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Acceleration and Tension in Multiple Pulleys

  1. Oct 10, 2015 #1
    1. The problem statement, all variables and given/known data
    Block "m1" sits on a horizontal frictionless surface. Block "m2" is hanging below the pulleys as shown. All of the pulleys are massless and frictionless. Given [m1, m2]. Determine:

    a. The tension in each rope.
    b. The acceleration of each block.

    assignment 5, prob 7.png
    2. Relevant equations
    Sum(F) = ma

    3. The attempt at a solution
    block m1:
    F = m1a
    Tension = m1a

    block m2:
    m2g - T - T = m2a
    m2g - 2T = m2a
    2T = m2g - m2a

    *insert tension found through working block m1

    2(m1a) = m2g - m2a
    2m1a + m2a = m2g
    a(2m1 + m2) = m2g
    a = m2g/(2m1 + m2)

    a. T = m1a
    b. Acceleration = m2g/(2m1 + m2)

    I've been been looking around the internet and asking my peers about this problem and we all seem to have varying answers. Could someone verify as to whether or not i'm doing this properly?

    Thanks
     
  2. jcsd
  3. Oct 10, 2015 #2

    Orodruin

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    You have assumed both masses have the same acceleration. Do they?
     
  4. Oct 10, 2015 #3
    Hm, might it be that block m1 has a greater acceleration due to the rope pulling directly on it? If so how would the acceleration differ?
     
  5. Oct 11, 2015 #4

    Orodruin

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    If mass 1 moves 1 cm, how far does mass 2 move? Hint: The rope is likely assumed to have a fixed length.
     
  6. Oct 11, 2015 #5
    I believe that mass 2 would also move one centimeter, or would the existence of the rope connected to the hook create a different outcome?
     
  7. Oct 11, 2015 #6

    Orodruin

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    I suggest you write the length of the rope as a function of the positions of the masses.
     
  8. Oct 11, 2015 #7

    Mister T

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    I recommend a pulley. Connect one to a string and use it to lift something. If you don't have a pulley make one out of a key ring. Just loop the string (or a shoe lace) through the ring and use it to lift the keys, just as you would to lift m2.
     
  9. Oct 11, 2015 #8

    ehild

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    Supposing mass m2 moves down by 1 cm. How much longer became both vertical pieces of the rope?
    The length of the whole rope is constant. How much shorter becomes the horizontal piece?
     
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