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    Mechanics:Acceleration of masses on pulley, rotation of rod

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    The first question involves an atwood machine, the second involves two different rods attached to hinges falling/rotating to the ground.

    See the jpeg for exact questions. The text is provided below simply for the benefit of the search engine:

    Atwood Machine

    A frictionless pulley with mass Mb is attached to the ceiling, in a gravity field g. Mass Mc is smaller than mass Ma. The tensions Tx, Ty, Tz, and the constant g are magnitudes. For each statement, select a response. Motion of Masses on a Pulley.
    Greater than Less than Equal to True False Ty is .... Tz +Tx.
    Greater than Less than Equal to True False Tz is .... Tx.
    Greater than Less than Equal to True False (Ma+Mc+Mb)g is .... Ty.
    Greater than Less than Equal to True False The magnitude of the acceleration of Ma is .... that of Mc.
    Greater than Less than Equal to True False The center-of-mass of Ma, Mc, and Mb does not accelerate.
    Greater than Less than Equal to True False Tz is .... (Mc)g.

    Rotating Rods

    Two uniform rods are connected to a table by pivots at one end. Rod B is longer than rod A. Both are released simultaneously from an initial angle q as shown in the figure. Notation: CM = center of mass; a = angular acceleration; ax = magnitude of horizontal acceleration; ay = magnitude of vertical acceleration. For each of the following statements, determine whether it is correct or incorrect.

    Correct Incorrect ax of the CM initially equals 0 for both rods.
    Correct Incorrect The density of the rods affect their rate of fall.
    Correct Incorrect aA and aB are the same initially.
    Correct Incorrect Just before landing, the CM of B has a smaller speed than the CM of A.
    Correct Incorrect Rods A and B hit the ground at the same time.
    Correct Incorrect aA and alphaB both increase with time.
    Correct Incorrect aA and aB are dependent on q.
    Correct Incorrect ay is initially equal for the CM of A and B.

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    Solution Preview

    Please see the attachment

    The accelerations of the masses and the tensions in the strings can be calculated in this way---
    As the pulley is frictionless it will apply no friction force between the pulley and the string in tangential direction and for that tension through the string remains the same. Hence Tx = Tz
    As the C.M. of the pulley is not moving the net vertical force on the pulley should be zero. Hence
    And as Ty = Tx + Tz + Mb
    So the responses

    1 Greater then
    2 Equal to

    As the tension in the string Tx = Ty is ...

    Solution Summary

    Two problems
    1. The acceleration of two masses on a pulley with mass is calculated
    2. The rotation of two rods pivoted at one end is compared.