Bungee Cord Force Constant from Work?

[CandyApples]

Homework Statement

A bungee jumper jumps with a mass of 61kg jumps off of a bridge. The massless bungee cord is 25m long and beyond that length acts as a spring. The jumper reaches the lowest point 42.9m below the bridge. Find the force constant which characterizes the bungee cord.

Homework Equations

W = F X d
F = -kx

The Attempt at a Solution

First I calculated the work for mg.
Wmg = 42.9 * 61(9.8) = 25646J

Since the object stops, the object has a net work of zero. So:
-25646 = 17.9 * F
F = -1433N

-1433 = -k(17.9)
k = 80N/m.

This seems far too low, could someone please tell me where my logic is flawed? I think it might be In the assumption that balancing net work accounts for the object stopping but i am not sure.

Thanks in advance!

 

[ehild]

The force exerted by a spring is not constant, as you assumed.

ehild

 

[tomcue]

I would like to point out that the calculation for the force constant of the bungee cord in this scenario may not be accurate. This is because the bungee cord does not act like a typical spring, as it also has the added effect of gravity and the changing acceleration of the jumper as they fall. Additionally, the mass of the bungee cord itself may also affect the calculations.

To accurately determine the force constant of the bungee cord, more information and measurements would be needed, such as the spring constant of the bungee cord itself and the actual distance the bungee cord stretches during the jump.

In conclusion, while the approach taken in this problem may provide a rough estimate of the force constant, it may not be entirely accurate due to the complexities of the bungee cord system. As a scientist, it is important to acknowledge the limitations and uncertainties in our calculations and to continue to seek more accurate and precise methods of measurement.