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Vector resolution and vector addition

  1. Oct 29, 2009 #1
    1. The problem statement, all variables and given/known data

    We were given six homework assignments for lab. We were required to find the force and angle through three given experiments.

    1. Experimental using a force table
    2. Graphically using head to tail, etc
    3. Analytical using basic means to find the answers

    2. Relevant equations

    I have two problems

    1st problem
    Vector resolution
    F1 = (.1)gN theta = 30
    F2 (.2)gN theta = 90
    F3 (.3)gN theta = 225

    2nd Problem
    Vector resolution
    F = (.3)gN theta = 60

    Find fx and Fy

    Find graphical answer, analytical answer and Experimental answer for each

    3. The attempt at a solution

    1st Problem attempt at solution

    Using the force table I got F = (.130)gN Theta = 150
    Using Graphical I got F = (.131)gN theta = 162

    Now my problem is with analytical

    I used these equations

    Rx = Rcostheta
    Ry = Rsintheta
    r = sqrt(rx^2 + ry^2)
    theta = arctan rx/ry

    rx = .1cos30 + .2cos90 + .3cos225 = -.1255
    ry = .1sin30 + .2sin90 + .3sin225 = .038

    R = sqrt( -.1255^2 + .038^2) = .131

    Theta = arctan .038/-.1255
    Theta = 343.2 ???? It seems grossly off. I feel like I am forgetting something, but our book does not even really cover three vectors. I had to look online for how to do it.


    2nd problem attempt

    Using force table
    Fx = .140gN
    Fy = .245 gN

    Using graphical (I plotted this like a 90 degree triangle
    Fx = .16gN
    Fy = .25gN

    Using analytical


    I know c^2 = a^2 + b^2 so .9 = a^2 + b^2

    b / sintheta = R / sin Y


    sin theta is the angle R casts onto A which equals 60
    Sin Y is the angle sides B and A make

    b / sin60 = .3/sin90

    b / .866 = .3

    b = .866(.3) = .2598

    so Fy = .2598

    .9 = .2598^2 + a^2
    .9 = .0675 + a^2
    .8325 = a^2 = .91

    so Fx = .91 ??? Why is it so low as compared to the graphical and experimental? I feel something is off. All of my other calculations were pretty dead on .
     
  2. jcsd
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