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 = 163 g located at ?1 = 24.1

Explanation / Answer

For equilibrium in X direction...: M1 cos theta1 + M2 cos theta2 + M3 cos theta3 = 0 M3 cos theta 3 = -0.163 * g cos 24.1 - 0.205 * g cos 275 = -1.634 For Y direction : M1 sin theta1 + M2 sin theta2 + M3 sin theta3 = 0 M3 sin theta 3 = -0.163 * g sin 24.1 - 0.205 * g sin 275 = 1.35 tan theta3 = 1.35 / -1.634 = -0.826 since sin is positive...and cos is negative...hence it will be in 2nd quadrant...theta 3 = 140.42 degree M3 = 1.35 / sin 140.42 = 2.119= m3 * g...so mass of 3rd block = M3 / g = 0.2159 kg...=216.9 g Ans : m3 = 216.9 g...........theta 3 = 140.42 degree Note : I have used M for weight...and m for mass...DONT GET CONFUSED

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