Conservation laws: Conservation laws are a great help when everything else fails. Although our knowledge about the applied forces in a system might be incomplete, conservation laws can still provide the answer.

A cube of mass $m$ and size $2a$ is sliding on a horizontal table with constant speed. At the edge of the table there is a nail almost fully embedded in the table. What is the minimum speed of the cube such that, after it hits the nail, it will rotate over the obstacle and fall off the table? $($Treat the head of the nail as a point with no geometrical dimensions.$)$