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 m = 0.145 kg located at 1-225° and a second mass m2 = 0.227 kg located at 2-291". Calculate the mass m3, and location (in degrees), 3, which will balance the system and the ring will remain stationary Number Number

Explanation / Answer

Fnet = T1 + T2 + T3 = 0

0.145g(cos22.5i + sin22.5j) + 0.227g(cos291i + sin291j) + m3 g (cos(theta)i + sin(theta)j) = 0

m3 cos(theta) = - 0.215 .... (i)

m3 sin(theta) = 0.156 .... (ii)

(ii)/(i) => tan(theta) = 0.156/(-0.215)

theta = 144 deg ....Ans

m3 = - 0.215 / cos144 = 0.266 kg ...Ans

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