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 = 28.5

Explanation / Answer

m1 = 161g = 0.161kg. Weight = (.161 x 9.81) = 1.579N.
m2 = 0.215kg., = 2.109N. weight.
Let's "rotate" the table 28.5 degrees anticlockwise, so m1 is at 0. That puts m2 at (287 - 28.5) = 258.5 degrees.
(258.5 - 180) = 78.5 degrees "west of south".
South component of m2 = (cos 78.5) x 2.109, = 0.420N.
West component = (sin 78.5) x 2.109, = 2.0666N.
Subtract South component from weight m1, = 0.8813N., acting North.
Weight of M3 = sqrt. (2.0666^2 + 0.8813^2), = 2.246N., divided by g = mass of 0.229kg., or 229g.
Direction = arctan (0.8813/2.0666) = 23.123 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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