An adventurous archaeologist crosses between two rock cliffs by slowly going han

Question

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 itexceeds 2.35 x 10^4 N, and our hero's mass is 83.1 kg.

1.) If the angle between the rope and the horizontal is 0 = 11.5 degrees, find the tension in the rope.

=  ?  N

2.) What is the smallest value the angle 0 can have if the rope is not to break?

can have if the rope is not to break?

I have no idea how to do these problems. Please show step by step with correct answers so I can try to understand.

THANK YOU!!!

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 itexceeds 2.35 x 104 N, and our hero's mass is 83.1 kg. If the angle between the rope and the horizontal is 0 = 11.5 degrees, find the tension in the rope. = ? N What is the smallest value the angle 0 can have if the rope is not to break?

Explanation / Answer

2.35 x 10^4 = 23500 N

mg = 83.1 x 9.8 =814.38 N

814.38/2 = 407.19

1)

407.19/sin(11.5) = 2042.4N each side

2)

arcsin(814.38/23500) = 1.98 degrees

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