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 m1 = 0.157 kg located at 1 = 26.5° and a second mass m2 = 0.215 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

The problem can be solved as follows:

F1 = m1*g = 0.157kg*9.81m/s^2 = 1.54N @ 26.5 deg = 1.38i + 0.687j
F2 = m2*g = 0.215kg*9.81m/s^2 = 2.11N @ 283 deg = 0.47i - 2.056j

Resultant F1+F2 = 1.85i -1.369j = 2.30N @ -36.5 degrees

So m3 must produce an opposing force of 2.30N at -36.5+180 deg = 143.5 deg

m3 = 2.30N / 9.81m/s^2 = 0.234 kg at 143.5 degrees

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