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Classical Mechanics - Pulleys System

  1. Jun 20, 2009 #1
    1. The problem statement, all variables and given/known data

    Consider the pulleys system in the picture. Assume both pulleys are frictionless. Assume the rope is massless and inextensible. Find the acceleration of the mass [tex] m_2 [/tex]


    2. Relevant equations



    3. The attempt at a solution

    I have solved the same problem with massless pulleys and I fail to see if their radii should be involved at all in the final result. So first notice that the acceleration of the mass [tex] m_2 [/tex] is half of the acceleration of the mass [tex] m_1 [/tex]. On [tex]m_1[/tex] we have:

    [tex] m_1 g - T = m_1 a[/tex]

    On [tex] m_2[/tex] we have:

    [tex]2T - (m+m_2)g = (m+m_2) \cdot \frac{a}{2} [/tex]

    which solves for

    [tex] a = \frac{2*(m + m_2 - 2 m_1)}{4 m_1 + m + m_2}[/tex]

    Anyone can offer any advice? In particular, how am I supposed to include the radius of the pulleys and the pulley that does not figure in the equation? Thank you!
     

    Attached Files:

  2. jcsd
  3. Jun 21, 2009 #2
    can you post the picture a different way? I can't see the attachment
     
  4. Jun 21, 2009 #3
    The picture is just like http://img84.imageshack.us/i/carrucoleesameot5.jpg/" [Broken]. Both pulleys have mass [tex] m[/tex] and radius [tex] r[/tex]. The mass labeled A is [tex] m_1[/tex] and B is [tex] m_2[/tex].

    It says my attachment is pending approval, maybe that is the problem.
     
    Last edited by a moderator: May 4, 2017
  5. Jun 21, 2009 #4

    Doc Al

    User Avatar

    Staff: Mentor

    (1) Since the pulleys have mass, you cannot assume that the tension in the rope is the same throughout. Treat each rope segment as having a different tension; Label the tensions T1, T2, and T3.
    (2) Don't ignore the rotational inertia of the pulleys. I presume that you can model the pulleys as uniform disks. (You'll need to analyze both pulleys.)
     
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