I'm not really into funky physics, so that theme was really hard for me, too.
I simply took "scale" out of the theme and was planning on making a game about chopping meat, and the goal was to estimate the right chopping angle to chop it into chunks of required sizes. So pretty similar concept to yours, except I was considering more freeform cutting instead of halving, and had the idea for a light-horror theme. :) But eventually I ditched that idea and made Balanced, a cozy card game about balancing a scale.