[Phys-L] Re: stretch it a bit

["Spagna Jr., George" <gspagna@RMC.EDU>]

Anthony asks:

-----Original Message-----
> From: Forum for Physics Educators [mailto:PHYS-L@list1.ucc.nau.edu] On
Behalf >Of Anthony Lapinski
> Sent: Tuesday, December 13, 2005 3:43 PM

> 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 to think of it:

For the shorter spring segment, to get the same extension for a given
applied force, it would require greater deformation of each turn of the
spring.

Another way:

The ideal spring is like our ideal, inextensible, mass-less strings, in
the sense that the tension at each point in the spring/string is the
same.  If I want to stretch the original spring dx, that stretches each
half by dx/2 - which means that the half springs are stiffer - based on
the usual way of measuring the spring constant.

**********************************************
     No position is so absurd that a philosopher cannot be

     found to argure for it."                     -- Michael Lockwood

**********************************************

Dr. George Spagna
Chair, Physics Department
Randolph-Macon College
P.O. Box 5005
Ashland, VA 23005-5505

phone: (804) 752-7344
fax: (804) 752-4724
e-mail: gspagna@rmc.edu
http://faculty.rmc.edu/gspagna
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