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Vector decomposition

  1. Aug 25, 2016 #1
    1. The problem statement, all variables and given/known data

    The force on an object is F = -11j. For the vector v =-i-5j, find:

    1. The component of F parallel to v
    2. The component of F perpendicular to v
    3. The work, W, done by force F through displacement v

    2. Relevant equations

    ProjvF = v dot F/ |v|2
    OrthvF = F - ProjvF
    W = D dot F

    3. The attempt at a solution

    F = < 0, -11> v = < -1, -5>

    1.
    ProjvF = -1(0) + -5(-11) / 12 + -52 = 55/26<-1, -5>
    ProjvF = <-2.115, -10.576>

    2.
    OrthvF = < 0, -11> - <-2.115, -10.576> = 0 + 2.115 , -11 +10.576 = <2.115, -0.424>
    OrthvF = <2.115, -0.424>

    3.
    W = <2.115, -0.424> dot < 0, -11> = 2.115(0) + -0.424(-11) = 4.664
    W = 4.664


    I am told that step 1 is correct, and the first value in step 2 is correct. I cannot figure out what I am missing on part 2, which is ultimately messing up step 3. Any help would be appreciated.
     
  2. jcsd
  3. Aug 25, 2016 #2

    BvU

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    In 3 you don't do ##\vec v\cdot\vec F## but you use the one that's perpendicular.
    In 2 I don't see what's wrong.
     
  4. Aug 25, 2016 #3
    Thanks, I see what I did wrong on part 3. Part 2 after redoing it again was expecting -0.42307, I rounded too soon it seems
     
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