The figure below shows a roller-coaster vehicle on a track. The vehicle is fully loaded with passengers and has a total mass of 520 kg. At point A, the vehicle is at the lowest point in a circular arc of radius 12.4 m. At point B, the vehicle is at the highest point of a circular arc of radius 15.8 m.
(a) If the vehicle has a speed of 15.0 m/s at point A, what is the magnitude of the force (in N) of the track on the vehicle at this point?
(b) What is the maximum speed (in m/s) the vehicle can have at point B in order for the vehicle to maintain contact with the track at all times (that is, so that it does not "jump" off the track)?