Asimple pendulum of mass m and length l hangs from a trolley of mass m running on smooth horizontal rails. the pendulum swings in a plane parallel to the rails. using the position x of the trolley and the angle of inclination θ of the pendulum as generalized co-ordinates, find the hamiltonian and show that x is ignorable.

Imagine that someone pushes one marble toward a motionless marble. would there still be action-reaction forces involved in the collision? how might the marbles’ motions be changed? ?

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?

Drag the tiles to the correct boxes to complete the pairs. match the jobs with the education requirements. childcare director clinical psychologist concierge cosmetologist vocational school and state licensure arrowright on-the-job training arrowright a ph. d. with licensure or certification, depending on the state in which you live arrowright a bachelor’s degree in early childhood development arrowright