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Adding vectors with the component method

  1. Jan 14, 2013 #1
    Hi! I know this is pretty basic... I'm teaching myself from a text book, and I got a different answer from the book...It doesn't have the problem worked out, just the answer. I just need to figure out what mistake I made.

    1. The problem statement, all variables and given/known data
    Find the resultant of the following forces: (a) 30N at an angle of 40°, with respect to the x-axis, (b) 120N at an angle 135°, (c) 60N at an angle of 260°

    The book's answer(and I'm assuming the correct one) is: 85.2N; 148 from +x axis

    2. The attempt at a solution
    First I name each vector
    30N, 40 deg is a | 120N, 135 deg is b | 60N 260 deg is c

    Next I find the x and y components for each vector
    ax = 30*cos(40) = 23;
    ay = 30*sin(40)
    ---
    bx = 120*cos(35) = 98.3;
    by = 120*sin(35) = 68.8
    ---
    cx = 60*sin(260) = -59.1;
    cy = 60*cos(260) = -10.4
    ---
    Next I find the x and y components of the resultant vector
    Rx = ax+bx+cx = 62.2
    Ry = ay+by+cy = 62.2

    Next I find the hypotenuse(i.e. the magnitude of the resultant vector)
    R = √((62.2)^2+(77.7)^2) = 99.5

    And finally I calculate the angle of the resultant vector
    θ = arctan(77.7/62.2) = 51.3
     
  2. jcsd
  3. Jan 14, 2013 #2

    gneill

    User Avatar

    Staff: Mentor

    Redo you calculations after fixing up the bits I've indicated. Be careful about the quadrant placement for the angle.
     
  4. Jan 14, 2013 #3
    Thank you! I 100% missed the "35" mistake haha. The cos/sin switch was on purpose, something about it being below the x-axis...Anyway, I worked through it all visually and mathematically and figured it out.

    I appreciate it!
     
    Last edited: Jan 14, 2013
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