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 (Figure 1). The rope will break if the tension in it exceeds 2.55×104 NN , and our hero's mass is 87.6 kgkg . 1. If the angle between the rope and the horizontal is θθtheta = 11.1 ∘∘, find the tension in the rope. 2. What is the smallest value the angle θθ can have if the rope is not to break?

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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 (Figure 1). The rope will break if the tension in it exceeds 2.55×104 NN , and our hero's mass is 87.6 kgkg .

1. If the angle between the rope and the horizontal is θθtheta = 11.1 ∘∘, find the tension in the rope.

2. What is the smallest value the angle θθ can have if the rope is not to break?

 

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