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Two Blocks and a Pulley Friction Problem

  1. Nov 6, 2016 #1
    1. The problem statement, all variables and given/known data

    System comprised blocks, a light frictionless pulley and connecting ropes (see diagram). The 9.0kg block is on a perfectly smooth horizontal table. The surfaces of the 12kg block are rough, with μk = .2 between the two blocks. If the 5.0 kg block accelerates downward when it is released, find its acceleration

    Fairly certain my solution is correct, just would love a second opinion!

    Diagram:
    6k5Im7W.png
    http://i.imgur.com/6k5Im7W.png


    2. Relevant equations


    3. The attempt at a solution

    So for the 12kg Block my reasoining for its forces was:
    Fnet = Ffriction - T1 = Ma = 0
    Fnormal = (12kg)(9.8 m/s^2 _ = 117.6
    ForceFriction = (.2)(11.6) = 23.52 N

    Then for the 9 KG block:
    Fnet = T2 - ForceFriction
    T2 - 23.52N = Ma
    T2 - 23.52N = (9kg)a
    23.52-T2 = (9 kg) a

    Then finally for the hanging 5.0 KG block:
    T2 - Fg = ma
    T2 - (5)(9.8) = (5)a
    T2 - 49N = 5(a)

    Then I simply solved the system of equations to find the value of A

    Set two equations for the 9kg and the 5kg block in terms of a

    (T2 - 49N)/5 kg = (23.52N - T2)/9kg
    Solving to find that T2 = 39.9
    Then simply plug that value back into T2 - 49N = 5a

    a = 1.82 m/s^2
     
  2. jcsd
  3. Nov 6, 2016 #2

    gneill

    User Avatar

    Staff: Mentor

    Looks good.
     
  4. Nov 6, 2016 #3
    Great. Thanks
     
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