Spring constant and length of string. *Need Explanation*

[Whitetiger101]

Homework Statement

200g weight
spring unstretched length: 0.238m
spring stretched( 200g hanging on spring): 0.305m

Problem: Need to find length of a cord long enough so that the 200g weight can have the best bungee jump ever (barely not touching the floor which is 10m high)

Homework Equations

K=mg/x

The Attempt at a Solution

I calculated the constant of the spring in Newtons per meter : 29N/m
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I don't get the constant, because the constant is just the length of the spring with the weight on it, and the spring stretches more then just 0.305m, speacialy if i drop it from 10m up.
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Please help me.
**Conclusion**
29N/m is (to me) a useless value and have no idea on how to get the length of string so that my "jumper" does not die.


Notes: i tried to make this as clear as possible.

Why i need help: Because i would like to know how bungee jumping works. (presentation in english class, need to understand all of it and not just read stuff on google.)

it is a demonstration so please help me i don't want to look like a fool infront of my class when my "jumper" hits the floor.

 

[JaWiB]

The spring constant tells you the force exerted by the spring given a certain amount of elongation. It also appears in the equation for potential energy stored in the spring:
F = kx
U = .5kx^2

Since total energy must be conserved, the gravitational potential energy that the "jumper" has before he jumps is equal to the energy stored in the bungee cord when he stops for a moment at the bottom (assuming none of his energy goes elsewhere). Since both the change in gravitational potential energy and the change in energy stored in the spring are related to the change in the jumper's height, you can set up equations and solve for the total distance he falls before stopping.

Keep in mind that real bungee cords probably don't follow Hooke's law.

 

[Whitetiger101]

Thank you very much.