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 held in place with a pin. 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 of each string. There is a mass of m1 = 0.154 kg located at and a second mass of m2= 0.220 kg located at . Calculate the mass m3, and location (in degrees), , which will balance the system so the pin can be removed and the ring will remain stationary. The acceleration due to gravity is g = 9.81 m/s2.

Explanation / Answer

Force due to m1 = m1g cos26.2 i + m1g sin26.2 j

= 1.347 i + 0.663 j

Force due to m2 = m2g cos278 i + m2g sin278 j

= 0.3i -2.135 j

F3 = m3g cos theta + m3g sin theta

F1 + F2 + F3 = 0

So, F3 = -1.647 i + 1.472 j

So, m3 cos theta = - 0.168,

m3 sin theta = 0.15

m3 = 0.225 kg

theta = 138.2 degrees

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