found this law and that law, which means
>nothing to me.  Finally, I found a webpage that also called it a
>constant pressure spring and displayed a large heavy duty spring
>that wound around itself, much like an alarm clock spring.
>
>It a zero length spring simply one that returns to its original
>shape after the force is released?

No.  If a spring doesn't return to it's original shape when the force
is released, then it's been permanently deformed - not a good thing!

>
>Thank you,
>Gerald Payton

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