Better understand the concept of static equilibrium a laboratory procedure asks

Question

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 m_1 = 0.145 kg located at theta_1 = 28.5 degree and a second mass m_2 = 0.223 kg located at theta_2 = 291 degree. Calculate the mass m_3, and location (in degrees), theta_3, which will balance the system and the ring will remain stationary. m_3 = theta_3 =

Explanation / Answer

Net Horizontal Force = 0.145 * cos28.5 + 0.223 * cos291

                                   = 0.2073 kg

Net Vertical Force = 0.145 * sin28.5 + 0.223 * sin291

                                   = - 0.139 kg

=> Mass M3 = sqrt(0.20732 + 0.1392)

                        = 0.2495 kg

=> angle theta3 = 180 - tan-1( 0.139/0.2073)

                              = 146.157 degree

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