1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook