A certain spring is found not to obey Hooke's law, it exerts a restoring force F.(z) = -az - Bz if it is stretched or compressed, where a = 60.0 N/m and B= 18.0 N/m?. The mass of the spring is negligible. • Part A Calculate the potential energy function U(z) for this spring. Let U=0 when z0. Express your answer in terms of z. ? U(z) = Submit Request Answer • Part B An object with mass 0.900 kg on a frictionless, horizontal surface is attached to this spring. pulled a distance 1.00 m to the right (the +z- direction) to stretch the spring, and released. What is the speed of the object when it is 0.50 m to the right of the z =0 equilibrium position? Express your answer in meters per second. ? v2 = m/s Submit Reguest Answer KReturn to Assignment Provide Feedback
A certain spring is found not to obey Hooke's law, it exerts a restoring force F.(z) = -az - Bz if it is stretched or compressed, where a = 60.0 N/m and B= 18.0 N/m?. The mass of the spring is negligible. • Part A Calculate the potential energy function U(z) for this spring. Let U=0 when z0. Express your answer in terms of z. ? U(z) = Submit Request Answer • Part B An object with mass 0.900 kg on a frictionless, horizontal surface is attached to this spring. pulled a distance 1.00 m to the right (the +z- direction) to stretch the spring, and released. What is the speed of the object when it is 0.50 m to the right of the z =0 equilibrium position? Express your answer in meters per second. ? v2 = m/s Submit Reguest Answer KReturn to Assignment Provide Feedback
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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![### Hooke's Law and Nonlinear Springs
#### Problem Statement:
A certain spring is found not to obey Hooke's law; it exerts a restoring force \( F_{x}(z) = -\alpha z - \beta z^{3} \) if it is stretched or compressed, where \( \alpha = 60.0 \, \text{N/m} \) and \( \beta = 18.0 \, \text{N/m}^2 \). The mass of the spring is negligible.
#### Part A:
**Question:**
Calculate the potential energy function \( U(z) \) for this spring. Let \( U = 0 \) when \( z = 0 \).
**Instruction:**
Express your answer in terms of \( z \).
**Input Field:**
\( U(z) = \) [Input box with mathematical symbols and functions toolbar]
**Submission Button:**
"Submit"
**Request Answer Button:**
"Request Answer"
#### Part B:
**Question:**
An object with mass \( 0.900 \, \text{kg} \) on a frictionless, horizontal surface is attached to this spring, pulled a distance \( 1.00 \, \text{m} \) to the right (the \( +z \)-direction) to stretch the spring, and released. What is the speed of the object when it is \( 0.50 \, \text{m} \) to the right of the \( z = 0 \) equilibrium position?
**Instruction:**
Express your answer in meters per second.
**Input Field:**
\( v_z = \) [Input box with mathematical symbols and functions toolbar] \( \text{m/s} \)
**Submission Button:**
"Submit"
**Request Answer Button:**
"Request Answer"
---
**Footer Section:**
**Buttons:**
"Return to Assignment"
"Provide Feedback"
---
This problem involves understanding the dynamics of a nonlinear spring, specifically requiring the calculation of the potential energy function and subsequently determining the speed of an object attached to the spring. Ensure you thoroughly analyze the force equation given and apply principles of energy conservation for solving Part B.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82e82db8-362b-4865-93d3-f20edd638ab0%2F085c1ccc-0a83-41d3-a303-9911e0b24c7f%2Fxr3w0ba_processed.png&w=3840&q=75)
Transcribed Image Text:### Hooke's Law and Nonlinear Springs
#### Problem Statement:
A certain spring is found not to obey Hooke's law; it exerts a restoring force \( F_{x}(z) = -\alpha z - \beta z^{3} \) if it is stretched or compressed, where \( \alpha = 60.0 \, \text{N/m} \) and \( \beta = 18.0 \, \text{N/m}^2 \). The mass of the spring is negligible.
#### Part A:
**Question:**
Calculate the potential energy function \( U(z) \) for this spring. Let \( U = 0 \) when \( z = 0 \).
**Instruction:**
Express your answer in terms of \( z \).
**Input Field:**
\( U(z) = \) [Input box with mathematical symbols and functions toolbar]
**Submission Button:**
"Submit"
**Request Answer Button:**
"Request Answer"
#### Part B:
**Question:**
An object with mass \( 0.900 \, \text{kg} \) on a frictionless, horizontal surface is attached to this spring, pulled a distance \( 1.00 \, \text{m} \) to the right (the \( +z \)-direction) to stretch the spring, and released. What is the speed of the object when it is \( 0.50 \, \text{m} \) to the right of the \( z = 0 \) equilibrium position?
**Instruction:**
Express your answer in meters per second.
**Input Field:**
\( v_z = \) [Input box with mathematical symbols and functions toolbar] \( \text{m/s} \)
**Submission Button:**
"Submit"
**Request Answer Button:**
"Request Answer"
---
**Footer Section:**
**Buttons:**
"Return to Assignment"
"Provide Feedback"
---
This problem involves understanding the dynamics of a nonlinear spring, specifically requiring the calculation of the potential energy function and subsequently determining the speed of an object attached to the spring. Ensure you thoroughly analyze the force equation given and apply principles of energy conservation for solving Part B.
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