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_1 = 0.161 kg located at theta_1 = 26.5 degree and a second mass m_2 = 0.227 kg located at theta_2 = 295 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

F1=m*g = 0.161[26.5 degree]*9.8=1.5778N[26.5 degree]

F2 = 0.227[295 degree]*9.8 = 2.2246N[295 degree]

F3[Adegree]

F = F1 + F2 + F3
F=1.5778N[26.5 degree] + 2.2246N[295 degree] + F3[A degree]

X = 1.5778xcos26.5+2.2246xcos295+F3*cosA=0
X = 2.352 + F3*cosA = 0
cosA = -2.352/F3.

Y = 1.5778xsin26.5+2.2246xsin295+F3*sinA=0
Y = -1.312+ F3*sinA = 0  
sinA = 1.312/F3

sinA/cosA = (1.312/F3)/(-2.352/F3) =
or, -0.5578 = TanA
A = -29.15 degree = 330.85 degree, Counter clock wise

F3*sinA = 1.312
F3 = 1.312/sinA = 1.312/sin330.85= -2.69 N[330.85 degree]

m3*g = -2.69
m3=-2.69/g =0.274 kg[330.85 degree]

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