Cord Weight Animation

Hi,
I am trying to make a rocket in Blender. I have done my reasearch and modeled the stages, payload, ETC of my rocket (all in different projects) But, I am trying to make the umbilical fly off the rocket like they do here (skip to 0.45):

But when I try to make the weight on the cord keyframe, it does not work. Here is the .blend file:
HaraLowerStage.blend (8.38 MB)