QUESTION 2

Objectives:

I . identify potential and kinetic energy in a situation and draw corresponding energy bar charts,

II . calculate gravitational and elastic potential energy,

III . draw & analyze potential energy functions, and (d) use conservation of energy to relate the total energy at one time to total energy at another time.



Bungee Jump: you will step off with zero initial vertical velocity from a platform a height h above the ground. The bungee cord will act like a giant extensional spring that will, you hope, provide an upward force on becoming taut. After weighing you (you have a mass M), the operator has selected a bungee cordwith an un-stretched length of d and a spring constant of k.

Consider yourself to be a single point – i. e., use the particle model.

Choosing the ground as your origin (and the z-axis directed upwards), answer the following questions about your bungee jumping adventure in terms of M, h, d, k, z, and the gravitational field strength, g. Answer with variables.



a)

Write an expression for the stretching ?L of the cord in terms of d and z and for the total potential energy U of the jumper-bungee-Earth system for each situation (consider the latter two situations together).

b)

Which type of potential energy ( UG or US ) is largest for large z (early in the fall)? For small z (late in the fall)?

c)

Sketch a graph of your gravitational potential energy, UG(z) vs your height, z, from z = 0 to z = h, on the left plot. Then sketch a graph of your elastic potential energy, US(z) on the center plot. Finally on the rightmost plot, sketch a graph of your total potential energy1 U(z) = UG(z) + US(z). Do these plots on your own without the help of a computer or calculator.