A20.8-kg box rests on a frictionless ramp with a 14.2° slope. the mover pulls on a rope attached to the box to pull it up the incline. if the rope makes an angle of 36.4° with the horizontal, what is the smallest force f the mover will have to exert to move the box up the ramp?

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?