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In a physics lab experiment, one end of a horizontal spring that obeys Hooke's law is attached to a wall. The spring is compressed x = 0.400 m, and a block with mass 0.300 kg is attached to it. The spring is then released, and the block moves along a horizontal surface. Electronic sensors measure the speed of the block after it has traveled a distance d from its initial position against the compressed spring. The measured values are listed in the table below. d (m) v (m/s) 0 0 0.05 0.85 0.10 1.11 0.15 1.24 0.25 1.26 0.30 1.14 0.35 0.90 0.40 0.36

In a physics lab experiment, one end of a horizontal spring that obeys Hooke's law is attached to a wall. The spring is compressed x = 0.400 m, and a block with mass 0.300 kg is attached to it. The spring is then released, and the block moves along a horizontal surface. Electronic sensors measure the speed of the block after it has traveled a distance d from its initial position against the compressed spring. The measured values are listed in the table below. d (m) v (m/s) 0 0 0.05 0.85 0.10 1.11 0.15 1.24 0.25 1.26 0.30 1.14 0.35 0.90 0.40 0.36

College Physics
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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**Problem Statement:** Use the work-energy theorem to derive an expression for \(v^2\) in terms of \(d\). Do not substitute the value of \(x_0\) into the expression. Express your answer in terms of some or all of the variables \(k\), \(m\), \(d\), \(x_0\), \(\mu_k\), and the acceleration due to gravity \(g\). --- **Expression Input:** \[ v^2(t) = \] Submit Request Answer **Graphical Elements:** 1. **Text Box**: Provided for entering the expression. 2. **Buttons/Icons**: - **Clipboard**: Possibly for pasting text. - **Formula**: For inserting structured mathematical expressions. - **Arrow Icons**: Typically represent undo, redo, and refresh actions. - **Question Mark**: For help or additional information. --- **Instruction for Students:** 1. **Apply the Work-Energy Theorem**: - \(\text{KE}_{\text{initial}} + \text{Work}_{\text{done}} = \text{KE}_{\text{final}}\) - Identify the initial and final kinetic energies and the work done on the object. 2. **Define Variables**: - \(k\): Spring constant - \(m\): Mass of the object - \(d\): Displacement - \(x_0\): Initial position - \(\mu_k\): Coefficient of kinetic friction - \(g\): Acceleration due to gravity 3. **Formulate the Expression**: - Use principles of energy conservation and dynamics to connect the given variables. Ensure you input the derived expression correctly into the provided text box before submitting for evaluation. ---
Transcribed Image Text:**Problem Statement:** Use the work-energy theorem to derive an expression for \(v^2\) in terms of \(d\). Do not substitute the value of \(x_0\) into the expression. Express your answer in terms of some or all of the variables \(k\), \(m\), \(d\), \(x_0\), \(\mu_k\), and the acceleration due to gravity \(g\). --- **Expression Input:** \[ v^2(t) = \] Submit Request Answer **Graphical Elements:** 1. **Text Box**: Provided for entering the expression. 2. **Buttons/Icons**: - **Clipboard**: Possibly for pasting text. - **Formula**: For inserting structured mathematical expressions. - **Arrow Icons**: Typically represent undo, redo, and refresh actions. - **Question Mark**: For help or additional information. --- **Instruction for Students:** 1. **Apply the Work-Energy Theorem**: - \(\text{KE}_{\text{initial}} + \text{Work}_{\text{done}} = \text{KE}_{\text{final}}\) - Identify the initial and final kinetic energies and the work done on the object. 2. **Define Variables**: - \(k\): Spring constant - \(m\): Mass of the object - \(d\): Displacement - \(x_0\): Initial position - \(\mu_k\): Coefficient of kinetic friction - \(g\): Acceleration due to gravity 3. **Formulate the Expression**: - Use principles of energy conservation and dynamics to connect the given variables. Ensure you input the derived expression correctly into the provided text box before submitting for evaluation. ---
In a physics lab experiment, one end of a horizontal spring that obeys Hooke's law is attached to a wall. The spring is compressed \( x_0 = 0.400 \, \text{m} \), and a block with mass \( 0.300 \, \text{kg} \) is attached to it. The spring is then released, and the block moves along a horizontal surface. Electronic sensors measure the speed \( v \) of the block after it has traveled a distance \( d \) from its initial position against the compressed spring. The measured values are listed in the table below. | \( d \, (\text{m}) \) | \( v \, (\text{m/s}) \) | |:-----------------------:|:-----------------------:| | 0.00 | 0.00 | | 0.05 | 0.85 | | 0.10 | 1.11 | | 0.15 | 1.24 | | 0.20 | 1.24 | | 0.25 | 1.26 | | 0.30 | 1.14 | | 0.35 | 0.90 | | 0.40 | 0.36 | These measurements illustrate the change in the speed of the block as it travels various distances from the point where the spring was initially compressed.
Transcribed Image Text:In a physics lab experiment, one end of a horizontal spring that obeys Hooke's law is attached to a wall. The spring is compressed \( x_0 = 0.400 \, \text{m} \), and a block with mass \( 0.300 \, \text{kg} \) is attached to it. The spring is then released, and the block moves along a horizontal surface. Electronic sensors measure the speed \( v \) of the block after it has traveled a distance \( d \) from its initial position against the compressed spring. The measured values are listed in the table below. | \( d \, (\text{m}) \) | \( v \, (\text{m/s}) \) | |:-----------------------:|:-----------------------:| | 0.00 | 0.00 | | 0.05 | 0.85 | | 0.10 | 1.11 | | 0.15 | 1.24 | | 0.20 | 1.24 | | 0.25 | 1.26 | | 0.30 | 1.14 | | 0.35 | 0.90 | | 0.40 | 0.36 | These measurements illustrate the change in the speed of the block as it travels various distances from the point where the spring was initially compressed.
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