Question

A bungee jumper with mass 59.5 kg jumps from a high bridge. After arriving at his lowest point, he oscillates up and down, reaching a low point seven more times in 43.0 s . He finally comes to rest 21.5 m below the level of the bridge. a)Estimate the spring stiffness constant of the bungee cord assuming SHM. b)Estimate the unstretched length of the bungee cord assuming SHM.

Answer 1

a). Frequency of oscillation of jumper,

then angular frequency of jumper will be

Now we know that for SHM, angular frequency can be written as

where k= spring stiffness constant

m= mass of jumper= 59.5kg

then using given and calculated values in above,

(ANS)

b). Now lets assume the situation of maximum stretch. At that point Restoring force of the cord will be exactly equal to the Weight of the jumper for that particular moment. Then

  ( where x= maximum stretch)

  

  

Equilibrium Length= 21.5m

Then Unstretched length of the bungee cord= Equilibrium Length - Maximum Stretch

(ANS)