Bethany, who weighs 420N, lies in a hammock suspended by two ropes tied to two trees. The left rope makes an angle of 45 degrees with the ground, the right one makes an angle of 30 degrees. Find the tension of the left rope. Find the tension of the right rope.

Answer 1

horizontal equation: sume of forces is zero.
Tl*cos45-Tr*cos60=0
vertical equation: sume of forces is zero.
Tl*sin45+Tr*sin60-420=0

You have two equations, two unknowns. Solve

Answer 2

412N and -227N? It said -227N wasn't the right answer.

Answer 3

All angles are measured CCW from +x-axis.
T1*Cos135 = -T2*Cos45.
T1 = T2.

T1*sin135 + T2*sin45 = -420*sin270.
0.707T1 + 0.707T2 = 420,
Replace T2 with T1 and solve for T1:

Answer 4

The right rope has a tension of 310 N for sure. But when I try to input it into bobpursley's two equations I can't find a value that fulfills both equations? If you know one of the ropes tensions for sure how do find the left rope's tension?

Answer 5

Eq1: T1* Cos135 = -T2*Cos30 .
T1 = 1.22T2.

Eq2: T1*sin135 + T2*sin30 = -420*sin270.
0.707T1 + 0.5T2 = 420, Replace T1 with 1.22T2:
0.863T2 + 0.5T2 = 420,
T2 = 308 N.
T1 = 1.22 * 308 = 376 N.

Both Eqs are satisfied.

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