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Tensions over a pulley, 3 objects connected with 2 strings

  1. Sep 25, 2009 #1
    1. The problem statement, all variables and given/known data
    The string connecting the m1 and the m2 passes over a light frictionless pulley. Given m1 = 6.51kg, m2 = 7.48kg, m3 = 9.75kg. The acceleration of gravity is 9.8 m/s2.

    1) Find the downward acceleration of m2 mass. Answer in units of m/s2

    2) Find the tension in the string connecting the m1 and m2 masses. Answer in units of N.

    3) Find the tension in the string connecting the m2 and the m3 masses. Answer in units of N.

    Picture is embedded in PDF, but easy to describe:
    A single pulley hanging from ceiling, on the right side of the pulley the string goes down to connect to m1. On the left side of the pulley the string goes down to connect to m2. Then a string connects m2 to m3 below it.

    I've already solved #1 and #2, I'm stuck on #3.

    2. Relevant equations
    a = [(m1 - m2) / (m1 + m2)] * g
    T = [(2m1 * m2) / (m1 + m2)] * g
    derived in class


    3. The attempt at a solution
    I extended those formulas to 3 masses (instead of just 2) to calculate the acceleration 4.42527 m/s2 and T1 = 92.6065 N.

    I've tried drawing force diagrams and adding the components to find T2 several ways, but I'm getting confused.

    This is a practice homework where we're given the answers - then our real homework is through UT and uses the same problems with different numbers; so I know my answers to 1 and 2 are correct, and #3 I'm not getting the correct answer. The answer is supposed to be 52.4036 N.
     
  2. jcsd
  3. Sep 25, 2009 #2

    Delphi51

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    Homework Helper

    Consider the forces on m3. There is m3*g down and the Tension up. Use
    sum of forces = ma
     
  4. Sep 25, 2009 #3
    Heh, figures it's way simpler than I was trying. I was trying to add the Tension of the first string over the pulley along with the weight of m1, then subtracting the weight of m2 and m3.

    Many thanks!
     
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