Question

It’s your birthday, and to celebrate you’re going to make your first bungee jump. You stand on a bridge 100 m above a raging river and attach a 30-m-long bungee cord to your harness. A bungee cord, for practical purposes, is just a long spring, and this cord has a spring constant of 40 N/m. Assume that your mass is 80 kg. After a long hesitation, you dive off the bridge. How far are you above the water when the cord reaches its maximum elongation?

Answer 1

Answer:

$X'=50.4\,m$

Explanation:

Given that:

Height of jump, $h=100\,m$

length of elastic cord, $l=30\,m$

spring constant of the cord, $k=40\,N.m^{-1}$

mass of the body that jumps, $m=80\,kg$

Force on the bungee elastic cord:

$F=m.g$

$F=80\times 9.8$

Now this force F will be responsible for the elongation in the elastic cord, so:

$F=k.x$ ............................(1)

where :

k = spring constant

x = extension in the elastic cord

using eq. (1)

$80\times 9.8=40\times x$

$x=19.6\,m$

So the cord stretches 19.6 meters more beyond its original length of 30 meters.

Hence, the remaining distance from the river surface at the bottom is:

$X'=100-(30+19.6)$

$X'=50.4\,m$