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Heavy Weight

What happens when to a spring if it's supporting a heavy weight?

I understand that it stretches further, but how could this occurance be calculated or explained? Is there a formula?
This is a picture of the spring and scenario I have in mind:

http://i40.tinypic.com/oilq0.jpg

In which a heavy weight would be attached to the end of the spring.

I'd really appreciate any help with this!

A spring's deformation dX is proportional to the force applied to or removed from the spring dF. And the constant of proportionality, k, is the so-called spring constant. So we have dF = k dX.

And there you are. Here's an example.

Assume k = 200 N/m is the spring constant. And there is no weight (no force) hanging from one end while the other end is affixed to a ceiling. So we have dF = 0 = k dX and thus dX = dF/k = 0/k = 0. So there is no deformation, the spring does not extend beyond its neutral length X.

Now add 100 N of weight to the hanging end and let go. We added dF = 100 N. So now we have dX = dF/k = 100/200 = 1/2 meters. And the spring has sprung, so to speak. It's now 1/2 meter extended beyond it neutral length. So if X = 2 meters when there is no weight (the neutral length), its length is now X + dX = 2 + 1/2 = 2.5 meters long with that 100 N weight attached.

OK then...let's attach another 100 N to the first one. We add 100 N; so we have dF = 100 N and the stretch, the deformation, is dX = dF/k = 100/200 = 1/2 m. Another half meter. So now the extended length is X + dX + dX = 2 + 1/2 + 1/2 = 3 meters with the two weights hanging on.

Works the other way, too. We can remove weights just as well.

Suppose we take away 50 N of weight. So now we have dF = -50 N, there are 50 Newtons less. In which case dX = dF/k = -50/200 = -1/4 meter. And now the length of the spring is:

X + dX + dX - dX = 2 + 1/2 + 1/2 - 1/4 = 2 3/4 meters.

Note. I use dF to emphasize this is a change in force, addition or subtraction, that causes a change in length dX.

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