Santa Claus and his loaded sleigh are sitting on your roof, which is covered with snow. The sled's two runners each have a length $L$ and width $W$, and the roof is inclined at an angle $\theta$ to the horizontal. The thickness of the snow between the runners and the roof is $H$. If the snow has properties of a Bingham plastic, derive an expression for the total mass ( $m$ ) of the loaded sleigh at which it will just start to slide on the roof if it is pointed straight downhill. If the actual mass is twice this minimum mass, determine an expression for the speed at which the sled will slide. (Note: Snow does not actually behave as a Bingham plastic!)