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 = 0.145 kg located at 1 = 28.5° and a second mass m2 = 0.215 kg located at 2 = 291°. Calculate the mass m3, and location (in degrees), 3, which will balance the system and the ring will remain stationary.

Explanation / Answer

Tensions in strings be T1 and T2 and T3

T1 = 1.42 N

T2=2.11 N

T3 = ?

Consider effects of T1 and T2
Vertical component forces = 0.678 -1.97 = -1.29 j
Horizontal component forces = 1.25 + 0.756 = 2.006 i


T3 = -2.01 i + 1.29 j
magnitude of T3 = 2.39 N
m3 = 0.243 Kg = 24.3 g

direction = 122.69 degrees

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