Sapling Learning understand the concept of static equilibrium a laboratory make

Question

Sapling Learning understand the concept of static equilibrium a laboratory 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 m 0.161 kg located at 26.5 and a second mass m2 0.223 kg located at 62 287°. Calculate system and the ring will remain stationary Number m, kg Number

Explanation / Answer

Given,

Mass, m1 = 0.161kg., Weight, w1= (0.161 x 9.81) = 1.58N.
Mass, m2 = 0.223kg., Weight, w2= (0.223 x 9.81) = 2.19N.
Let's "rotate" the table 26.5 degrees anticlockwise, so m1 is at 0. That puts m2 at (287 - 26.5) = 260.5 degrees.
(260.5 - 180) = 80.5 degrees "west of south".
South component of m2 = (cos 80.5) x 2.19 = 0.36N.
West component = (sin 80.5) x 2.19, = 2.16N.
Subtract South component from weight m1, = 1.58-0.36 = 1.22N., acting North.
Weight, w3 = sqrt. (2.16^2 + 1.22^2), = 2.48N.,
Mass, m3 = 2.48/9.81 = 0.253kg

Direction = arctan (1.22/2.16) = 29.46 degrees South of East.,
Now "rotate" the table back the 26.5 degrees clockwise, (26.5 + 29.46 + 90) = 145.96 degrees, is where to place the m3 of 0.253kg. (The "90" is because east is 90 deg. from North, and the 29.46 was from East).

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