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Math Help - two forces

  1. #1
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    two forces

    two forces of 115 lb and 215 lb acting on an object have a resultant of magnitude 275 lb. find the angle between which the given forces act.

    use law of cosines
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  2. #2
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    arccos -0.327....
    =arccos 0.327..
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  3. #3
    MHF Contributor Unknown008's Avatar
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    If you can make a sketch, this would help you a lot.

    Let's call the force 115 lb being along a vector OA and the 215 lb force along a vector OB. Lastly, OC being the vector along the resultant 275 lb force.

    using the cosine rule, we can get the angle OBC.

    275^2 = 215^2 + 115^2 - 2(115)(215)cos OBC

    Now, if you have your sketch, you'll know that OACB is a parallelogram. You are looking for angle AOB, the angle between the two forces. You have OBC and you know that angle OBC = angle OAC and angle AOB = angle ACB. Then, we know that in a quadrilateral, the sum of angles is 360 degrees. You can find angle AOB now.

    I hoped it helped!
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