Teaching Physics with the Physics Suite Edward F. Redish Problems Sorted by Type | Problems Sorted by Subject | Problems Sorted by Chapter in UP

The bungee jumper

 On a visit to New Zealand, I watched a woman bungee jumping from a high bridge. In this activity, an operator attaches an elastic rope to the jumper. The jumper then jumps off the bridge. She falls freely until she reaches the unstretched length of the rope. Then, the rope begins to stretch and slow her to a stop. It yanks her back up and she oscillates up and down for a while. When she is nearly stopped, the operator of the jump pulls on the elastic rope and hauls her back up to the bridge. In order to use common symbols, let’s call the jumper’s mass, m, the unstretched length of the rope, L0, the height of the bridge above the water, H, the elastic constant of the rope, k, and the gravitational field strength, g.

a) Write an expression for the energy of the jumper-rope system in terms of symbols that can be used to describe her descent.

b) How fast is she falling when she reaches the length of the unstretched rope?

c) The approximate values of the symbols for this case are: m = 50 kg, L0 = 8 m, H = 150 m, and g = 10 N/kg. If the elastic rope stretches an extra 4 m to bring her to a stop, what is its spring constant, k?