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 = 28.5° and a second mass m2 = 0.219 kg located at 2 = 275°. Calculate the mass m3, and location (in degrees), 3, which will balance the system and the ring will remain stationary.

m3 = ?

=?   

Explanation / Answer

F1 = m1*g = 0.157kg*9.81m/s^2 = 1.54N @ 28.5 deg = 1.35i + 0.734k

F2 = m2*g = 0.219kg*9.81m/s^2 = 2.14N @ 275 deg = 0.186i - 2.131k

F1 + F2 = 1.536i - 1.397k = 2.076N @ -42.29 degree = -42.29 + 180

m3 = 2.076N / 9.81 = 211.6g at 137.71 angle

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