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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

    PhanthomJay

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    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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