44. Starting from rest, a 64.0-kg person bungee jumps fromQIC a tethered hot-air balloon 65.0 m above the ground. Thebungee cord has negligible mass and unstretched length25.8 m. One end is tied to the basket of the balloon and theother end to a harness around the person's body. The cordis modeled as a spring that obeys Hooke's law with a springconstant of 81.0 N/m, and the person's body is modeled as a particle. The hot-air balloon does not move. (a) Expressthe gravitational potential energy of the person-Earth sys-tem as a function of the person's variable height y above theground. (b) Express the elastic potential energy of the cordas a function of y. (c) Express the total potential energy ofthe person-cord-Earth system as a function of y. (d) Plot agraph of the gravitational, elastic, and total potential ener-gies as functions of y. (e) Assume air resistance is negligible.Determine the minimum height of the person above theground during his plunge. (f) Does the potential energygraph show any equilibrium position or positions? If so, atwhat elevations? Are they stable or unstable? (g) Determinethe jumper's maximum speed.

Since, there is a question with multiple sub-parts posted by you, we will solve the first three…

Answered: 44. Starting from rest, a 64.0-kg…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter7: Conservation Of Energy

Section: Chapter Questions

Problem 78P

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A bungee cord is essentially a very long rubber band that can stretch up to four times its unstretched length. However, its spring constant vanes over its stretch [see Menz, P.G. “The Physics of Bungee Jumping.” The Physics Teacher (November 1993) 31: 483-487]. Take the length of the cord to be along the direction and define the stretch as the length of the cord minus its un-stretched length that is, (see below). Suppose a particular bungee cord has a spring constant, for of and for. (Recall that the of (Recall that the spring constant is the slope of the force versus its stretch (a) What is the tension in the cord when the stretch is 16.7 m (the maximum desired for a given jump)? (b) How much work must be done against the elastic force of the bungee cord to stretch It 16.7 m? Figure 7.16 (credit modification of work by Graeme Churchard)
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