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Thread: Statics problem

  1. #1
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    Statics problem

    Can I get some help with problem 2.53 shown below?
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  2. #2
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    let $\displaystyle \theta$ be the angle AB makes with the horizontal

    $\displaystyle \phi$ be the angle BC makes with the horizontal

    $\displaystyle T$ = wire tension

    $\displaystyle W$ = weight of aerailist

    $\displaystyle \sum{F_x} = 0$

    $\displaystyle (T+35)\cos{\theta} = T\cos{\phi}$

    $\displaystyle \sum{F_y} = 0$

    $\displaystyle (T+35)\sin{\theta} + T\sin{\phi} = W$


    let the length of $\displaystyle AB = x$ ... then the length of $\displaystyle BC = 8-x$

    let $\displaystyle h$ = vertical distance (amount of "dip") point B is below AC

    $\displaystyle h^2 = x^2 - 2.5^2$

    $\displaystyle h^2 = (8-x)^2 - 5.45^2$

    $\displaystyle (8-x)^2 - 5.45^2 = x^2 - 2.5^2$

    solve for $\displaystyle x$, then you can determine

    $\displaystyle \cos{\theta} = \frac{2.5}{x}$

    $\displaystyle \cos{\phi} = \frac{5.45}{8-x}$

    finally, solve your system of force equations for T and W.
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