Realizing that she often doesn't have her students' full attention during class, a professor devises an elaborate device on which to stand while she lectures. (Figure 1) The pulley is placed so that the string makes a 45.0-degree angle with the beam. The beam is uniform, 5.00 meters long, and has weight . The professor stands 2.00 meters from the pivot point and has weight . As an incentive to her students, the professor attaches a light basket to the center of mass of the beam and tells them that every student who gets an A on the next test gets to put a ball of mass 4 kilograms into the basket. There are enough students in the class that if a high percentage get A's, the weight of the basket will hoist the professor into the air. How many students have to get A's on the test to hoist the professor up into the air?