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Physics

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A 50.0-kg person takes a nap in a backyard hammock. Both ropes supporting the hammock are at an angle of 15.0degrees above the horizontal. Find the tention of the ropes.

  • Physics -

    Draw a free body diagram. Then perform a static force balance.

  • Physics -

    2Tsin15=mg=0
    2Tsin15=mg
    T=mg/(2sin15)
    T=(50)(9.8)/(2sin15)

  • Physics -

    T=490/(2sin15)
    T=490/.517
    T=948

  • Physics -

    M*g = 50 * 9.8 = 490 N.

    Eq1: T1*Cos15 + T2*Cos165 = 0
    T1*Cos15 = -T2*Cos165
    T1 = T2

    Eq2: T1*sin15 + T2*sin165 = -490[270].
    0.259T1 + 0.259T2 = 0 + 490
    Replace T1 with T2:
    0.259T2 + 0.259T2 = 490
    0.518T2 = 490
    T2 = 947 N. = T1

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