My friends and I got into an argument about whether it was more damaging to hit an object with a heavy rod or a light rod. The sides of the argument go something like:
"If you swing the light rod, you'll be able to swing it much faster and therefore do the most damage!"
"Yes, but if it's too light there won't be enough mass behind it and it won't damage as much!"
I have been toying around with this question for a few months and I have yet to come up with a satisfactory answer. I'm setting up the problem like this:
Person A is swinging a rigid rod of mass $m$ and fixed length $L$ at Object B located at a fixed distance $d$ away. Imagine Person A is swinging the rod much like a baseball player would swing to hit a ball. Person A has a fixed power $P$ to input to the rod over distance $d$ before making impact with Object B.
Given input power $P$, rod length $L$, and swing distance $d$, what is the optimal mass $m$ of the rod to maximize the damage of Object B?
For simplicity, I'm modeling the power application to be over a linear rather than angular distance, and I'm modeling Object B as a spring with spring constant $k$ attached to a fixed wall. Effects of gravity should be ignored. Also, for now ignore the constraints of human strength and assume we can swing anything as heavy as we like.