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Pully with three masses

  1. Jul 16, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the relation between the mass of block 1 and the mass of block 2. Assume that the pullies are massless and frictionless and that the rope is inelastic. All masses are unknown.
    Possible answers: mblock2 = mblock1

    mblock2 > mblock1
    mblock2 < mblock1

    The system below is at rest.
    ch4_clip_image001_0013.gif

    2. Relevant equations
    F = mg = T


    3. The attempt at a solution
    I'm quite clueless on how to approach this problem, but this is how far I came.
    m1*g - T1 = m1*a
    m2*g - 0.5*T2 = m2*a

    ∑F = m1*a + m2*a = m1*g - T1 +m2*g - 0.5*T2

    I'm not sure how to go any further.

    Thanks in advance for the help!
     
  2. jcsd
  3. Jul 16, 2016 #2
    Focus on Pulley with block 2. Since the pulley is at rest, the sum of forces on that pulley equals zero.
     
  4. Jul 16, 2016 #3
    So T1 + T3 - m2*g = 0 ?
    m1*g + m3*g = m2*g
    m1 + m3 = m2 ?
    Am I approaching this problem the right way now?

    I found out that I made a mistake in the possible answers. It should be:
    mblock2 = 2*mblock1
    mblock2 > 2*mblock1
    mblock2 < 2*mblock1
     
  5. Jul 16, 2016 #4

    TSny

    User Avatar
    Homework Helper
    Gold Member

    The rope has the same tension throughout.
     
  6. Jul 16, 2016 #5
    Yes correct. Now notice that the tension should be the same so ##T_1=T_3##.
     
  7. Jul 16, 2016 #6
    If T1 = T3 then m1 = m3
    This means that m2 = 2*m1 ?

    But now I face another problem because according to my teacher, the answer should have been: m2 < 2*m1
     
  8. Jul 16, 2016 #7
    Is the rope considered to be massless?
     
  9. Jul 16, 2016 #8
    It doesn't state that the rope is massless, so I guess not.
     
  10. Jul 16, 2016 #9
    I meant to say that the rope has mass
     
  11. Jul 16, 2016 #10
    If the rope is massless then what we did here is correct and your teach is wrong.

    However, if the rope is NOT massless, then the tension forces ##T_1+T_3## have to lift the weight of the segment of rope that is attached to pulley 2, so it will be ##T_1+T_3=m_2g+m_rg## where m_r the mass of the rope along the circumference of pulley 2.
     
  12. Jul 16, 2016 #11
    The rope is indeed not massless.
    Thank you very much for your help.
     
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