(Solved): The rail for a roller coaster in an amusement park stands vertically. The central portion of a trac ...

The rail for a roller coaster in an amusement park stands vertically. The central portion of a track is circular, of radius $$r$$, as shown. What is the minimum speed for the carts (treated as a particle) at the top of the track? Neglect the size of carts and the thickness of the track.