Problem $17\mathrm{.}1281$

The uniform bar $AB$ of mass $m$ and length $L$ is leaning against the corner with $$~~$0.$ A small box is placed on top of the bar at $A.$ End $B$ of the bar is given a slight nudge so that end A starts sliding down the wall as $B$ slides along the floor. Assuming that friction is negligible between the bar and the two surfaces against which it is sliding, and neglecting the weight of the box, determine the angle $$ at which the box will lose contact with the bar.