Continuation of a problem from Lecture. A car in an amusement park ride rolls without friction around a track. The car starts from rest at point A at a height h above the bottom of the loop. Treat the car as a particle. (a) What is the minimum value of h (in terms of R) such that the car moves around the loop without falling off at the top (point B)? (b) If h = 3.50R and R = 14.0 m, compute the speed, radial acceleration, and tangential acceleration of the passengers when the car is at point C, which is at the end of a horizontal diameter. Show these acceleration components in a diagram, approximately to scale. (c) Show that if the car goes all the way around the circular loop without losing contact with the track at the top, then the difference between the normal contact forces acting on a passenger at the bottom and the top of the loop equals 6 times the passenger's weight. In other words, the passenger would feel more than 6 g's at the bottom of the loop! This exceeds normal human tolerance and is the reason why roller coaster loops aren't circular but rather teardrop shaped ("clothoid" loops). NOTE: Don't assume that the normal contact force on the car due to the track is necessarily zero at the top of the loop.