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2 masses suspended over a pulley, finding a mistake

  1. Jun 6, 2014 #1
    1. The problem statement, all variables and given/known data
    http://i.imgur.com/1j19V0n.jpg
    Two masses are suspended from a pulley as on the pic. I have pulleys radius R and moment of inertia I and masses m1 m2.


    2. Relevant equations



    3. The attempt at a solution

    So 2nd law of motion:

    [tex] N_{1} - m_{1}g=m_{1}a [/tex]
    [tex] m_{2}g-N_{2} = m_{2}a [/tex]
    [tex] (N_{2}-N_{1})R=Iε=\frac{Ia}{R} [/tex]

    I get N's from 3rd equation and add two first ones

    [tex] N_{2}-N_{1}=\frac{Ia}{R^{2}} [/tex]
    [tex] g(m_{2}-m_{1}) + N_{1} - N_{2} = (m_{1}+m_{2})a[/tex]

    sub N's to second equation

    [tex] g(m_{2}-m_{1}) - \frac{Ia}{R^{2}} = (m_{1}+m_{2})a[/tex]
    [tex] g(m_{2}-m_{1}) = (m_{1}+m_{2})a + \frac{Ia}{R^{2}}[/tex]
    [tex] g(m_{2}-m_{1}) = a(m_{1}+m_{2}+\frac{I}{R^{2}}) [/tex]
    [tex] \frac{g(m_{2}-m_{1})}{m_{1}+m_{2}+\frac{I}{R^{2}}} = a [/tex]

    Now, it's wrong as there should be 2I and not I. Where did I make a mistake?
     
  2. jcsd
  3. Jun 6, 2014 #2

    ehild

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    Homework Helper
    Gold Member

    Your solution is correct.

    ehild
     
  4. Jun 6, 2014 #3
    Uh, thanks, it seems that prof made a mistake.
     
  5. Jun 6, 2014 #4

    ehild

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    Homework Helper
    Gold Member

    Everybody can make mistakes.... :biggrin:

    ehild
     
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