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 = 0.165 kg located at theta_1 = 28.5 degree and a second mass m_2 = 0.219 kg located at theta_2 = 283 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

force in X direction

0.165*g cos(28.5) +0.219 sin(13) g i^

1.90577991505 i^

Force in Y direction

0.165*g sin(28.5) -0.219 cos(13) g j^

-1.32097387619 j^

net = 2.31882924472 angle -34.7274101037

so answer is

m3 = 0.23637403106 Kg at an angle

145.272589896 degrees

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