Bungee Jumping With Energy Conservation
- Dave Nero
This simulation plots the mechanical energy of a bungee jumper. The properties of the bungee cord and the mass of jumper are adjustable. Click the play icon in the bottom left corner to begin the jump. Click again to pause. If you want to jump again, click on the "Reset" button. You can change most parameters during the jump, but the results may seem strange, since energy won't be conserved. If you check or uncheck "Bungee Cord Has Mass", you must then click "Reset" for the bungee cord and jumper to be redrawn. Enabling "Bungee Cord Has Mass" requires a lot of processing power and may make the simulation run slowly. By default, previous graphs are kept between jumps, but the "Clear Graphs" button will erase them. Note that the energy graph is auto-scaled, so Etot will always start near the top of the graph, regardless of its numerical value. If your jumper hits the ground or if the acceleration is too large, a warning will appear and the simulation will stop. Try again with different parameters. The symbol K is used for kinetic energy, Ug is used for gravitational potential energy, and Us is used for the elastic (spring) potential energy in the bungee cord. Unlike a spring, it is assumed that the spring constant of the bungee cord is zero when compressed.
- There are three bungee cords to choose from. Each has a different spring constant and mass per length (only applicable if "Bungee Cord Has Mass" is enabled). Can a 40 kg person use any of the three cords? What about a 120 kg person?
- The simplest case is to neglect the mass of the cord and damping. How do each of these inclusions change what happens during the jump? What kind of effect do they have on how far the jumper falls and the maximum acceleration experienced?
- When "Bungee Cord Has Mass" is enabled, there are times when the magnitude of the downward acceleration is larger than 9.8 m/s2. This is a real effect. Why does it happen? (Can you draw a free body diagram?)