Will the Rope Hold the Archaeologist Safely?

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SUMMARY

The discussion centers on the tension in a rope supporting an archaeologist crossing between two cliffs. The maximum tension the rope can withstand is 29,500 N, while the archaeologist's mass is 93.8 kg. The correct calculation for the tension in the rope, considering the angle of 11.0 degrees, results in a value of approximately 2408.796 N. Additionally, the smallest angle at which the rope can safely hold the archaeologist without breaking is 0.89 degrees, achieved by evenly distributing the weight across both sides of the rope.

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An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope . The rope will break if the tension in it exceeds 2.95EE4 (2.95 x 10^4) , and our hero's mass is 93.8 .

<img src=http://session.masteringphysics.com/problemAsset/1041292/5/YF-05-42.jpg>

A. If the angle between the rope and the horizontal is = 11.0, find the tension in the rope.
B. What is the smallest value the angle can have if the rope is not to break?

The following answers are incorrect:
A. 4817.6 N
B. 1.78 degrees
 
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Do you have your calculations at all?

Also the link you have posted is broken.
 
You did what many people get wrong. You forget to evenly distrubute the weight of the person to both sides of the rope. Since he is in the exact middle then you will divide his weight in half and put them on both the "y" dimension.

From this I got a) 2408.796 N
b) .89 degrees

Notice these are exactly half of your answer this is because I halved the weight of each side.
 

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