The physics behind the avalanche
Imagine a mass of snow, stones or volcano ashes on a slope of a mountain. It is a slope of degrees. The coefficient of static friction between this two surfaces is . The mass of the object is m.
F1 is the force of gravity, F2 is the reaction of the slope, F3 is the force of friction.
We select the Cartesian coordinates xy (as shown on the picture).
From the Newton's second law :
ma = F1 + F2 + F3
ay is acceleration in y dimension :
ay = 0
F1x is the component vector of F1 along coordinate x, ax is the acceleration of the object.
The Newton's second law in x dimension :
max = F1x F3
F1x = F1sin
g is acceleration due to gravity
F1 = mg
F3 = mgcos
max = mg sin - mgcos
ax = g (sin - cos)
(ax > 0) <=> (sin > cos)
When ax > 0, the avalanche goes down !