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 (Fig. 1) The rope will break if the tension in it exceeds&nbsp;4.50⋅104N and our hero's mass is 86.5 kg.&nbsp;Figure 1&nbsp;a) If the angle&nbsp;θ&nbsp;is&nbsp;13.0∘, find the tension iin the rope.b) What is the smallest value the angle&nbsp;θ&nbsp;can have if the rope is not to break?&nbsp;

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 (Fig. 1) The rope will break if the tension in it exceeds&amp;nbsp;4.50⋅104N and our hero&#039;s mass is 86.5 kg.&amp;nbsp;Figure 1&amp;nbsp;a) If the angle&amp;nbsp;θ&amp;nbsp;is&amp;nbsp;13.0∘, find the tension iin the rope.b) What is the smallest value the angle&amp;nbsp;θ&amp;nbsp;can have if the rope is not to break?&amp;nbsp;

krolaniaN · Accepted Answer

Each half of the rope exerts a vertical force of T⋅sin⁡(θ)  or 2⋅T⋅sin⁡(θ)=M⋅g  So T=((86.5 kg⋅9.8 ms2 )2⋅sin⁡13)=1884 N  For the minimum angle sin⁡(θ)=M⋅g2⋅T  =847.7 N9⋅104 N So θ minimum =.54deg