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A block A of mass m1 lies on a rough horizontal surface. It is tied to a light string that goes over a smooth pulley at the table’s edge, and the other end carries a hanging block B of mass m2. If block A is moving along the table and the coefficient of kinetic friction between A and the table is μk, what is the tension in the string?

1. (m2 − μk m1)g/(m1 + m2)
2. m1m2(1 + μk)g/(m1 + m2)
3. m1m2(1 − μk)g/(m1 + m2)
4. (m2 + μk m1)g/(m1 + m2)

Correct answer: m1m2(1 + μk)g/(m1 + m2)

Solution

System acceleration a=(m2 - mu_k m1)g/(m1+m2). For the hanging block, m2 g - T = m2 a, so T = m2(g-a) = m1 m2 (1+mu_k) g/(m1+m2).

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