To better understand the concept of static equilibrium a laboratory procedure as

Question

To better understand the concept of static equilibrium a laboratory procedure asks the student to make a calculation before performing the experiment. The apparatus consists of a round level table in the center of which is a massless ring. There are three strings tied to different spots on the ring. Each string passes parallel over the table and is individually strung over a frictionless pulley (there are three pulleys) where a mass is hung. The table is degree marked to indicate the position or angle of each string. There is a mass m1 = 0.161 kg located at ?1 = 26.5

Explanation / Answer

F1 = m1*g = 0.157kg*9.81m/s^2 = 1.54N @ 26.2 deg = 1.382i + 0.680k

F2 = m2*g = 0.215kg*9.81m/s^2 = 2.11N @ 278 deg = 0.294i - 2.089k

F1 + F2 = 1.676i - 1.409k = 2.190N @ -40 deg (320 deg)

so required F3 is 2.190N @ -40 +180 deg = 140 deg

m3 = 2.19N / 9.81 = 223g at angle 140 deg

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