Question

A bungee cord is 30.0 {\rm m} long and, when stretched a distance x, it exerts a restoring force of magnitude kx. Your father-in-law (mass 92.0 kg) stands on a platform 45.0 {\rm m} above the ground, and one end of the cord is tied securely to his ankle and the other end to the platform. You have promised him that when he steps off the platform he will fall a maximum distance of only 41.0 {\rm m} before the cord stops him. You had several bungee cords to select from, and you tested them by stretching them out, tying one end to a tree, and pulling on the other end with a force of 380 N.When you do this, what distance will the bungee cord that you should select have stretched?

Answer 1

d = 0.62m

Step-by-step explanation:

To figure out the distance the bungee cord will stretch, you have to find the spring constant k of the cord. To find the spring constant, I will use the concept of energy conservation.

The energy with the father in law on the platform at height h₁:

(1)
`E=mgh_1`

The energy with him at the lowest point h₂:

(2)
`E=mgh_2+(1)/(2)kx^2`

Setting both equations equal and solving for k:

`k=(h_1-h_2)(2mg)/(x^2)`

The distance d the bungee cord will stretch with a force F:

`d = (F)/(k)=(Fx^2)/(2mg(h_1-h_2))`