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Math Help - Finding the angles of a pulley using vector

  1. #1
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    Finding the angles of a pulley using vector

    Find \phi and \theta
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  2. #2
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    Re: Finding the angles of a pulley using vector

    Break the force at w2 into horizontal and vertical components. The horizontal component is T_1cos(\theta)- T_2cos(\phi)= 0 while the vertical force is T_1 sin(\theta)+ T_2 sin(\phi)= w2. In terms of the weights, T_1= w_1 and T_2= w_3. Solve the two equations w_1cos(\theta)- w_3cos(\phi)= 0 and w_1 sin(\theta)+ w_3sin(\phi)= w_2 for \theta and \phi.
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  3. #3
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    Re: Finding the angles of a pulley using vector

    Quote Originally Posted by HallsofIvy View Post
    Break the force at w2 into horizontal and vertical components. The horizontal component is T_1cos(\theta)- T_2cos(\phi)= 0 while the vertical force is T_1 sin(\theta)+ T_2 sin(\phi)= w2. In terms of the weights, T_1= w_1 and T_2= w_3. Solve the two equations w_1cos(\theta)- w_3cos(\phi)= 0 and w_1 sin(\theta)+ w_3sin(\phi)= w_2 for \theta and \phi.
    The answer book gives me

    \theta = sin^{-1}( \frac{w_1^2+w_2^2-w_3^2}{2w_1w_2})

    and

    \phi = sin^{-1}( \frac{w_2^2+w_3^2-w_1^2}{2w_2w_3})

    any idea?
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