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 = 148 g located at ?1 = 26.2

Explanation / Answer

For equilibrium in X direction...: M1 cos theta1 + M2 cos theta2 + M3 cos theta3 = 0 M3 cos theta 3 = -0.148 * g cos 26.2 - 0.205 * g cos 278 = -1.582 For Y direction : M1 sin theta1 + M2 sin theta2 + M3 sin theta3 = 0 M3 sin theta 3 = -0.148 * g sin 26.2 - 0.205 * g sin 278 = 1.35 tan theta3 = 1.35 / -1.582 = -0.85 since sin is positive...and cos is negative...hence it will be in 2nd quadrant...theta 3 = 139.63 degree M3 = 1.35 / sin 139.63 = 2.08 = m3 * g...so mass of 3rd block = M3 / g = 0.212 kg...=212.48 g Ans : m3 = 212.48g...........theta 3 = 139.63 degree Note : I have used M for weight...and m for mass...DONT GET CONFUSED

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