A spring and block are in the arrangement of the figure. When the block is pulled out to x = +4.0 cm, we must apply a force of magnitude 360 N to hold it there. We pull the block to x = 12.0 cm and then release it. How much work does the spring do on the block when the block moves from x₁ = +5.0 cm to (a) x = +3.0 cm, (b) x = -3.0 cm, (c) x= -5.0 cm, and (d) x = -9.0 cm? F=0 vooooooo x positive F negative ooo mom 0 (a) (b) (c) d Block attached to spring x negative F, positive ·x x x
A spring and block are in the arrangement of the figure. When the block is pulled out to x = +4.0 cm, we must apply a force of magnitude 360 N to hold it there. We pull the block to x = 12.0 cm and then release it. How much work does the spring do on the block when the block moves from x₁ = +5.0 cm to (a) x = +3.0 cm, (b) x = -3.0 cm, (c) x= -5.0 cm, and (d) x = -9.0 cm? F=0 vooooooo x positive F negative ooo mom 0 (a) (b) (c) d Block attached to spring x negative F, positive ·x x x
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter9: Energy In Nonisolated Systems
Section: Chapter Questions
Problem 38PQ
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![### Understanding the Work Done by a Spring on a Block
#### Setup Description:
A spring and block are illustrated in the setup shown in the image. When the block is pulled out to \( x = +4.0 \, \text{cm} \), a force of magnitude \( 360 \, \text{N} \) must be applied to hold it in place. The block is then pulled to \( x = 12.0 \, \text{cm} \) and released.
### Key Questions:
1. How much work does the spring do on the block when the block moves from \( x_i = +5.0 \, \text{cm} \) to:
- (a) \( x = +3.0 \, \text{cm} \)
- (b) \( x = -3.0 \, \text{cm} \)
- (c) \( x = -5.0 \, \text{cm} \)
- (d) \( x = -9.0 \, \text{cm} \)
### Diagrams:
#### Diagram (a):
- Position: \( x = 0 \)
- Description: The block is at rest at the equilibrium position where \( F_s = 0 \) (no spring force is acting on the block).
![Diagram (a)](https://linktodiagram)
#### Diagram (b):
- Position: \( 0 < x < 12.0 \, \text{cm} \)
- Description: The block is pulled in the positive \( x \)-direction. Here, \( x \) is positive and the spring force \( F_s \) is negative, opposing the direction of the applied force.
![Diagram (b)](https://linktodiagram)
#### Diagram (c):
- Position: \( x < 0 \)
- Description: The block is pushed in the negative \( x \)-direction. Here, \( x \) is negative and the spring force \( F_s \) is positive, again opposing the direction of applied force.
![Diagram (c)](https://linktodiagram)
#### Diagram (d):
- Position: \( x < 0 \)
- Description: The block is further pushed in the negative \( x \)-direction beyond the position in Diagram (c), resulting in a more significant positive spring force \( F_s \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18107b7c-8d8e-412b-a2cd-6addf4186be2%2F957cde0e-1f21-4329-aae2-4b93d6ac432e%2Fpa6hg5c_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding the Work Done by a Spring on a Block
#### Setup Description:
A spring and block are illustrated in the setup shown in the image. When the block is pulled out to \( x = +4.0 \, \text{cm} \), a force of magnitude \( 360 \, \text{N} \) must be applied to hold it in place. The block is then pulled to \( x = 12.0 \, \text{cm} \) and released.
### Key Questions:
1. How much work does the spring do on the block when the block moves from \( x_i = +5.0 \, \text{cm} \) to:
- (a) \( x = +3.0 \, \text{cm} \)
- (b) \( x = -3.0 \, \text{cm} \)
- (c) \( x = -5.0 \, \text{cm} \)
- (d) \( x = -9.0 \, \text{cm} \)
### Diagrams:
#### Diagram (a):
- Position: \( x = 0 \)
- Description: The block is at rest at the equilibrium position where \( F_s = 0 \) (no spring force is acting on the block).
![Diagram (a)](https://linktodiagram)
#### Diagram (b):
- Position: \( 0 < x < 12.0 \, \text{cm} \)
- Description: The block is pulled in the positive \( x \)-direction. Here, \( x \) is positive and the spring force \( F_s \) is negative, opposing the direction of the applied force.
![Diagram (b)](https://linktodiagram)
#### Diagram (c):
- Position: \( x < 0 \)
- Description: The block is pushed in the negative \( x \)-direction. Here, \( x \) is negative and the spring force \( F_s \) is positive, again opposing the direction of applied force.
![Diagram (c)](https://linktodiagram)
#### Diagram (d):
- Position: \( x < 0 \)
- Description: The block is further pushed in the negative \( x \)-direction beyond the position in Diagram (c), resulting in a more significant positive spring force \( F_s \
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