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: Moving pulley question

  1. Jan 11, 2013 #1
    1. The problem statement, all variables and given/known data
    Find acceleration of block 1, knowing that the mass of block 1 is 2kg and of block 2 is 4kg. You may ignore friction and pulley mass.

    2. Relevant equations

    Fr = ma

    3. The attempt at a solution

    I Drew free body diagrams to block 1, 2 and the pulley, then made the equations:
    \sum F_{r2} = m_2a_2\\
    P_2 - T_2 = m_2a_2\\
    \sum F_{rpulley} = m_{pulley}*a\\
    2T_2 = T_1\\
    \sum F_{1}=m_1a_1\\
    T_1=m_1a_1\rightarrow T_2 = \frac{m_1a_1}{2}

    \\\\a_1=2a_2 \rightarrow T_2=\frac{m_1(2a_2)}{2} = m_1a_2

    \\(Substituting\ in \ first\ equation)\\
    P_2-(m_1a_2)= m_2a_2\\
    a_2(m_2+m_1) = m_2*g\\\\
    a_2=\frac{m_2g}{m_2+m_1} = 6.53\frac{m}{s^2}\rightarrow a_1 = 13.06\frac{m}{s^2}
    The answer, however, is supposed to be 4.4 m/s²

    Thanks in advance!
  2. jcsd
  3. Jan 11, 2013 #2


    User Avatar

    Staff: Mentor

    Is ##a_1 = 2 a_2## true?
  4. Jan 11, 2013 #3
    Well, I think it is, isn't it?

    If 1 moves a distance "d", 2 will move only d/2 because the rope has to run on both sides of the pulley.
  5. Jan 11, 2013 #4


    User Avatar

    Staff: Mentor

    On the other hand, if 1 moves a distance "d", the pulley "takes" a length "d" of rope from both sides of the pulley. This rope can only come from the free end holding m2.


    Attached Files:

  6. Jan 11, 2013 #5
    Wow, that... that makes a lot of sense, so in fact a1 = 2a2

    Thanks a lot, gneill!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook