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Free Body Diagram Forces of a Rope Hoisting a Weight via Pillars

  1. Nov 6, 2014 #1
    So I am designing an apparatus to lift a 500g load up 500mm and I am trying to find reactions. I have filled in these values in my head with my own logic but I dont know how to do the maths and if I am right or not.
    I can do the initial position ok but it is the final position I am unsure of.
    Here is what I have done:
    https://www.dropbox.com/s/mirvwr2h13aajfp/Screenshot 2014-11-06 16.50.00.png?dl=0
     
  2. jcsd
  3. Nov 10, 2014 #2

    PhanthomJay

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    When you pull up the load to its final position, the rope as you have noted on the right side of the left pillar has a horizontal tension component of 15 N and a vertical tension component of 2.5 N. Or a rope tension using Pythagoras Theorem of about 15.2 N.
    Now presumably as you are pulling up the rope, you have some sort of pulley or smooth rounded edge at the top of the pillars. In which case, the tensions on both sides of the pulley are the same, and in which case the vertical component of the rope tension at the pulling end or anchored end is 15.2/sq rt 2 or about 10.7 N and the horizontal component is also 10.7 N. Thus, the pillar reaction is 13.2 N up and 4.3 N left. In other words, you have an unbalanced horizontal load inward at the pulley on the pillar top. You also have a ground line overturning moment at the pillar base, so the pillar requires fixity there.
    Now once you snub off the rope between supports, ensure straightness of the pillar, and anchor your pulling end to the ground, then your ground line reaction is 17.5 N up, as you note, no horizontal component at base of pillar and no moment there either.
     
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