= (b) In the figure below, block 1 of mass m₁ slides from rest along a frictionless ramp from height h 2.50 m and then collides with stationary block 2, which has mass m2 = 2.00m₁. After the collision, block 2 slides into a region where the coefficient of kinetic friction k is 0.500 and comes to a stop in distance d within that region. What is the value of distance d if the collision is (a) elastic and (b) completely inelastic? Frictionless 2
= (b) In the figure below, block 1 of mass m₁ slides from rest along a frictionless ramp from height h 2.50 m and then collides with stationary block 2, which has mass m2 = 2.00m₁. After the collision, block 2 slides into a region where the coefficient of kinetic friction k is 0.500 and comes to a stop in distance d within that region. What is the value of distance d if the collision is (a) elastic and (b) completely inelastic? Frictionless 2
College Physics
10th Edition
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Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter6: Momentum And Collisions
Section: Chapter Questions
Problem 29P: a man of mass m1 = 70.0 kg is skating at v1 = 8.00 m/s behind his wife of mass m2 = 50.0 kg, who is...
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![### Problem Description
In the figure below, block 1 of mass \( m_1 \) slides from rest along a frictionless ramp from height \( h = 2.50 \, \text{m} \) and then collides with stationary block 2, which has mass \( m_2 = 2.00m_1 \). After the collision, block 2 slides into a region where the coefficient of kinetic friction \( \mu_k \) is 0.500 and comes to a stop in distance \( d \) within that region. What is the value of distance \( d \) if the collision is:
(a) Elastic
(b) Completely inelastic?
### Diagram Description
The diagram associated with the problem includes the following elements:
- **Frictionless Ramp**: The ramp is curved and smooth, allowing block 1 to slide without any friction.
- **Block 1**: Positioned at the top of the frictionless ramp with height \( h \).
- **Block 2**: Initially stationary and situated at the bottom of the frictionless ramp.
- **Kinetic Friction Region**: After collision, block 2 encounters a rough surface with a kinetic friction coefficient \( \mu_k = 0.500 \).
### Analyzing the Problem
To solve this problem, we need to address two scenarios: elastic collision and completely inelastic collision.
#### (a) **Elastic Collision**
1. **Initial Potential Energy (PE) of Block 1**:
\[ PE = m_1gh \]
2. **Kinetic Energy (KE) at Bottom of Ramp**:
\[ KE = \frac{1}{2}m_1v_1^2 \]
\[ m_1gh = \frac{1}{2}m_1v_1^2 \rightarrow v_1 = \sqrt{2gh} \]
3. **Velocity of Block 1 before Collision**:
\[ v_1 = \sqrt{2 \cdot 9.8 \cdot 2.50} \approx 7 \, \text{m/s} \]
4. **Velocity of Both Blocks after Elastic Collision**:
For an elastic collision:
\[ v_{1f} = \frac{(m_1 - m_2)}{(m_1 + m_2)}v_1 \quad \text{and} \quad v_{2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F701927fd-ceaf-4fad-8338-7d1e3c22653c%2F31eb9e20-7433-4f1e-885b-a7ab8875a949%2Fr67d26u_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Description
In the figure below, block 1 of mass \( m_1 \) slides from rest along a frictionless ramp from height \( h = 2.50 \, \text{m} \) and then collides with stationary block 2, which has mass \( m_2 = 2.00m_1 \). After the collision, block 2 slides into a region where the coefficient of kinetic friction \( \mu_k \) is 0.500 and comes to a stop in distance \( d \) within that region. What is the value of distance \( d \) if the collision is:
(a) Elastic
(b) Completely inelastic?
### Diagram Description
The diagram associated with the problem includes the following elements:
- **Frictionless Ramp**: The ramp is curved and smooth, allowing block 1 to slide without any friction.
- **Block 1**: Positioned at the top of the frictionless ramp with height \( h \).
- **Block 2**: Initially stationary and situated at the bottom of the frictionless ramp.
- **Kinetic Friction Region**: After collision, block 2 encounters a rough surface with a kinetic friction coefficient \( \mu_k = 0.500 \).
### Analyzing the Problem
To solve this problem, we need to address two scenarios: elastic collision and completely inelastic collision.
#### (a) **Elastic Collision**
1. **Initial Potential Energy (PE) of Block 1**:
\[ PE = m_1gh \]
2. **Kinetic Energy (KE) at Bottom of Ramp**:
\[ KE = \frac{1}{2}m_1v_1^2 \]
\[ m_1gh = \frac{1}{2}m_1v_1^2 \rightarrow v_1 = \sqrt{2gh} \]
3. **Velocity of Block 1 before Collision**:
\[ v_1 = \sqrt{2 \cdot 9.8 \cdot 2.50} \approx 7 \, \text{m/s} \]
4. **Velocity of Both Blocks after Elastic Collision**:
For an elastic collision:
\[ v_{1f} = \frac{(m_1 - m_2)}{(m_1 + m_2)}v_1 \quad \text{and} \quad v_{2
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