# Starting from rest, a 64.0-kg person bungee jumps from a tethered balloon 65.0 m above the ground…

Starting from rest, a 64.0-kg person bungee jumps from a tethered balloon 65.0 m above the ground (Fig. P8.11). The bungee cord has negligible mass and unstretched length 25.8 m. One end is tied to the basket of the hot-air balloon and the other end to a harness around the persons body. The cord is modeled as a spring that obeys Hookes law with a spring constant of 81.0 N/m, and the persons body is modeled as a particle. The hot-air balloon does not move. (a) Express the gravitational potential energy of the personEarth system as a function of the persons variable height y above the

Starting from rest, a 64.0-kg person bungee jumps from a tethered balloon 65.0 m above the ground (Fig. P8.11). The bungee cord has negligible mass and unstretched length 25.8 m. One end is tied to the basket of the hot-air balloon and the other end to a harness around the persons body. The cord is modeled as a spring that obeys Hookes law with a spring constant of 81.0 N/m, and the persons body is modeled as a particle. The hot-air balloon does not move. (a) Express the gravitational potential energy of the personEarth system as a function of the persons variable height y above the ground. (b) Express the elastic potential energy of the cord as a function of y. (c) Express the total potential energy of the person cordEarth system as a function of y. (d) Plot a graph of the gravitational, elastic, and total potential energies as functions of y. (e) Assume air resistance is negligible. Determine the minimum height of the person above the ground during his plunge. (f) Does the potential energy graph show any equilibrium position or positions? If so, at what elevations? Are they stable or unstable? (g) Determine the jumpers maximum speed.

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