Engineering
Physics
Conservation of Energy
SHM of Spring Block System
Acceleration
Question

Staring from rest, a 64.0−kg person bungee jumps from a tethered hot air balloon 65.0m above the ground. The bungee cord has negligible mass and unstretched length 25.8m 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 81.N/m and the person's body is modeled as a particle. the hot-air balloon does not move. Plot a graph of the gravitational elastic and total potential energies as functions of y

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Solution
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Goriven mass of person = 64 kg/m
spring constant, = 81 N/m
length of card, ℓ = 25.8 m
Height (Initial) = 65.0 m = H
Gravitational potential energy = mighty)

 Max GPE mgH (GPE)

= 64 × 9.8 × 6= 40768 Joule 

For jumping h decreases, GPE decreases
Elastic porkential energy a stactching of cord Initially stretching is zero; stretching increas EPE also increases.

EPE ∝ → EPE ky

GPE ∝ mg[– h(y)]

GPE EPE = constant 

mg[– h(y)] + ky