Unwinding spool of rope I want a spool of rope to unwind natural...

 

I made this one using a curve and a curve modifier on a mesh. I have a hook on the curve so that I can pull it.

I need a way to unwind the rope natural: this means starting from the top layer, and the rope should move side to side. Like this...



How can I achieve this. I tried using soft body physics but the rope has to go through many small whole and interact in such a way which I couldn't get it to work. Also I don't really need physics so is there a way to achieve this?

Thanks for any help.
I'd do it layer after layer (they must be separate). You simply need to move the upper layer to the side one diameter of the rope per one rotation. Let's say diameter is 10 mm, so each rotation the upper layer moves 10 mm to the right (on your file). Then the next layer the opposite direction.