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 = 0.157 kg located at ?1 = 22.5

Explanation / Answer

Note that

mx = mcosA
my = msinA

Thus,

m1 = 0.145, A = 24.5 deg components:

m1x = 0.13194 kg
m1y = 0.06013 kg

m2 = 0.219 kg, A2 = 283 deg components:

m2x = 0.04926 kg
m2y = -0.21339 kg

Thus, to cancel these, m3 = -(m1 + m2),

m3x = -0.1812 kg
m3y = 0.15325 kg

Thus, the magnitude and direction is

m3 = 0.237 kg   [ANSWER]
direction = 319.8 degrees   [ANSWER]

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