Spring stretching under its own weight

[tlutz]

I remember solving this problem in calculus years and years ago, but am struggling with it now. I’m working with a long, weak extension spring hanging vertically, and the spring constant is small enough that the spring stretches under its own weight. How can I calculate the amount of stretch due to the spring’s weight at any given point along its length?

 

[GregLocock]

I get roughly:

delta at coilbound length l is

the integral between 0 and l

of (L-x)*rho*(g*x*c) dx

L is total coilbound spring length, rho is mass per unit length of compressed spring, c is some sort of compliance per unit length.

Looks easy to me!

Cheers

Greg Locock

Cheers

Greg Locock