What is the spring constant for the bungee cord used in the given scenario?

[Bryson Stevens]

Homework Statement

A 84.0-kg bungee jumper steps off a bridge with a light bungee cord tied to her and to the bridge. The unstretched length of the cord is 15.0 m. The jumper reaches reaches the bottom of her motion 38.0 m below the bridge before bouncing back. We wish to find the time interval between her leaving the bridge and her arriving at the bottom of her motion. Her overall motion can be separated into an 15.0-m free-fall and a 23.0-m section of simple harmonic oscillation.

Homework Equations

KE = 1/2mv^2
Uk = 1/2kx^2
f = 1/2pi sqrt(k/m)

The Attempt at a Solution

I have already determined the amount of time the jumper spends in free fall using basic kinematics. My question is how to calculate the spring constant. Is there a way to pull the angular frequency out of this situation, if so the equation f = 1/2pi sqrt(k/m) would make it easy, or do you have to use the various energies 1/2mv^2 and 1/2kx^2 to find the spring constant?

Thanks in advance.

 

[JeremyG]

do you have to use the various energies 1/2mv^2 and 1/2kx^2 to find the spring constant?

Yes, this would be the most direct way of obtaining the spring constant k. Have you tried this?

 

[Bryson Stevens]

I tried that by setting the kinetic energy due to gravity equal to the potential energy in the spring and did not get the correct answer.

 

[JeremyG]

What was your value of k? Can you show us your working?

 

[haruspex]

I tried that by setting the kinetic energy due to gravity equal to the potential energy in the spring and did not get the correct answer.

You don't need involve KE at all to find k.