Asmall airplane with full fuel tanks, but no occupants or baggage, has a mass of 1.17×103kg and a center of gravity that is 2.58 m behind the nose of the airplane. the pilot’s seat is 2.67 m behind the nose, and the baggage compartment is 4.30 m behind the nose. a 75 kg pilot boards the plane and is the only occupant. if the center of gravity of the airplane with pilot can be no more than 2.76 m behind the nose for in-flight stability, what is the maximum mass that the baggage compartment can hold?

Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes. these cyclotrons typically accelerate h- (the hydride ion, which has one proton and two electrons) to an energy of 5 mev to 20 mev. this ion has a mass very close to that of a proton because the electron mass is negligible—about 1 2000 of the proton’s mass. a typical magnetic field in such cyclotrons is 1.9 t. (a) what is the speed of a 5.0-mev h-? (b) if the h- has energy 5.0 mev and b = 1.9 t, what is the radius of this ion’s circular orbit?