An object is placed 45 cm in front of a crystal ball. the crystal ball has a radius of 14 cm, and is made from a glass with an index of refraction of n = 1.5.
find the position of the final image once the rays have gone through the two faces, as measured from the second face. is a virtual object formed anywhere in the analysis? yes or no

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.