Starting from rest, a 64.0-kg person bungee jumps from a tethered hot-air balloo

Q: Starting from rest, a 64.0-kg person bungee jumps from a tethered hot-air balloo

(a) Ug = - GM*m/(y+R) G= grav. constant M= mass of earth m=64kg R= Radius of earth g (9.8) can be written as g= GM/(R^2) => GM =g* R^2 So Ug can also be written in terms of 'g' as Ug= - g* R^2*m/(y+R) => Ug= - (627.2* R^2)/(y+R) where, R= Radius of earth. (b) Us = 0 for 40 Us=43.5*(40-y)^2 for 0

ID: 1893794 • Letter: S

Question

Starting from rest, a 64.0-kg person bungee jumps from a tethered hot-air balloon 63.0 m above the ground. The bungee cord has negligible mass and unstretched length 23.0 m. One end is tied to the basket of the balloon and the other end to a harness around the person's body. The cord is modeled as a spring that obeys Hooke's law with a spring constant of 87.0 N/m, and the person's body is modeled as a particle. The hot-air balloon does not move.

(a) Express the gravitational potential energy of the person-Earth system as a function of the person's variable height y above the ground. (Use the following as necessary: y and use 9.8 instead of g. Do not include units in your response.)
Ug =

(b) Express the elastic potential energy of the cord (when stretched) as a function of y. (Use the following as necessary: y and use 9.8 instead of g. Do not include units in your response.)
Us =

(c) Express the total potential energy of the person-cord-Earth system as a function of y. (Use the following as necessary: y and use 9.8 instead of g. Do not include units in your response.)
for y > 40, Ug + Us =
for y < 40, Ug + Us =

(d) Assume air resistance is negligible. Determine the minimum height of the person above the ground during his plunge.

(e) Does the potential energy graph show any equilibrium position or positions? If so, at what elevations? Are they stable or unstable?
There is a ....... equilibrium at y = ........ ?

(f) Determine the jumper's maximum speed.

Explanation / Answer

(a) Ug = - GM*m/(y+R) G= grav. constant M= mass of earth m=64kg R= Radius of earth g (9.8) can be written as g= GM/(R^2) => GM =g* R^2 So Ug can also be written in terms of 'g' as Ug= - g* R^2*m/(y+R) => Ug= - (627.2* R^2)/(y+R) where, R= Radius of earth. (b) Us = 0 for 40 Us=43.5*(40-y)^2 for 0

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Starting from rest, a 64.0 kg person bungee jumps from a tethered balloon h = 65

Starting from rest, a 64.0-kg person bungee jumps from a tethered hot-air balloo

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Starting from rest, a 64.0-kg person bungee jumps from a tethered hot-air balloo

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