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Homework Help: Laws of Motion question?

  1. Sep 11, 2010 #1
    1. The problem statement, all variables and given/known data

    In the system shown all pulleys are light and smooth and all strings are light and inextensible. A block of mass m = 20 kg is attached to the movable pulley. A constant force, F, applied at the free end of the string, makes the point of application of force move down with a constant acceleration of 4 m/s^2. The applied for F is (g = 10 m/s^2)

    a) 40 N
    b) 80 N
    c) 120 N
    d) 160 N

    2. Relevant equations

    F = ma

    For the block,

    mg - 2T = ma
    20*10 - 2T = 20a
    200 - 2T = 20a

    For the free end of the string,

    F - T = ma

    But there is no mass. Hence

    F - T = 0
    F = T

    3. The attempt at a solution

    Is what I have done so far correct? I know that the free end of the string and the block have different accelerations, but how do I relate them? The figure for this is here:

    http://img299.imageshack.us/img299/166/47373170.png [Broken]
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 11, 2010 #2


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    Science Advisor
    Homework Helper
    Gold Member

    You are correct so far. Now all you have to do is determine the acceleartion of the mass. You're given that the acceleration of the point force is 4m/s^2. Now you have to do a little imagination to realize that if the Force, F, moves down say 2 feet, the 2nd pulley and mass must move up by___ ft. (The acceleration of the mass will be less than 4). Watch your signage in your first equation for the mass acceleration.
    Last edited: Sep 11, 2010
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