Inclined Plane Friction

A block on a ramp, held by friction until the slope gets too steep. Gravity splits into a part pressing the block into the surface and a part pulling it down the slope. Friction can match that down-slope pull only up to a ceiling, $\mu_s m g \cos\theta$. Once the slope passes the critical angle $\theta_c = \arctan\mu_s$, the ceiling is exceeded, the block breaks free, and friction drops to its lower kinetic value, so the block accelerates at $a = g(\sin\theta - \mu_k\cos\theta)$. The scene shows the force vectors on the block; the diagnostic below plots the down-slope pull against the friction limit, so the crossover at $\theta_c$ and the static-to-kinetic drop are both visible.