Heavy vs. Light Bungee Jumpers: Stored Energy Explained

[Sam1234]

Homework Statement

Bungee jumpers use an elastic rope to halt their fall when they are just a short distance from the ground. Using the idea of stored energy, explain whether heavy jumpers should use a shorter or longer length of rope than lighter jumpers.

Homework Equations

W=mg
strain energy = 1/2*k*x

The Attempt at a Solution

The work here is done my the weight of the jumper. We have W=mg. Assume that k is constant for a rope, we have that F=mg=k*Delta x ==> Delta x is larger when m is larger, so the jumper might height the ground. He should use a shorter rope.

This is how i would answer the question, but it doesn't use the concept of stored energy and I was hoping someone could help me with that.

 

[Fightfish]

I don't think the assumption that k remains the same for the longer and shorter ropes is valid. If the ropes are identical in every respect except their length, then their effective k should differ, similar to the case of springs being attached in series.