This will only work if you have unlimited version of maya.
Create a simple curve (the length should be the same as the length of your rope), go to dynamics menu mode hair->Make selected curves dynamic. Its hard to explain what it does so you should just play around and see, also, hit F1 and look up the info there. Basically it will simulate the behavior of a rope. To get the best simulation you will probably have to play with the settings.
Now to attach the model (cylinder representing rope) to the curve, i dont really know how to do it right, if it was for myself i would use tons of locators parented to the curve and ten parent some joints to those locators, then rig the cylinder using these joints, but it's a mess and you should not do it, someone else here will hopefully know how to do i right.