Hooke's Law: inconsistent spring constants what

[tambourine]

Homework Statement

A 70 kg bungee jumper leaps off a bridge. She is tied to a 12 m long bungee cord and falls a total of 31 m. Calculate:

a) the spring constant of the bungee
b) the maximum acceleration experience by the jumper

Homework Equations

F = kx

Eg = Ee
where g is gravitational potential energy and e is elastic energy

The Attempt at a Solution

at her maximum stretch, force of the "spring"/bungee Fs = Fg = mg

x= 31 - 12 = 19

k= F/x = mg/x
k = 70 (9.81) / 19
k= 36.14

but this number didn't seem right so i did:

let height be zero at maximum stretch

Eg = Ee
mgh = 1/2kx^2
70(9.81)(31) = 1/2k(19)^2
k = 117.9

both methods make perfect sense to me, but the spring constants are different so i must have missed something. what did i do wrong/which method is correct? and how can i find her maximum acceleration?

 

[jamesrc]

If the force of the bungee at maximum stretch were equal to her weight, what would make her bounce back up? Wouldn't she just hang there?

The second method is the correct one; use that value of k for the rest of the problem.

 

[tambourine]

ohhh

so then for part b it would be:

F = ma = kx - mg
70a = 117.9 (19) - 70(9.81)
a = 22.2