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Weighed Centroid Proof?

  1. Aug 13, 2012 #1
    Given the formula for the weighted centroid, C of a system of parallel forces
    Fi acting at points Pi, show that two weights W and 3W, acting respectively
    at points P1, P2, are together equivalent to a single weight 4W acting at P,
    where P lies on the line segment joining P1 to P2 and P1 P : P P2 = 3 : 1.


    OC = (Ʃi opi.Fi)/ (ƩFi)


    Any one know how to prove it ? revising and this came up in a test last year its not in my notes?
     
  2. jcsd
  3. Aug 15, 2012 #2

    haruspex

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    Is that the formula as you're given it? The forces are vectors, so it would more logically be written
    OC. (ƩFi) = (Ʃi opi.Fi)
    You have the choice of where to place the origin. Where will you place it? Having done that, can you fill in the RHS of the formula using the W & 3W set-up?
     
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