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A laboratory on the concept of static equilibrium uses an apparatus called a force table. The...

A laboratory on the concept of static equilibrium uses an apparatus called a force table. The force table consists of a round, level platform marked in degree increments about its circumference. In the center of the table sits a massless ring, to which three strings are tied. Each string is strung over a separate pulley clamped to the edge of the platform, and then tied to a freely-hanging mass, so that each string is under tension and the ring is suspended parallel to the table surface.

A mass of ?1=0.157 kg is located at ?1=26.5∘ , and a second mass of ?2=0.215 kg is located at ?2=295∘ . Calculate the mass ?3 and the angular position ?3 (in degrees) that will balance the system and hold the ring stationary over the center of the platform.

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