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Math Help - Stuck on magnitude of vector problem

  1. #1
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    Stuck on magnitude of vector problem

    I have this problem that is as follows:

    Two equal forces acting from the same point, their resultant has a magnitude of 30N (newtons) and are at 60 degrees from one another. Calculate the magnitude of each equal forces.

    The answer turns out to be 10sqrt3 which if squared equals 300. the problem im having is I can't figure out two forces with magnitudes of 10sqrt3 can have a magnitude of 30.
    I continue to end up with uneven answers.

    I did cosine law and sine law. that ends up giving me one force at 15 and another at approximately 25.

    I tried R^2 = F1^2 +F2^2 =
    R=sqrt(F1^2+F2^2)=
    and if they are equal I figured R/2 would give me the magnitude

    then I tried both the law of cosine and sine. im missing something
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  2. #2
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
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    What you did is really confusing...

    Make a sketch, let the two forces be F.

    From that sketch, you'll see that:

    R^2 = F^2 + F^2 - 2(F)(F)\cos(120)

    You know R, find F.

    Anyway, no need to solve. Simplifying this gives:

    R^2 = 2F^2 - 2F^2(-0.5)

    R^2 = 2F^2 + F^2

    R^2 = 3F^2

    So,

    F^2 = \dfrac{30^2}{3}

    F = \sqrt{300} = 10\sqrt3

    EDIT: Here's a sketch to help you. Note that I used a technique called completing the parallelogram of forces.

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