When the three blocks in the figure below are released from rest, they accelerat

Question

When the three blocks in the figure below are released from rest, they accelerate with a magnitude of 0.215 m/s2. Block 1 has mass M, block 2 has 8M, and block 3 has 8M. What is the coefficient of kinetic friction between block 2 and the table?

Blocks 1 and 3 are connected to Block 2 via separate cords and are on opposite sides of Block 2. Blocks 1 and 3 are also hanging freely in the air. Block 2 is connected to both Blocks 1 and 3 by the separate cords, but sits on a table. Neglect the pulleys and assume negligible mass for the rope.

Any help is appreciated, I've done all kinds of free-body diagrams for all 3 systems and tried to make enough equations to solve for mu(k), unfortunately I'm unable to.

Explanation / Answer

Block 2 T2 – T1 – µ 8 mg = 0.215 . 8m Block 1 T1 – mg = 0.215 m Block 3 8mg – T2 = 8m . 0.215 8m(g – 0.215) – m( g + 0.215 ) – µ . 8mg = 0.215 . 8m µ . 8g = 8g – 16 . 0.215 – g – 0.215 µ = 7g – 17 . 0.215 / 8 g = 0.828

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