Physics in New Guinness World Record

Physics in New Guinness World Record

This week when I was laying around at home I was scrolling my Facebook feed and came across a video of a new Guinness World Record that was recently set.  A man from the United Kingdom completed the highest bungee dunk.  After watching the video, the first thing that came to mind was the amount of physics that was involved in order to precisely land this jump.

https://www.youtube.com/watch?v=xIvUYlXUD3c

The physics principles that are involved are conservation of mechanical energy and springs.
It says that the total jump was 73.41 m, the man weighs approximately 95 kg, and the spring coefficient of the bungee cord is 60 N/m and the unstretched length is 20 m.

We can figure out the equilibrium length if the man is just hanging on it:

mg/k = (95 kg)(9.8 m/s)/60 N/m = 15.5 m

We can also figure out what his fastest speed will be:

mgho = 1/2 mv^2 + mghm + 1/2 kx^2

(95 kg)(9.8m /s^2 )(73.41m) = 1/2 (95 kg) v^2 +(95kg)(9.8m /s^2 )(73.41m − 20m − 15.5m )+ 1/2(60N/m)(15.5)^2

v= 23.3 m/s or 52.2 mph

We can also figure out how far from the ground he will be:

mgho = 1/2 kx^2 + mghm

(95kg)(9.8m/s^2 )(73.41m) = 1/2(60 N/m)(x)^2 +(95kg)(9.8m/s^2 )(73.41m − 20m − x)
0=17.5x^2-931x-18620
x=44.9 m + 20 =64.9 m --> 8.51 m off the ground

His Max acceleration:
Fmax = mamax = −kx − mg = −(60N ×(−44.9m)) −(95kg× 9.8m/s^2 ) = 1763 N
F = ma → (95kg)a = 1763N → a = 18.6 m/s^2
or 3.8 g's