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 = 22.5 degree and a second mass m_2 = 0.219 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.

Explanation / Answer

m1 = 0.161 Kg @ 22.5o
m2 = 0.219 Kg @ 295o
m3 = ? Kg @ ?

Now Solving for eq,
m1 * cos(22.5) + m2 * cos(65) = m3 * cos()
0.161 * cos(22.5) + 0.219 * cos(65) = m3 * cos()
0.241 = m3 * cos() -----------1

m2 * sin(65) - m1 * sin(22.5) = m3 * sin()
0.219 * sin(65) - 0.161 * sin(22.5) = m3 * sin()
0.137 = m3 * sin() ------2

Solving eq 1 & 2
= tan^-1(0.137/0.241)
= 29.62o

0.137 = m3 * sin(29.62)
m3 = 0.277 Kg

Mass, m3 = 0.277 Kg

3 = 180 - 29.62
3 = 150.4o

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