Answer to Question #258520 in Physics for kds

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 it exceeds 25,000 N. Our hero’s mass is 90 kg. (a) If the angle is 10º, find the tension in the rope. (b) What is the smallest value the angle can have if the rope is not to break?

Answer 1

(a) The tension:

$$2T\sin\theta=mg,\\\space\\ T=\frac{mg}{2\sin\theta}=2539.6\text{ N}.$$

(b) The smallest angle:

$$\theta=\arcsin\frac{mg}{2T}=1.01°.$$