Two blocks, one of mass M and one of mass 3M, are connected by a massless string over a pulley that is a uniform disk of mass 2M and moment

Question

Two blocks, one of mass M and one of mass 3M, are connected by a massless string over a pulley that is a uniform disk of mass 2M and moment of inertia MR^2. The two masses are released from rest, and the masses accelerate as the pulley rotates. Assume there is negligible friction between the pulley and the axle. What is the linear acceleration, a, of the masses?

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Nick 3 years 2021-09-04T11:33:11+00:00 1 Answers 18 views 0

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    2021-09-04T11:34:50+00:00

    Answer:

    4.9 m/s²

    Explanation:

    Let T be the tension in the string

    If a is the linear acceleration in the direction of the 3M mass, the equation of motion on the 3M mass is

    3Mg – T = 3Ma  (1)

    Since the mass M moves upwards, its equation of motion is

    T – Mg = Ma      (2)

    From (2)

    T = Ma + Mg

    substituting T into (1), we have

    3Mg – (Ma + Mg) = 3Ma

    3Mg – Ma – Mg = 3Ma

    collecting like terms, we have

    3Mg – Mg = 3Ma + Ma

    2Mg = 4Ma

    dividing both sides by 4M, we have

    2Mg/4M = 4Ma/4M

    g/2 = a

    a = g/2

    Since g = 9.8 m/s²,

    a = 9.8 m/s²/2

    a = 4.9 m/s²

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