At Six Flags New England in Agawam, Massachusetts, a ride called the Cyclone is a giant roller coaster that ascends a 34.1-m hill and then drops
21.9 m before ascending the next hill. The train of cars has a mass of 4727 kg.
a) How much work is required to get an empty train of cars from the ground
to the top of the first hill?
b) What power must be generated to bring the train to the top of the first hill in 30.0 s?
c) How much PE is converted into KE from the top of the first hill to the bottom of the 21.9-m drop?

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?