**Problem 6: Bungee Jump Calculation**An 80-kg person does a bungee-jump from a bridge 100 m above a river, using a 30 m long bungee cord. The bungee cord is effectively a spring with a spring constant of 40 N/m. How far above the water’s surface will the person be when the cord reaches its maximum extension?---In this problem, we are tasked with finding the distance a person is above the water when the bungee cord is fully extended. We can use principles from physics, including concepts from gravitational potential energy, spring force, and energy conservation, to solve this.**Key considerations:**1. **Initial Potential Energy:** - Calculate the gravitational potential energy at the start. - \( \text{Potential energy} = m \cdot g \cdot h \) - where \( m = 80 \, \text{kg} \), \( g = 9.8 \, \text{m/s}^2 \), \( h = 100 \, \text{m} \).2. **Spring Potential Energy at Maximum Extension:** - Use Hooke’s law to calculate spring potential energy. - \( \text{Spring potential energy} = \frac{1}{2} \cdot k \cdot x^2 \) - where \( k = 40 \, \text{N/m} \) and \( x \) is the extension of the bungee cord beyond its natural length.3. **Energy Conservation:** - Equate initial potential energy to spring potential energy + remaining gravitational potential energy when the cord is fully extended.**Objective:**- Find \( x \) (the extension).- Calculate the remaining height (\( h_{\text{remaining}} \)) above the water surface.This problem provides an interesting application of energy concepts in a real-world scenario such as bungee jumping, illustrating the conversion of energy types and the utility of mathematical modeling in predicting physical outcomes.

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6. An 80-kg person does a bungee-jump from a bridge 100m above a river, using a 30m long bungee cord. The bungee cord is effectively a spring with a spring constant of 40N/m. How far above the water's surface will the person be when the cord reaches its maximum extension?

6. An 80-kg person does a bungee-jump from a bridge 100m above a river, using a 30m long bungee cord. The bungee cord is effectively a spring with a spring constant of 40N/m. How far above the water's surface will the person be when the cord reaches its maximum extension?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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