I wish to check the safety factor of a steel cable that I've designed to catch a heavy bar that rotates freely due to the gravitational force acting on it.
From the upright position, I'm assuming that the bar has a rotational velocity of 0rad/s before rotating about a lower hinge (hence, gaining rotational kinetic energy), and comes to a stop when the cable goes from slack (sagging cable) to taut (straight - full length).
I've currently modelled the cable as a spring where the rotational kinetic energy is converted to elastic potential energy within the cable upon a small extension. This may be where I've made a mistake since cables don't alway follow Hooke's law and the elastic extension I've found doesn't seem to account for the momentum. Based on this, I'm guessing that I've gone about this problem the wrong way. I'll attach my working with some example numbers below.
Any help or guidance on this will be hugely appreciated!