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.

Answer 1

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

Answer 2

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

Answer 3

both above wrong...stupid!!!!

Answer 4

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.