Inclined Plane with Smooth and Rough Sections (Energy/Work)
Analyze motion on an incline that has distinct smooth and rough segments, typically using energy conservation or work-energy theorem to find friction coefficient or stopping point.
The upper half of an inclined plane with inclination $\phi$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by (1) $2\sin\phi$ (2) $2\cos\phi$ (3) $2\tan\phi$ (4) $\tan\phi$