A force table is a circular table with a small ring that is to be balanced in the center of the table. The ring is attached to three hanging masses by strings of negligible mass that pass over frictionless pulleys mounted on the edge of the table. The magnitude and direction of each of the three horizontal forces acting on the ring can be adjusted by changing the amount of each hanging mass and the position of each pulley, respectively. Given a mass m1 = 0.040 kg pulling in the positive x-direction, and a mass m2 = 0.030 kg pulling in the positives y-direction, find the mass (m3) and the angle (θ, counterclockwise from the positive x-axis) that will balance the ring in the center of the table.
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