The 15 kg block A slides on the surface for which coefficient of kinetic friction is 0.3. The block has a velocity of 11 m/s when it is a distance, s, that is 4 m from the 10 kg block B. The unstretched spring has a stiffness of 1000 N/m. The coefficient of restitution is 0.6. The coefficient of friction is the same for both blocks. Determine the maximum compression of the spring due to the collision. WWW A B
The 15 kg block A slides on the surface for which coefficient of kinetic friction is 0.3. The block has a velocity of 11 m/s when it is a distance, s, that is 4 m from the 10 kg block B. The unstretched spring has a stiffness of 1000 N/m. The coefficient of restitution is 0.6. The coefficient of friction is the same for both blocks. Determine the maximum compression of the spring due to the collision. WWW A B
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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![### Problem Statement
A 15 kg block A slides on a surface with a coefficient of kinetic friction of 0.3. The block has a velocity of 11 m/s when it is at a distance \( s \) of 4 meters from a 10 kg block B. The unstretched spring has a stiffness of 1000 N/m. The coefficient of restitution is 0.6. The coefficient of friction is the same for both blocks. Determine the maximum compression of the spring due to the collision.
### Diagram Explanation
- **Blocks and Surface**: There are two blocks labeled A and B positioned on a flat surface with block B being connected to a fixed wall by a spring with stiffness \( k \).
- **Block A**:
- Mass: 15 kg
- Initial Velocity: 11 m/s
- Distance \( s \): 4 meters from block B
- **Block B**:
- Mass: 10 kg
- **Spring**:
- Stiffness \( k \): 1000 N/m
- Initially unstretched
- **Friction**:
- Coefficient of kinetic friction: 0.3
- Acts on both block A and block B equally
- **Coefficient of Restitution**: 0.6
### Tasks
- Determine the maximum compression of the spring due to the collision.
### Detailed Explanation
First, we need to calculate the initial kinetic energy of block A as it slides towards block B. We will account for the energy lost due to friction over the distance \( s \). Then, we will use the principles of conservation of momentum and energy to analyze the collision between the blocks and the spring compression.
#### Step-by-Step Solution
1. **Initial Kinetic Energy of Block A**:
\[
KE_{A, \text{initial}} = \frac{1}{2} m_A v^2 = \frac{1}{2} \times 15 \, \text{kg} \times (11 \,\text{m/s})^2 = 907.5 \,\text{J}
\]
2. **Work Done by Friction on Block A**:
\[
W_{\text{friction}} = \mu \cdot m_A \cdot g \cdot s = 0.3 \cdot 15 \,\text{kg](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd20dfe5a-a4c1-4793-9f05-a80ad59a67d4%2F5d830329-4d41-498f-aebe-e1f8b75ae8d4%2Fm6aund6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A 15 kg block A slides on a surface with a coefficient of kinetic friction of 0.3. The block has a velocity of 11 m/s when it is at a distance \( s \) of 4 meters from a 10 kg block B. The unstretched spring has a stiffness of 1000 N/m. The coefficient of restitution is 0.6. The coefficient of friction is the same for both blocks. Determine the maximum compression of the spring due to the collision.
### Diagram Explanation
- **Blocks and Surface**: There are two blocks labeled A and B positioned on a flat surface with block B being connected to a fixed wall by a spring with stiffness \( k \).
- **Block A**:
- Mass: 15 kg
- Initial Velocity: 11 m/s
- Distance \( s \): 4 meters from block B
- **Block B**:
- Mass: 10 kg
- **Spring**:
- Stiffness \( k \): 1000 N/m
- Initially unstretched
- **Friction**:
- Coefficient of kinetic friction: 0.3
- Acts on both block A and block B equally
- **Coefficient of Restitution**: 0.6
### Tasks
- Determine the maximum compression of the spring due to the collision.
### Detailed Explanation
First, we need to calculate the initial kinetic energy of block A as it slides towards block B. We will account for the energy lost due to friction over the distance \( s \). Then, we will use the principles of conservation of momentum and energy to analyze the collision between the blocks and the spring compression.
#### Step-by-Step Solution
1. **Initial Kinetic Energy of Block A**:
\[
KE_{A, \text{initial}} = \frac{1}{2} m_A v^2 = \frac{1}{2} \times 15 \, \text{kg} \times (11 \,\text{m/s})^2 = 907.5 \,\text{J}
\]
2. **Work Done by Friction on Block A**:
\[
W_{\text{friction}} = \mu \cdot m_A \cdot g \cdot s = 0.3 \cdot 15 \,\text{kg
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