An industrial physicist wishes to specify the properties of a concave makeup mirror, which is supposed to provide an upright and enlarged image of the user's face. the physicist wants a magnification factor of two, and he assumes that the user's face will be 28 cm in front of the mirror. what radius of curvature should be specified (in cm) for the fabrication of these mirrors?

Two masses are connected by a rope that hangs over a pulley as shown below. the pulley is a uniform cylinder of radius 푅=0.381meters and mass 푀=3.1푘푔. initially 푚"is on the ground and 푚#rests 2.5 meters above the ground. if the system is released, use conservation of energy to determine the speed of 푚#just before it strikes the ground. assume the pulley bearing is frictionless.