Question

Q.2 Imagine a bungee jumper stepping out of a platform initially with kinetic zero energy. Let us take the system to be the bungee jumper, the bungee cord and the Earth and let us assume that the thermal energy of the system do not change during the jump.

MODEL:

We can treat the bungee jumper as a particle.

The bungee cord is a perfect spring of zero mass, spring constant k and position at rest ye.

The system is taken to be the bungee jumper, the bungee cord and the Earth.

The coordinate system has y pointing up and the ground is taken to be y = 0.

Drag is negligible

A. You have a bit of a debate with friends about when you begin to slow down: as soon as the bungee cord “kicks in” (starts pulling on you) or sometime later in your fall. Using free-body diagrams and Newton’s Second Law, construct an argument to answer this question.

B. Write an expression for the stretching ??of the cord and for the total potential energy ? of the jumper-bungee-Earth system in terms of ℎ,?,? and ? before and after the bungee cord “kick in”.

C. What is the total energy of the system ???? during the jump? (It should be one very simple expression that’s valid for your entire trip. Use only ?,ℎ,?,? and ? as necessary.)

D. Write a conservation of energy equation that you could use to solve for your speed ?at any point ?for which the bungee cord has begun to stretch. (You don’t need to solve for?as long as you see that it could be done using your expression.)

Answer 1