A mountain climber, in the process of crossing between two cliffsby a rope, paus

Question

A mountain climber, in the process of crossing between two cliffsby a rope, pauses to rest. She weighs 551N. As the drawing shows, she is closer to the left cliff than tothe right cliff, with the result that the tensions in the left andright sides of the rope are not the same. Find the tensions in therope to the left and to the right of the mountain climber. (Fromthe figure = 70.0°and = 73.5°.)
TL = Enter a number. 1 N TR = Enter a number. 2 N Enter a number. Enter a number. TL = Enter a number. 1 N TR = Enter a number. 2 N

Explanation / Answer

vertical: L cos70 + R cos73.5 = 551...................(2)
Now, we have two equations and two unknowns. Solve for Land then for R.
Equation (1) can be reduced to R = 0.98 L.............(3)
Plug (3) into (2)
L cos70 + (0.98L) cos73.5 = 551
Solve for L you get L = 891.1 Newtons
R = 0.98* 891.1 = 873.3 Newtons

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