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The science
Point-mass model. The avalanche is treated as one sliding mass on a path of local slope angle theta(s) (s = distance along the path). Newton's second law along the path with Coulomb friction and a velocity-squared (turbulent) drag, as in the Voellmy-Salm / PCM models used in hazard mapping:
dv/dt = g (sin theta - mu cos theta) - v^2 / Ld
Writing e = v^2/2 and differentiating along s gives d e / d s = g (sin theta - mu cos theta) - 2 e / Ld, which this page integrates with fourth-order Runge-Kutta (1 m steps); the stopping point is where e reaches zero.
Terminal speed and energy line. On a uniform slope the speed saturates at v_T = sqrt(Ld g (sin theta - mu cos theta)). Without drag the work done by friction is mu g integral cos(theta) ds = mu g L, so the stop point lies on the line from the start with slope H/L = mu (Heim's rule, the basis of the alpha-beta empirical run-out angles).
Impact pressure. A building meets a dynamic pressure about 0.5 rho v^2 (rho about 300 kg/m^3 for dense flow), shown in kPa as a physical hazard indicator.
Checks. (1) v^2 = 2 g (sin theta - mu cos theta) s on a 35 degree plane against the numerical solution; (2) terminal speed against v_T; (3) with drag removed, H/L equals mu on the current profile.
Simplifications. A single point mass with constant mu and Ld: no entrainment, no depth or width, no density change, no lateral spreading, no centripetal increase of normal force in curves. Real avalanches need calibrated 2D depth-averaged codes; this is a teaching model. Inanimate terrain and a building only.