The national aeronautics and space administration (nasa) studies the physiological effects of large accelerations on astronauts. some of these studies use a machine known as a centrifuge. this machine consists of a long arm, to one end of which is attached a chamber in which the astronaut sits. the other end of the arm is connected to an axis about which the arm and chamber can be rotated. the astronaut moves on a circular path, much like a model airplane flying in a circle on a guideline. the chamber is located 13.0 m from the center of the circle. at what speed must the chamber move so that an astronaut is subjected to 4.50 times the acceleration due to gravity?