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Math Help - Resultant

  1. #1
    Member
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    Dec 2007
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    Resultant

    Two forces magnitude 5N and 7N act on a body. The angle between the forces is 55 degrees. The resultant has magnitude R and acts at an anlge to Ѳ to the 5N force , as shown in the diagram. Calculate R and Ѳ.

    thanks
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  2. #2
    MHF Contributor
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    Hi

    R \cos\theta = 5 + 7 \cos(55)
    R \sin\theta = 7 \sin(55)

    R^2 = (R \cos\theta)^2 + (R \sin\theta)^2 = (5 + 7 \cos(55))^2 + (7 \sin(55))^2 = 74 + 70 \cos(55)
    R = \sqrt{74 + 70 \cos(55)} = 10.68 N

    \sin\theta = \frac{7 \sin(55)}{\sqrt{74 + 70 \cos(55)}}

    \theta = 32.4\, deg

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