- #1

patrickmoloney

- 94

- 4

## Homework Statement

A bungee jumper of mass [itex]m[/itex] attaches a light elastic string to his foot, and the other end to railing of a bridge on which he stands. The string has natural length [itex]l_0[/itex] and modulus of elasticity [itex]\lambda[/itex]. Write down the energy equation. use conservation of energy to find the maximum distance the jumper descends after stepping off the bridge.

## Homework Equations

Gravitational potential energy = [itex]mgh[/itex]

Elastic Potential energy = [itex]\frac{1}{2}kx^2[/itex]

Kinetic energy = [itex]\frac{1}{2}mv^2[/itex]

## The Attempt at a Solution

I understand the principles of energy conversion during a bungee jump. So during the first interval, stepping of the bridge, the only force acting on the system(bungee jumper) is gravity(free fall). As the bungee jumper falls, the gravitational potential energy is converted into kinetic energy. When he reaches the point where the bungee cord begins to stretch, gravitational potential energy begins to be converted into the elastic potential energy of the cord. Eventually, all of the kinetic energy is also converted into potential energy of the cord, and he comes to rest for a short period of time.

I'm not really sure how to write this in mathematics. I can probably make thing easier by setting up a coordinate system with an origin. If I used the origin at [itex]l_0[/itex] below the bridge since that would 0 some terms in the conservation equation.

I found the relationship between the spring constant and elasticity, which is [tex]k = \frac{\lambda}{L}[/tex]

The conservation of energy is [tex]PE_i + KE_i = PE_f + KE_f[/tex]. I'm not really sure how to tie this all together. Do I have to model a differential equation or is it simpler than that?

I apprecitate any help,

Thanks