1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Vector problem

  1. Mar 20, 2009 #1
    given 3 forces working on one object with dimentions of 6x2

    F1=4500N (from the front at an anlge of 39)
    F2=9000N (from the front at an angle of -α )
    F3=2250N (grom the back at an angle of 180)

    see diagram below:
    http://picasaweb.google.com/devanlevin/DropBox?authkey=Gv1sRgCL_4l4PpvP_YsQE#5315263399457681474 [Broken]

    what must the angle α be in order for the total force applied to be parallel to the line AB, ?

    F=F1+F2+F3 (vectors)

    Fx=4500*cos(39) + 9000*cos(α) - 2250
    =2250(2*cos(39) + 4*cos(α) - 1)

    Fy=4500*sin(39) -9000*sin(α)

    now in order for this vector to be parallel to AB, it must be at the same angle,-->

    2/6=[2250(2*sin(39)-4*sin(α))] / [2250(2*cos(39) + 4*cos(α) - 1)]

    (2*cos(39) + 4*cos(α) - 1) = (6*sin(39)-12*sin(α))
    cos(α)+3*sin(α) = 0.8054

    from here i am stuck, i need to find some trigonometrical identity to help me out, alternatively, another way to solve the problem
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 20, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi Dell! :smile:

    (i haven't checked how you got there, but …)

    Hint: to solve an equation like this, put it in the form cos(A)cos(α)+sin(A)sin(α) = … :wink:
  4. Mar 20, 2009 #3
    i dont understand, could you continue a bit
  5. Mar 20, 2009 #4


    User Avatar
    Science Advisor
    Homework Helper

    well, for example, if it was cos(α)+sin(α) = 0.8054, you could write that as

    cos(α)/√2 + sin(α)/√2 = 0.8054/√2

    ie cos(π/4)cos(α) + sin(π/4)sin(α) = 0.8054/√2

    so cos(α - π/4) = 0.8054/√2 :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook