How much work is done by the spring in pushing the block from its initial position at x = -5.00 cm to x = 2.64 cm? %3D

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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### Transcription for Educational Website

**Description:**

A block of mass \( m = 3.98 \, \text{kg} \) is attached to a spring, which is resting on a horizontal frictionless table. The block is pushed into the spring, compressing it by \( 5.00 \, \text{cm} \), and is then released from rest. The spring begins to push the block back toward the equilibrium position at \( x = 0 \, \text{cm} \). 

The graph shows the component of the force (in Newtons) exerted by the spring on the block versus the position of the block (in centimeters) relative to equilibrium. Use the graph to answer the questions.

**Question:**

How much work is done by the spring in pushing the block from its initial position at \( x = -5.00 \, \text{cm} \) to \( x = 2.64 \, \text{cm} \)?

---

**Graph Explanation:**

- **Axes:** 
  - The horizontal axis represents the position \( x \) of the block in centimeters (cm) relative to the equilibrium position, ranging from -5 cm to 5 cm.
  - The vertical axis represents the force \( F_x \) exerted by the spring on the block in Newtons (N), ranging from -6 N to 6 N.

- **Line:** 
  - The graph shows a straight line with a negative slope, indicating the linear relationship between the force exerted by the spring and the position of the block.
  - The line crosses the y-axis at 6 N when \( x = -5 \, \text{cm} \), and decreases to -6 N at \( x = 5 \, \text{cm} \).

This setup illustrates Hooke's Law, where the force exerted by a spring is proportional to the displacement from its equilibrium position, \( F = -kx \), with \( k \) being the spring constant.
Transcribed Image Text:### Transcription for Educational Website **Description:** A block of mass \( m = 3.98 \, \text{kg} \) is attached to a spring, which is resting on a horizontal frictionless table. The block is pushed into the spring, compressing it by \( 5.00 \, \text{cm} \), and is then released from rest. The spring begins to push the block back toward the equilibrium position at \( x = 0 \, \text{cm} \). The graph shows the component of the force (in Newtons) exerted by the spring on the block versus the position of the block (in centimeters) relative to equilibrium. Use the graph to answer the questions. **Question:** How much work is done by the spring in pushing the block from its initial position at \( x = -5.00 \, \text{cm} \) to \( x = 2.64 \, \text{cm} \)? --- **Graph Explanation:** - **Axes:** - The horizontal axis represents the position \( x \) of the block in centimeters (cm) relative to the equilibrium position, ranging from -5 cm to 5 cm. - The vertical axis represents the force \( F_x \) exerted by the spring on the block in Newtons (N), ranging from -6 N to 6 N. - **Line:** - The graph shows a straight line with a negative slope, indicating the linear relationship between the force exerted by the spring and the position of the block. - The line crosses the y-axis at 6 N when \( x = -5 \, \text{cm} \), and decreases to -6 N at \( x = 5 \, \text{cm} \). This setup illustrates Hooke's Law, where the force exerted by a spring is proportional to the displacement from its equilibrium position, \( F = -kx \), with \( k \) being the spring constant.
**Question: What is the maximum speed of the block?**

**Input Field:**

- Maximum speed: [_____________] m/s

*Note for Educational Website:*

This section is designed for users to input their calculated value of the maximum speed of a block, expressed in meters per second (m/s). There are no graphs or diagrams associated with this input field.
Transcribed Image Text:**Question: What is the maximum speed of the block?** **Input Field:** - Maximum speed: [_____________] m/s *Note for Educational Website:* This section is designed for users to input their calculated value of the maximum speed of a block, expressed in meters per second (m/s). There are no graphs or diagrams associated with this input field.
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