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Confusion over the reduction of force for pulleys

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  1. Oct 9, 2014 #1
    1. The problem statement, all variables and given/known data
    A window washer pulls herself upward using the bucket-pulley apparatus shown in the figure. How hard must she pull downward to raise herself slowly at constant speed? The mass of the person plus the bucket is 71kg .
    GIANCOLI.ch04.p32.jpg
    2. Relevant equations
    F of gravity = mg
    F effort = mg/2

    3. The attempt at a solution
    I found out later that using a pulley reduces the force to half, so I did Force = mg/2 which is the correct answer. I am confused because according to this website http://www.explainthatstuff.com/pulleys.html and http://www.ehow.com/how-does_5231254_much-weight-pulley-off_.html , two wheels are needed for a reduction of force by one half. There is only a single wheel on the pulley for the window washer.
    howpulleyswork1.gif howpulleyswork2.gif

    In other words, the force to pull the window washer up should be equal to to her weight (mg) and not half of that. Did I misread something or is one of the websites wrong?
     
  2. jcsd
  3. Oct 9, 2014 #2

    ehild

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    Homework Helper
    Gold Member

    The window washer set-up is different from the cases when the load is lifted by an external force. The window-washer lifts himself. Draw the free-body diagram: the force he pulls the rope is equal to the upward force the rope pulls him. This is the tension T in the rope, and it is applied also to the bucket. So the bucket and window-washer experience 2T force from the rope, and mg downward force from gravity.

    ehild
     
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