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A movie stunt performer 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 stunt performer's mass is 80.0 kg, the vine is 11.5 m long, and the speed of the stunt performer at the bottom of the swing has been determined to be 7.00 m/s. What is the minimum tension force (in N) the vine must be able to support without breaking?

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Answer:

1125.66956 N

Explanation:

m = Mass of stunt performer

g = Acceleration due to gravity = 9.81 m/s²

v = Velocity of the swing = 7 m/s

T = Tension

r = Radius of the swing = Length of vine = 11.5 m

From the free body diagram

[tex]T-mg-m\frac{v^2}{r}=0\\\Rightarrow T=mg+m\frac{v^2}{r}\\\Rightarrow T=m(g+\frac{v^2}{r})\\\Rightarrow T=80(9.81+\frac{7^2}{11.5})\\\Rightarrow T=1125.66956\ N[/tex]

The minimum tension force the vine must be able to support without breaking is 1125.66956 N

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