Starting from rest, a 64.0-kg person bungee jumpsfrom a tethered hot-air balloon 65.0 m
Chapter 8, Problem 80(choose chapter or problem)
Starting from rest, a 64.0-kg person bungee jumpsfrom a tethered hot-air balloon 65.0 m above theground. The bungee cord has negligible mass andunstretched length 25.8 m. One end is tied to thebasket of the balloon and the other end to a harnessaround the persons body. The cord is modeledas a spring that obeys Hookes law with a spring constantof 81.0 N/m, and the persons body is modeledas a particle. The hot-air balloon does not move.(a) Express the gravitational potential energy of thepersonEarth system as a function of the personsvariable height y above the ground. (b) Express theelastic potential energy of the cord as a function ofy. (c) Express the total potential energy of the personcordEarth system as a function of y. (d) Plot agraph of the gravitational, elastic, and total potentialenergies as functions of y. (e) Assume air resistanceis negligible. Determine the minimum height of theperson above the ground during his plunge. (f) Doesthe potential energy graph show any equilibrium positionor positions? If so, at what elevations? Are theystable or unstable? (g) Determine the jumpers maximumspeed.
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