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 held in place with a pin. 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 of each string. There is a mass of m1 = 0.163 kg located at ?1 = 22.0

Explanation / Answer

m1 = 163g = 0.163kg. Weight = (.163 x 9.81) = 1.54N.
m2 = 0.225kg., = 2.109N. weight.
Let's "rotate" the table 22 degrees anticlockwise, so m1 is at 0. That puts m2 at (287 - 22) = 265 degrees.
(265 - 180) = 85 degrees "west of south".
South component of m2 = (cos 85) x 2.109, = 0.6587N.
West component = (sin 78.1) x 2.109, = 2.0637N.
Subtract South component from weight m1, = 0.8813N., acting North.
Weight of M3 = sqrt. (2.0637^2 + 0.8813^2), = 2.244N., divided by g = mass of 0.229kg., or 229g.
Direction = arctan (0.8813/2.0637) = 23.125 degrees S of E.,
Now "rotate" the table back the 26.2 degrees clockwise, (26.2 + 23.125 + 90) = 139.325 degrees, is where to place the m3 of 229g. (The "90" is because east is 90 deg. from North, and the 23.125 was from E).

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