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Math Help - Magnitude of the reultant force Help

  1. #1
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    Magnitude of the reultant force Help

    300N is on the x-axis (-300,0)
    and 200N (100,173) is in a 60 degree angle from the x-axis
    How do I find the magnitude of the resultant force and the angle it makes w/ the positive x-axis?

    Thanks in advanced.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by khuezy View Post
    300N is on the x-axis (-300,0)
    and 200N (100,173) is in a 60 degree angle from the x-axis
    How do I find the magnitude of the resultant force and the angle it makes w/ the positive x-axis?

    Thanks in advanced.
    Let \bold F_1=\left<-300,~0\right>~N and \bold F_2=\left<100,~173\right>~N

    The resultant force vector \bold R=\bold F_1+\bold F_2\implies \bold R=\left<-300+100,~0+173\right>~N\implies \color{red}\boxed{\bold R=\left<-200,~173\right>~N}

    The magnitude of the resultant force would be ||\bold R||=\sqrt{(-200)^2+(173)^2}\implies \color{red}\boxed{||\bold R||\approx 264.44~N}

    I leave it for you to find the angle, given that \vartheta=\tan^{-1}\left(\frac{R_y}{R_x}\right)

    Does this make sense?

    --Chris
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  3. #3
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    ic

    thanks a lot
    the angle is arctan(173/-200) + 180 = 139.1degree?
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by khuezy View Post
    thanks a lot
    the angle is arctan(173/-200) + 180 = 139.1degree?
    Yes!

    --Chris
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