Question

A bungee jumper with mass 63.5 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 40.0 s. He finally comes to rest 28.5 m below the level of the bridge. Calculate the spring stiffness constant AND the unstretched length of the bungee cord. Please help with step by step explanation!

Answer 1

Since he does 8 periods in 40 seconds 1 period takes 40s/8=5s, lets call this T. From formula T=2pii*sqrt(m/k) we can solve k (spring's stiffness constant). k=m/(T^2/(2pii)^2), k=100,275...N/m.

Then F=xk, where F is the stretching force caused by the jumper, F=mg, 63,5kg*9,81m/s^2=622,935N. x is the amount the thing has stretched so x=F/k, x=622,935N/100,275...N/m=6,2122m.

Thereby the cord's original lenght is 28,5m-6,2122...m=22,2877...m.

Correctly rounded ansvers k=100N/m and unstretched lenght 22,3m.