An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope...

generals336

generals336

Answered

2021-02-20

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 4.50104N and our hero's mass is 86.5 kg.

 Figure 1 a) If the angle θ is 13.0, find the tension iin the rope.

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

 

Answer & Explanation

krolaniaN

krolaniaN

Expert

2021-02-21Added 86 answers

Each half of the rope exerts a vertical force of Tsin(θ)
or 2Tsin(θ)=Mg
So T=((86.5 kg9.8 ms2 )2sin13)=1884 N
For the minimum angle sin(θ)=Mg2T
=847.7 N9104 N So θ minimum =.54deg

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