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A simplified model of a bungee jump can be analyzed in two sections: a freefall section in which the bungee cord has not yet begun stretching and a section in the lower portion of the jump in which the bungee cord stretches and exerts a force on the jumper. The cord is assumed to exert zero force on the jumper until its length exceeds its maximum unstretched length. Determine the maximum unstretched length of a bungee cord of spring constant 100 N/m such that a 70-kg jumper will not hit the ground when jumping from a height of 45 m.

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Answer:

[tex]20.14\ \text{m}[/tex]

Explanation:

m = Mass of person = 70 kg

k = Spring constant = 100 N/m

h = Total length of the bungee cord = 45 m

The energy balance of the system is

[tex]mgh=\dfrac{1}{2}kx^2\\\Rightarrow x=\sqrt{\dfrac{2mgh}{k}}\\\Rightarrow x=\sqrt{\dfrac{2\times 70\times 9.81\times 45}{100}}\\\Rightarrow x=24.86\ \text{m}[/tex]

Maximum unstretched length would be [tex]h-x=45-24.86=20.14\ \text{m}[/tex].

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