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A Pulley problem

  1. Sep 24, 2012 #1

    Sorry guys but uploading the image didnt work so i post it on imageshack. Here is the link: http://imageshack.us/f/208/apib.jpg/

    So the quastion is:

    In the image the pulley is a uniform cylindrical disk of mass m and radius r. The strings are massless and there is no friction. If the system is initially at rest, find the speed of the blocks after they have moved a distance d.

    2. Relevant equations

    E = E + W

    K = 1/2Iω^2

    3. The attempt at a solution

    Let's say that the potential energy is set at 0 when the blockmoves from y=d --> y=0.

    Then the starting energy becomes (m1+m2)gh = 2mgd

    Translating to kinetic energy, ΔU =(1/2)(2m)v2 - (1/2)Iω2

    Because our pulley also has a mass m, and I =(1/2)mr2

    ΔU = mv2 -(1/4)m(r2ω2) = mv2-(1/4)mv2 (Using v =rω)

    So ΔU = (3mv2)/4 = 2mgd

    And my answer is:

    v =√[(8gd)/3]

    My book say the answer is : v =√[(4gd)/5]. So im wondering what im doing wrong?
  2. jcsd
  3. Sep 24, 2012 #2


    User Avatar

    Staff: Mentor

    Only one block is falling through distance d; Check your change in gravitational PE.
  4. Sep 24, 2012 #3
    So there is no 2mgh? Just mgh?

    I still can't figure out how i can get 5 there.
  5. Sep 24, 2012 #4
    From top,
    T1=ma ...(1)
    mg-T2=ma ....(2)
    (T2-T1)r=Iα=1/2(mr2) a/r .....(3)

    From rest,

    Work done by mother earth =ΔE
    mgd=2(1/2 mv2) + 1/2 Iω2
    mgd=mv2+ 1/2 (1/2 m r2) (v/r)2

    mgd=mv2+ 1/4 mv2

    Add: Using conservation of energy
    Last edited: Sep 24, 2012