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

AI Thread Summary
The discussion focuses on deriving an expression for the acceleration of a bungee jumper, denoted as x double dot, while ensuring the maximum acceleration does not exceed 3g. Participants clarify the use of elastic energy versus elastic potential energy, emphasizing that only force equations are necessary for the solution. The key equation presented is mg - T = ma, which leads to challenges in isolating acceleration due to the variable x. A suggestion is made to relate acceleration directly to displacement, indicating that an equation connecting x double dot and x should be derived. The conversation concludes with encouragement to solve the derived equation for further clarity.
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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