When Is It Energetically Favorable for Rock to Split?

[Tom Segal]

When is it energetically favourable for a piece of rock to crumble into two pieces?

I couldn't paste latex code here for the life of me so I attached a pdf containing my calculation. It is obviously wrong because it leads to the fact that a box-shaped rock of height sqrt(2) (say meters) would like to collapse (in the absence of bonding energy) to 2 box-shaped pieces of rock of size 1, with no regard to the length/width of either the original rock or the 2 new ones.

What am I missing? Which is the right way to tackle this?

Thanks

 

[Valerie Park]

!The best time for a piece of rock to crumble into two pieces is when the potential energy of the two pieces is lower than the potential energy of the original piece. To calculate this, we need to calculate the potential energy of the two pieces relative to the potential energy of the original piece. We can do this by calculating the difference between the gravitational potential energy of the two pieces and the gravitational potential energy of the original piece. This can be done using the equation U = mgh, where m is the mass of the rock, g is the acceleration due to gravity, and h is the height of the rock. If the difference in potential energy is negative, then it is energetically favourable for the rock to crumble into two pieces.