A small toy car of mass m is released from rest on an inclined track that starts as high as twice the radius of the loop the loop which is on the floor. How high is it above the floor when it leaves the track, neglect friction.
The answer is 1.67R but I don't know why.
The Attempt at a Solution
I would've thought that since there is no friction all the potential energy would be converted to kinetic energy at the bottom of the incline, and start of the loop the loop, and the car would go up to a height of 2R, though it does make sense that a circle of radius 2R, flattened out so it was just 2 vertical lines infinitesimally close together, would be taller than 2R I'm not sure what to do with that idea. I know in most loop-the-loop problems you use the radial acceleration equally V-squared over R equation but in this situation I'm puzzled.