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Learning Goal: A bungee jumper wants to jump off the edge of a bridge that spans a river below. The jumper has a mass m, and the surface of the bridge is a height h above the water. The bungee cord, which has length L when unstretched, will first straighten and then stretch as the jumper falls. Assume the following: . The bungee cord behaves as an ideal spring once it begins to stretch and has spring constant k. The jumper does not actually jump but simply steps off the edge of the bridge and falls straight downward. The jumper's height is negligible compared to the length of the bungee cord. Thus, the jumper can be treated as a point particle.

Learning Goal: A bungee jumper wants to jump off the edge of a bridge that spans a river below. The jumper has a mass m, and the surface of the bridge is a height h above the water. The bungee cord, which has length L when unstretched, will first straighten and then stretch as the jumper falls. Assume the following: . The bungee cord behaves as an ideal spring once it begins to stretch and has spring constant k. The jumper does not actually jump but simply steps off the edge of the bridge and falls straight downward. The jumper's height is negligible compared to the length of the bungee cord. Thus, the jumper can be treated as a point particle.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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### Part B - The Spring Constant of the Bungee Cord **Question:** If the jumper just touches the surface of the river on the first downward trip (i.e., before the first bounce), what is the spring constant \(k\)? Ignore all dissipative forces. **Express your answer in terms of \(L\), \(h\), \(m\), and \(g\).** **Solution Input Area:** Below the question prompt, there is an input field where the solution can be entered. The input area includes the following options: - **Equation editor buttons**: These include symbols and functions useful for writing equations, such as: - **\(\sqrt{} \) (Square root)** - **\(\sum\) (Summation)** - **\(\int\) (Integral)** - **\(\vec{}\)** (Vector notation) - **\(\infty\)** (Infinity) - Various Greek letters (e.g., \(\alpha\), \(\beta\), \(\gamma\)) - **Text and symbols** buttons for variable names and other characters Below the input area, there is a "Submit" button that allows the user to submit their answer for grading. **Diagrams and Graphs:** There are no diagrams or graphs directly shown in this image. The question purely revolves around theoretical calculation and expression using the given symbols and constants. **User Interface Elements:** - **Correct**: This text with a check mark indicates that a part of the question has already been completed correctly. - **View Available Hint(s)**: Clicking on this expands hints that may help solve the problem. - **Provide Feedback**: This option allows users to give feedback on the problem or the interface. - **Next >**: The button to proceed to the next question or section. **Miscellaneous:** - On the bottom of the screen, there are laptop widgets showing that various applications are open, including the Start menu, browser, messaging apps, and system settings. The time and date also indicate that this screenshot was taken at 10:07 PM on 6/25/2022. **Notes:** Please ensure to use classical mechanics principles, such as conservation of energy or Hooke’s law, to derive the expression for the spring constant \(k\) in terms of the given parameters.
Transcribed Image Text:### Part B - The Spring Constant of the Bungee Cord **Question:** If the jumper just touches the surface of the river on the first downward trip (i.e., before the first bounce), what is the spring constant \(k\)? Ignore all dissipative forces. **Express your answer in terms of \(L\), \(h\), \(m\), and \(g\).** **Solution Input Area:** Below the question prompt, there is an input field where the solution can be entered. The input area includes the following options: - **Equation editor buttons**: These include symbols and functions useful for writing equations, such as: - **\(\sqrt{} \) (Square root)** - **\(\sum\) (Summation)** - **\(\int\) (Integral)** - **\(\vec{}\)** (Vector notation) - **\(\infty\)** (Infinity) - Various Greek letters (e.g., \(\alpha\), \(\beta\), \(\gamma\)) - **Text and symbols** buttons for variable names and other characters Below the input area, there is a "Submit" button that allows the user to submit their answer for grading. **Diagrams and Graphs:** There are no diagrams or graphs directly shown in this image. The question purely revolves around theoretical calculation and expression using the given symbols and constants. **User Interface Elements:** - **Correct**: This text with a check mark indicates that a part of the question has already been completed correctly. - **View Available Hint(s)**: Clicking on this expands hints that may help solve the problem. - **Provide Feedback**: This option allows users to give feedback on the problem or the interface. - **Next >**: The button to proceed to the next question or section. **Miscellaneous:** - On the bottom of the screen, there are laptop widgets showing that various applications are open, including the Start menu, browser, messaging apps, and system settings. The time and date also indicate that this screenshot was taken at 10:07 PM on 6/25/2022. **Notes:** Please ensure to use classical mechanics principles, such as conservation of energy or Hooke’s law, to derive the expression for the spring constant \(k\) in terms of the given parameters.
**Bungee Jumping** **Learning Goal:** A bungee jumper wants to jump off the edge of a bridge that spans a river below. The jumper has a mass \( m \), and the surface of the bridge is a height \( h \) above the water. The bungee cord, which has length \( L \) when unstretched, will first straighten and then stretch as the jumper falls. **Assume the following:** - The bungee cord behaves as an ideal spring once it begins to stretch and has spring constant \( k \). - The jumper does not actually jump but simply steps off the edge of the bridge and falls straight downward. - The jumper's height is negligible compared to the length of the bungee cord. Thus, the jumper can be treated as a point particle. **Use \( g \) for the magnitude of the acceleration due to gravity**
Transcribed Image Text:**Bungee Jumping** **Learning Goal:** A bungee jumper wants to jump off the edge of a bridge that spans a river below. The jumper has a mass \( m \), and the surface of the bridge is a height \( h \) above the water. The bungee cord, which has length \( L \) when unstretched, will first straighten and then stretch as the jumper falls. **Assume the following:** - The bungee cord behaves as an ideal spring once it begins to stretch and has spring constant \( k \). - The jumper does not actually jump but simply steps off the edge of the bridge and falls straight downward. - The jumper's height is negligible compared to the length of the bungee cord. Thus, the jumper can be treated as a point particle. **Use \( g \) for the magnitude of the acceleration due to gravity**
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