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

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 2.50x104N , and our hero's mass is 83.4kg . You may want to review For help with math skills, you may want to review: For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Two dimensional eguilibrium. If the angle between the rope and the horizontal is theta = 11.6 degree, find the tension in the rope. What is the smallest value the angle theta can have if the rope is not to break?

Explanation / Answer

2Tsin(theta) = mg

max(T) = 2.5 x 10^4 N

So min(theta) = sin^(-1) (mg/2T) = sin^(-1) (0.01634) = 0.9366 degrees

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