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Pulleys Homework Question

  1. Nov 9, 2009 #1
    1. The problem statement, all variables and given/known data
    The original question is: What are the accelerations of the two masses?

    pulleys.jpg

    Given:
    M=8kg
    m=3kg
    g=10m/s^2
    Fapp=120N

    Assume all pulleys and strings are massless and frictionless

    My problem is whether there is a mechanical advantage in the question so I should divide the acceleration of the smaller mass by 2, and the acceleration of the larger mass by 4.


    2. Relevant equations

    F=ma

    3. The attempt at a solution

    Since the two masses are independent of each other, I thought that the accelerations of both masses were seperate.

    So, for the first mass,

    F = 2T - mg
    ma = 2T - mg

    I thought that tension force was equal to the applied force so,

    a = [2(120) - (3)(10)]/3
    a = 70m/s^2


    For the second mass,

    F = 2T - Mg
    Ma = 2T - Mg
    a = [2(120) - (8)(10)]/8
    a = 20m/s^2

    The reason I believe that there is a mechanical advantage is because if you pull the string by 1m, then the small mass will only move up by 0.5m, and the large mass, 0.25m
     
  2. jcsd
  3. Nov 9, 2009 #2
    I don't understand the question itself. If you hold the string end still, the large mass will fall and pull the small mass up. What are they actually asking you?

    I just read what you wrote for givens again. Are you asking what a is for each mass if 120N of tension?

    If so, simply apply F=ma on each one and one string has one tension T=120N, so for small mass: 2T-3g=3a and for large: 8g-2T=8a, sub in T and solve for a for each (they will be different a values for large and small masses).
     
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