1. String one has 15 g on its mass hanger and is located at an angular position of 90°. String two has 30 g of mass on the mass hanger and is located at an angular position of 270°. Is there a third string that can be added such that it brings the system into equilibrium if the angular position of this third string is not 90° or 270°? Support your answer with a detailed explanation or mathematical analysis.
2. String one has a mass of 5 g on its mass hanger (which has 5 grams of mass) and string three has a mass of 25 g on a 5 g mass hanger. You look in the box and there is only one mass hanger and a single 5 g mass inside. Is it possible to adjust the angular positions of the strings (draped over pulleys of course) so that the system is in equilibrium? Support your answer with a detailed explanation or mathematical analysis.