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An online video daredevil is filming a scene where he swings across a river on a vine. The safety crew must use a vine with enough strength so that it doesn't break while swinging. The daredevil's mass is 80.0 kg, the vine is 12.0 m long, and the speed of the daredevil at the bottom of the swing has been determined to be 8.60 m/s. What is the minimum tension force (in N) the vine must be able to support without breaking

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Answer:

[tex]1277.867\ \text{N}[/tex]

Explanation:

m = Mass of person = 80 kg

r = Radius of swing = 12 m

g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]

The tension in the rope would be

[tex]T=mg+\dfrac{mv^2}{r}\\\Rightarrow T=80\times 9.81+\dfrac{80\times 8.6^2}{12}\\\Rightarrow T=1277.867\ \text{N}[/tex]

The tension in the rope is [tex]1277.867\ \text{N}[/tex].

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