# A Falling Chain

A chain hanging from a string just touches the surface of the weighing machine. The string is burnt, and the chain falls on the weighing machine. What would be the weight registered on the weighing machine?

I came across certain standard solutions that claimed that the weight displayed by the weighing machine would be $3mgx/l$ when $x$ lies on the table provided $0<x<l$. However the solutions seemed to assume that the tension in the part of the chain that is falling down is $0$ without any justification, and I couldn't come up with a satisfactory explanation.

Could anybody explain, based on what principles do we state that the tension in the string should be 0?

• How about: Nobody is pulling on it apart from both sides, so there can't be any tension?
– Danu
Sep 23, 2014 at 7:35
• I am not sure if that is principally sound. There's this external impulsive normal force that acts on the chain when it hits the table. However how can the fact that the chain is not being pulled prove that the tension in the chain is 0 for the chain that is falling? That part does have an acceleration. Your argument could be used to state that the part of the chain that falls down on the machine does not have any tension. Sep 23, 2014 at 14:44