To better understand the concept of static equilibrium a laboratory procedure as
ID: 1590145 • Letter: T
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 = 0.149 kg located at 1 = 24.5° and a second mass m2 = 0.223 kg located at 2 = 283°. Calculate the mass m3, and location (in degrees), 3, which will balance the system and the ring will remain stationary.
Explanation / Answer
T1 = m1*g*cos28.5i + m1*g*sin28.5 j
T1 = (0.149*9.81*cos28.5)i + ((0.149*9.81*sin28.5)) j
T1 = 1.28i + 0.697 j
T2 = (0.223*9.81*cos283)i + (0.223*9.81*sin283) j
T2 = 0.492 i - 2.13 j
T1 + T2 + T3 = 0
T3 = -(T1+T2)
T3 = -1.772 i + 1.433 j
T3 = sqrt(1.772^2+1.433^2) = 2.28 N
m3 = T3/g = 0.232 kg <<------------answer
theta3 = tan^_1(1.433/1.772) = 141.03 <<------------answer
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