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 = 0.153 kg located at 1 = 28.5° and a second mass m2 = 0.227 kg located at 2 = 295°. Calculate the mass m3, and location (in degrees), 3, which will balance the system and the ring will remain stationary.

Explanation / Answer

F1 = m1 g (cos28.5i + sin28.5j)

F2 = m2 g (cos295i + sin295j)

F3 = m2 g (cos(theta)i + sin(theta)j)

F1 + F2 + F3 = 0

(0.153 cos28.5 + 0.227 cos295 + m3 cos(theta) ) g i + (0.153 sin28.5 + 0.227 sin295 + m3 sin(theta))g j = 0

m3 cos(theta) = - 0.134 - 0.096 = - 0.23 ..... (i)

m3 sin(theta) = 0.133 ..... (ii)

(ii)/(i) => tan(theta) = - 0.577

theta = 150 deg

m3 = 0.266 kg

Ans: 0.266 kg and 150 deg

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