What is the speed of the box when it is at position x2
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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Question
![## Problem
A block of mass \( m \) is attached to a spring with unstretched length \( l_0 \), as shown. The spring is initially compressed to a length \( x_1 < l_0 \). After being released from rest, the box moves to the right. What is the speed of the box when it is at position \( x_2 \)? Neglect friction and assume the values \( g = 9.81 \, \text{m/s}^2 \), \( m = 1.5 \, \text{kg} \), \( k = 0.2 \, \text{N/m} \), \( l_0 = 0.5 \, \text{m} \), \( x_1 = 0.2 \, \text{m} \), and \( x_2 = 0.6 \, \text{m} \).
### Diagrams
**Compressed Spring Diagram**
- The first diagram shows a spring compressed to length \( x_1 \) with a block of mass \( m \) next to it. The spring is held against a wall, pushing against the block.
**Extended Spring Diagram**
- The second diagram displays the spring extended to length \( x_2 \) with the block of mass \( m \) at the end of the spring. The block has moved to the right from its initial position due to the release of the spring's potential energy.
**Unstretched Spring Diagram**
- This is a smaller illustration of the spring at its natural, unstretched length \( l_0 \).
Note that the figures are labeled with respective positions before and after the spring's release, and annotations indicate the initial compression and later extension points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd23cf25f-e0e1-420e-8dcb-8ea8662c7deb%2Ff1a07af5-773d-4c8b-9604-7621c3619afa%2Fugq423e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Problem
A block of mass \( m \) is attached to a spring with unstretched length \( l_0 \), as shown. The spring is initially compressed to a length \( x_1 < l_0 \). After being released from rest, the box moves to the right. What is the speed of the box when it is at position \( x_2 \)? Neglect friction and assume the values \( g = 9.81 \, \text{m/s}^2 \), \( m = 1.5 \, \text{kg} \), \( k = 0.2 \, \text{N/m} \), \( l_0 = 0.5 \, \text{m} \), \( x_1 = 0.2 \, \text{m} \), and \( x_2 = 0.6 \, \text{m} \).
### Diagrams
**Compressed Spring Diagram**
- The first diagram shows a spring compressed to length \( x_1 \) with a block of mass \( m \) next to it. The spring is held against a wall, pushing against the block.
**Extended Spring Diagram**
- The second diagram displays the spring extended to length \( x_2 \) with the block of mass \( m \) at the end of the spring. The block has moved to the right from its initial position due to the release of the spring's potential energy.
**Unstretched Spring Diagram**
- This is a smaller illustration of the spring at its natural, unstretched length \( l_0 \).
Note that the figures are labeled with respective positions before and after the spring's release, and annotations indicate the initial compression and later extension points.
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