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Pulley Problem: Find the acceleration of M2 & M3

  1. Oct 24, 2016 #1
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    1. The problem statement, all variables and given/known data

    Pulley is mass less accelerating downward at 2.0 m/s2.
    M1 = 4.0 kg
    M2 = 2.0 kg
    M3 = 3.0 kg

    Find the acceleration of M2 & M3.

    2. Relevant equations

    I made up the slope positive pointing up.
    Since M2 and M3 have the same acceleration, a2=a3 ⇒ a
    Since it's accelerating downwards, Apy = -2.0 m/s2

    Mass 1:
    ΣF1y = m1a1y
    T-m1g = m1a1y
    T = m1a1y + m1g (1)

    Mass 2:
    ΣF2y = m1ay
    T-T1 = m2ay (2)

    Mass 3:
    ΣF3y = m3ay
    T1-m3g = m3ay (3)

    Pulley:
    apy = (a1y+ay) / 2 (4)

    3. The attempt at a solution
    I added eq. (2) & (3) to get rid of T1
    T-m3g = m2ay+m3ay (5)

    I plugged eq. (1) into (5)
    m1a1y + m1g - m3g = ay(m2+m3)

    Solve for a1y:
    a1y = (ay(m2+m3) - m1g + m3g) / m1 (6)

    Plug (6) into (4)

    apy = [ (ay(m2+m3) - m1g + m3g) / m1) + ay ] / 2

    Solve for ay:
    ay = (m1g-m3g+2m1apy) / m2+m3+m1) = 2.87 m/s2

    By the answer key, the acceleration for m2 and m3 is -2.87 m/22. How do I know that is negative and not positive? Is it because m2 + m3 have a higher mass than m1, thus when the pulley is accelerating downwards, m1's acceleration points up and m2 & m3's acceleration point down?
     
    Last edited: Oct 24, 2016
  2. jcsd
  3. Oct 24, 2016 #2
    I get 2.87 downward. Let "a" be the downward acceleration of m2 and m3 relative to the pulley. So the total downward acceleration of m2 and m3 is (a+2). Using this approach, what is the upward acceleration of m1?
     
  4. Oct 24, 2016 #3
    The acceleration of m1 would be -1.13 m/s2. I think I finally caught my mistake. Since the pulley is accelerating downwards, the accelerations for m1, m2 & m3 are downwards as well. Then, solving the following equations using a negative sign on all accelerations, I get 2.87 downward:

    Mass 1:
    T = -m1a1y + m1g (1)

    Mass 2:
    T-T1 = -m2ay (2)

    Mass 3:
    T1-m3g = -m3ay (3)

    Is this the right approach for this problem?
     
  5. Oct 24, 2016 #4
    I can't follow your notation, but if you get 2.87, you must have done it right.
     
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