Spring Constant? Velocity?

Question

Lincoln goes bungee jumping. He has a mass of 102 kg.

a. After his jump, Lincoln hangs from the cord motionless, with the cord stretched by 15 m. What is the spring constant of the bungee cord?

b. At the bottom of his jump, the cord was stretched 22 m past its natural length. What was Lincoln's velocity when he bounced up far enough to reach the equilibrium point you used in part (a)?

Answer 1

(a)

 

x = displacement from equilibrium = 15 m

 

kx = mg => k = mg / x = (102 kg)(9.8 m/s^2) / (15 m) = 66.64 N/m

 

(b)

 

A = maximum displacement from equilibrium in part (a) = (22 m - 15 m) = 7 m

 

At equilibrium point, spring PE = 0, v is maximum

 

(1/2) mv^2 = (1/2) kA^2

 

v = sqrt[kA^2 / m] = sqrt[(66.64 N/m)((7 m)^2 / (102 kg)] = 5.66 m/s