Question

A bungee jumper jumps (with no initial speed) from a tall bridge attached to a light elastic cord (bungee cord) of unstretched length L. The cord first straightens and then extends as the jumper falls. This prevents her from hitting the water! Suppose that the bungee cord behaves like a spring with spring constant k = 90 N/m. The bridge is h = 100 m high and the jumper's mass is m = 65 kg. Use g = 10 m/s2.
(a) What is the maximum allowed length L of the unstretched bungee cord (in m) to keep the jumper alive? (Assume that the spring constant doesn't depend on L)
(b) Before jumping, our jumper verified the spring constant of the cord. She lowered herself very slowly from the bridge to the full extent of the cord and when she is at rest she measured the distance to the water surface. What was the measured distance (in m)?

Answer 1

a) assuming hitting the water equals death,

energy equations

The change in potential energy of the jumper will equal the change in spring potential energy of the cord.

PE = PS

mgh = ½kx²

x = √(2mgh / k)

x = √(2(55)10(90) /100)

x = 31.5 m

the maximum drop will equal the stretch in the cord length plus the un-stretched cord length

h = L + x
L = h - x
L = 90 - 31.5
L = 58.5 m


b)
F = ma
F = kx
mg = kx
x = mg/k
x = 55(10) / 100
x = 5.5 m

d = 90 - (58.5 + 5.5)
d = 26 m