*110.  A mountain climber, in the process of crossing between two cliffs by a rope, pauses to rest. She weighs 535 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.

Free Body diagram

Since the climber is not moving, acceleration is zero and

Notice how the angles are defined, they are not in the usual orientation, so for the horizontal we actually need sin not cos.

 

 

 

 

Substitute from x equation for TL

 

 

 

 

 

 

Now we can find TL from the earlier derived equation

 

 

 

 

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This page last updated on January 11, 2020