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 = 0.157 kg located at ?1 = 22.0

Explanation / Answer

sum forces in the x

0.157*9.81*cos(22) + 0.215*9.81*cos(275) + Fx = 0

Fx = 1.307

sum forces in the y

0.157*9.81*sin(22) + 0.215*9.81*sin(275) + Fy = 0

Fy = 2.11

so F = sqrt(1.30762 + 2.11^2)=2.4

thus m3 = F/g = 2.4/9.81=0.245 kg

angle = arctan(y/x) = arctan( 2.11/1.307)= 58.22 degrees

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