Physics Bungee Jump: Recommended Elastic Length & Spring Constant for Open House

[sxr001]

For next year's Physics Open House the Department is planning to set up a bungee jump from

the top of the physics building. Assume that one end of an elastic band will be firmly attached

to the top of the building and the other to the waist of a courageous participant. The

participant will step off the edge of the building to be slowed and brought back up by the

elastic band before hitting the ground (we hope). Estimate the length and spring constant of

the elastic you would recommend using.





This is presented as a Fermi problem so I only need rough approximations, however, I think I am supposed to account for damping effects and I don't really know where to start

 

[kreil]

Estimate some of the basic quantities you will need: the height of the building, the weight of the participant, etc...

Next, think about the fall itself:

(1) The participant of mass m starts from rest at height h above the ground with total potential energy U=mgh. Energy in the system is conserved, so this is the total energy of the system.

(2) The participant freefalls a distance L equal to the length of the bungee. At this point in time the velocity can be found from the kinetic energy, since you know the total energy and the potential energy at this instant.

(3) The bungee begins stretching and introduces a drag force toward the top of the building equal to -kx.

(4) The participant continues falling until the drag force aimed upward cancels with the force due to gravity aimed downward.This is just a start, as you may also want to incorporate the weight of the bungee cord and other factors.

Anyway, hope this helps get you started.

 

[sxr001]

Thank you Kreil, that does help a lot. I hadn't thought of using conservation of energy.
:)