Notes on using BungeeDuck.xls

This spreadsheet allows students to explore a mathematical model of a bungee jumping duck through graphs of acceleration velocity and displacement as well as elastic gravitational and kinetic energies.

Background: The ideas of energy conservation, Hooke’s law and elastic potential energy.

It could also be used to explore aspects of partial SHM.

Questions for students:

• What are the natural length and modulus of elasticity of the bungee rope?
• What is the mass of the jumper (to the nearest whole number)?
• What modeling assumptions do you think are being made?
• Find the extension of the rope if the bungee jumper was hanging in equilibrium on the rope.
  Call this point E.
• What is happening in the motion at this point?
• Explain the shape of the acceleration graph. What is significant about the points where the acceleration is zero?
• Explain the shape of the velocity graph. What is significant about the points where the velocity is zero?
• Explain why the maximum on the displacement graph corresponds to the minimum on the acceleration graph.
• Explain the shapes and relationship between the energy graphs.
• Calculate the exact value of the maximum velocity.
• Taking x to be the displacement of the duck from E find in terms of x a formula for the resultant force acting on the duck. What does this tell you about the motion?