Above is a roller coaster. There are 5 points of interest. (1) We are interested in the maximum height that the loop, point C, can be and the coaster still make it around the loop in terms of the height of point A. Assume no friction. (2) Now friction plays a role. If 1/3 of the energy is lost to friction between points A and C, now how high will point C be to make it around the loop in terms of point A? (3) If friction is involved, how do the speeds at points B and C compare? (4) If 1/3 of energy is lost between points C and E, and the car is to stop moving once it reaches point E, how high will point E be in terms of the height of point A?