Question

1.A 60.2 kg bungee jumper jumps from a bridge. She is tied to a 13.8 m long bungee cord and falls a total of 34.4 m. Calculate the spring constant k of the bungee cord.

2.Calculate the maximum acceleration experienced by the jumper.

Im stuck on the first because Im not sure which equation is relevant for this situation. I tried using Uel=1/2 kx^2 where Uel is equal to Ugrav but this did not work out.

Also, when I get the answer to 1, Im not sure what to do. All I know is that it's going to be less than gravity due to the spring force.

Answer 1

nevermind #1, i got it, i was using the wrong distance for the gravitational force.

Please help with #2!

Answer 2

1. Since is a dynamic problem, you do NOT just divide the weight M g by the maximum extension (20.6m) to get the spring constant, k. The maximum extension is twice the equilibrium extension. Instead, set the maximum potential energy change
M g * 34.4 m equal to the maximum stored potential energy in the cord at the maximum extension (where V = 0), (1/2) k (20.6 m)^2

k = 2 M g * 34.4/(20.6)^2

2. The net force acting upwards while the rope is being stretched is
k (y - 13.8) - Mg. (y is being measured positive downwards). The maximum upward force is
k*20.6 -Mg. Compute that and divide it by M for the maximum acceleration. It will exceed g.