I did a search and couldn't quite find what I was looking for; if this has been posted before kindly direct me to the thread and I will just read that. This is not a homework problem, and my question is meant to be conceptual; however I am aware that this problem is often given as a homework problem, so I lay the disclaimer early. Basically, suppose you had a caternary where both ends were pretty much right next to each other. According to my instructor, if you released one of the ends so that the chain suddenly starts falling (let's assume free fall), the time rate of change of momentum of the "free end" (part of the rope that is falling) is somehow always equal to the force exerted on the center of the mass of the system. My question is: why? Is there a rigorous mathematical justification for this? Intuitively it seems plausible, but my mind is too paranoid to accept just that. Thanks for your time.