Please Help! A bungee jumper who has a mass of 75.0 kg leaps off a very high pla
ID: 1787285 • Letter: P
Question
Please Help!
A bungee jumper who has a mass of 75.0 kg leaps off a very high platform. A crowd excitedly watches as the jumper free-falls, reaches the end of the bungee cord, then gets "yanked" up by the elastic cord, again and again. One observer measures the time between the low points for the jumper to be 9.50 s. Another observer realizes that simple harmonic motion can be used to describe the process because several of the subsequent bounces for the jumper require 9.50 s also. Finally, the jumper comes to rest a distance of 40 m below the jump point. Calculate the following. (a) the effective spring constant for the elastic bungee cord. (b) its unstretched length (m)
I figured out the constant to be 32.81 N/m, but I can't figure out the unstretched length.
Explanation / Answer
(A) T = 2 pi sqrt(m / k)
9.50 / 2pi = sqrt(75 / k )
k =32.8 N/m
(B) Fnet = kd - m g = 0
32.8 d = 75 x 9.8
d = 22.4
L = L0 + d
40 = L0 + 22.4
L0 = 17.6 m