A roller coaster car of mass 520 kg is initially going 22 m/s along a horizontal track. The track makes a vertical loop of radius 11 m. Assume that the track is constructed so that the roller coaster cannot fall off the track even if is hanging directly below the track. This means that the track can exert a force on the car toward as well as away from the track in the direction perpendicular to the track. Neglect friction between the wheels and the track.
(a) Does the car have enough initial velocity to make it around the loop? If it does not, where does it stop and turn around? If it does, what is its speed at the top of the loop?
(b) Now suppose that the roller coaster has a conventional track where the car sits on top of the track. This means that the track can exert a force on the car only away from the track in the direction perpendicular to the track. Now the car can fall off the track if it is not going fast enough. Does this car make it around the loop? If not, at what angle does it fall off the track?