Calculate the tension in the two ropes if the person is motionless. Person weighs 76kg and 15 degree angle rope one and 10 degree angle rope 2

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  1. M*g = 76 * 9.8 = 745 N.=Wt. of person.

    T1*Cos(180-15) + T2*Cos10 = -745*cos270.
    -0.966T1 + 0.985T2 = 0.
    T2 = 0.981T1

    -500i + T1*sin(180-15) + T2*sin10 = 0.
    Replace T2 with 0.981T1:
    -500i + T1*sin165 + 0.966T1*sin10 = 0.
    -500i + 0.259T1 + 0.168T1 = 0.
    -500i + 0.427T1 = 0.
    0.427T1 = 500i.
    T1 = 1172i = 1172N.[90o].
    T2 = 0.981*1172i = 1149i = 1149N[90o].

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  2. Correction:

    M*g = 76*9.8 = 745 N. = Wt. of person.

    T1*Cos(180-15) + T2*Cos10 = -745*Cos270.
    -0.966T1 + 0.985T2 = 0.
    T2 = 0.981T1.

    -745 + T1*sin(180-15) + T2*sin10 = 0.
    Replace T2 with 0.981T1:
    -745 + T1*sin(180-15) + 0.981T1*sin10=0.
    -745 + 0.259T1 + 0.170T1 = 0.
    -745 + 0.429T1 = 0.
    0.429T1 = 745.
    T1 = 1735 N.
    T2 = 0.981 * 1735 = 1702 N.

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