Solve Bungee Jump Issue: Derive Expression for x Double Dot, Show mg >= kh/4

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SUMMARY

The discussion focuses on deriving an expression for the acceleration (x double dot) of a bungee jumper, considering the forces acting on the jumper, including gravitational force (mg) and spring force (kx/h). The key conclusion is that the maximum allowable acceleration is limited to 3g, and the condition mg must be greater than or equal to kh/4 is established. Participants clarify that the use of elastic energy is unnecessary for this derivation, emphasizing a force-based approach instead.

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  • Understanding of Newton's Second Law of Motion
  • Familiarity with spring mechanics and Hooke's Law
  • Knowledge of basic calculus, particularly derivatives
  • Concept of gravitational force and its implications in dynamics
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Aihara
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Homework Statement


Typical bungee jumper. Rope has natural length h, spring constant k, man has mass m.

The safety limit for the max acceleration of the man is 3g. Derive an expression for x double dot, and show mg *greater or same than* kh/4

Homework Equations


Well I'm sure everyone knows them
I'm confused about Elastic Energy (kx^2) and Elastic Potential Energy (kx^2/2l), which do I use?


The Attempt at a Solution


I'm got four pages of working but not get where I want.
The acceleration (a) isn't constant, so are we trying to get an expression for a in terms of time or string extension...

At a random point after the rope has started extending mg - T = ma. so mg - kx/h = ma
so rearrange for acceleration... but then the x won't cancel and I can't show what I was asked too...

Thanks
 
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Welcome to PF!

Aihara said:
At a random point after the rope has started extending mg - T = ma. so mg - kx/h = ma
so rearrange for acceleration... but then the x won't cancel and I can't show what I was asked too...

Thanks

Hi Aihara! Welcome to PF! :smile:

(You won't need energy, only force)

why should the x cancel? :confused:

a = x'', so you should get an equation relating x'' and x …

then solve it. :smile:
 

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