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Math Help - angle between two ropes

  1. #1
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    angle between two ropes

    Allie, Beth, and Cathy are having a 3 way tug of war. Allie is pulling with a force of 30N, Beth with 50N, and Cathy with 70N. If the system is in equilibrium, what is the angle between Allie's rope and Beth's rope.

    I used the cosine law, and

    cos\theta=\frac{{30}^2+{50}^2-{70}^2}{2\cdot 30\cdot 50}

    \theta = 120

    But the answer is 60, because 180-120=60. Why?
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  2. #2
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    tug of war

    Quote Originally Posted by chengbin View Post
    Allie, Beth, and Cathy are having a 3 way tug of war. Allie is pulling with a force of 30N, Beth with 50N, and Cathy with 70N. If the system is in equilibrium, what is the angle between Allie's rope and Beth's rope.

    I used the cosine law, and

    cos\theta=\frac{{30}^2+{50}^2-{70}^2}{2\cdot 30\cdot 50}

    \theta = 120

    But the answer is 60, because 180-120=60. Why?
    Hi chengbin,

    I set up two force diagrams for Allie and Beth.Cathy pulled with a force of70N so the opposing force has to be 70N.Theforces perpendicular to 70 must be equal and opposite By setting up two equations in xand y the lateral force is 18.5 .The 30N diagram gives opposing force 23.6 and the 50N diagram opposing force is 46.4 I got 59.8 for the angle between Allie and Beth's ropes using tangents to determine the acute angles in each force diagram


    bjh
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