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Pulley dynamics problem 12-205 Hibbeler

  1. Apr 11, 2012 #1
    1. The problem statement, all variables and given/known data
    I have posted the snapshot.


    2. Relevant equations
    I have written the distances from the datum line. Since we have two threads, I got two
    equations.
    [tex]2S_A +S_C=L_1[/tex]

    [tex](S_B -S_C)+(h-S_C)=L_2 [/tex]

    where L1 and L2 are the lengths of the strings excluding the
    parts which remain constant in time.



    3. The attempt at a solution


    I can now relate B and A as

    [tex]\dot{S_A}=-\frac{\dot{S_B}}{4} [/tex]

    [tex]\ddot{S_A}=-\frac{\ddot{S_B}}{4} [/tex]

    So I get [itex]\dot{S_A} =-1 [/itex] , which means the block A is going upwards.
    Now the problem says that the speed of the cable being pulled at B is decreasing
    at the rate of 2 ft/s2. So that means [itex]\ddot{S_B}=-2 ft/s^2[/itex].
    So I get [itex]\ddot{S_A}= 0.5 [/itex]. I got the first answer right. I have question about
    the interpretation of the second answer. Since [itex]\ddot{S_A}[/itex] is positive, does
    it mean the speed of block A is increasing ?. My second numerical answer is correct
    though.
     

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  3. Apr 12, 2012 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    hi issacnewton! :smile:
    A's velocity is -1 downward, ie 1 upward.

    A's acceleration is positive downward, ie negative upward, so the speed of 1 upward is decreasing. :wink:
     
  4. Apr 12, 2012 #3
    tim, makes perfect sense. these pulley problems sometime throw me...
     
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