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A 54.0 kg person takes a nap in a (lightweight) backyard hammock. Both ropes supporting the hammock are at an angle of 16.9° above the horizontal. Find the tension in the ropes.

  • physics -

    2Tsin16.9=mg=0
    2Tsin16.9=mg
    T=mg/2sin16.9
    T=54(9.8)/2sin16.9
    T=529.2/sin16.9
    T=529.2/.581
    T=912

  • physics -

    2Tcos16.9=W,
    but W=mg=54x9.8=529.2N,
    T=W/2c0s16.9
    T on each cord is to be 276.54N

  • physics -

    both above wrong...stupid!!!!

  • physics -

    M*g = 54 * 9.8 = 529.2 N. = Wt. of the person.

    Eq1: T1*Cos16.9 = -T2*Cos(180-16.9).
    0.957T1 = 0.957T2.
    T1 = T2.

    Eq2: T1*sin16.9 + T2*sin(180-16.9) = -529.2[270o].
    0.291T1 + 0.291T2 = 529.2.
    Replace T1 with T2:
    0.291T2 + 0.291T2 = 529.2
    0.581T2 = 529.2
    T2 = 910 N. = T1.

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