A mountain climber, in the process of crossing between two cliffs by a rope, pau

Question

A mountain climber, in the process of crossing between two cliffs by a rope, pauses to rest. She weighs 560 N. As the drawing shows, she is closer to the left cliff than to the right cliff, with the result that the tensions in the left and right sides of the rope are not the same. Find the tensions in the rope to the left and to the right of the mountain climber

Explanation / Answer

the tensions in the rope to the left of the mountain climber = T1 the tensions in the rope to the right of the mountain climber = T2 ---------------------------- T1 sin65 - T2 sin80 = 0 >>>>> T2 = T1 sin65/sin80 >>>>>> T2 = T1 (0.92029) T1 cos65 + T2 cos80 = m g T1 cos65 + T1 (0.92029) cos80 = 560 T1 (0.42262 + (0.92029)*(0.17365)) = 560 T1 = 961.49 N T2 = T1 (0.92029) = 961.49 * (0.92029) = 885 N the tensions in the rope to the left = T1 = 961 N the tensions in the rope to the right = T2 = 885 N

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