Final Project Assignment

Final Project Assignment - Final Project Suppose that you...

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Final Project Suppose that you have been hired to design a bungee jump. The length of the bungee cord is L , and the bungee jump platform is assumed to be at height, h = 0, with h increasing in the downward direction ( g is positive and assumed to be 9.81 m/s 2 ). Using numerical integration techniques, you will look at the trajectory of a bungee jumper from the platform to the end of the cord extension. Background: The bungee jump consists of two phases: free fall and bungee extension. 1. Free Fall During the free fall the jumper is only subjected to two forces: gravity, F g = mg and drag, F d = - C d v 2 . This makes the acceleration on the jumper a ( t ) = 1 m X F = g - C d m v 2 where C d is the coefficient of drag, and m is the mass of the jumper. The free fall is active as long as the distance traveled is less than the length of the cord ( h L ). Using numerical integration (discussed in class), the velocity at time t new can be updated as v new = v old + Δ ta = v old + Δ t ± g - C d m v 2 old ² In addition, the height can be updated as h new = h old + Δ tv new The new velocity and position then become the old velocity and position for the next iteration. 2. Bungee Extension The bungee cord is modeled as a spring force with a spring constant k . Accordingly, the additional force added by the bungee is F s = k Δ x where x = h - L is the distance traveled since the bungee became active. This makes the new acceleration on the jumper
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Final Project Assignment - Final Project Suppose that you...

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