#10 In the figure, block 1 of mass m1 slides from rest along a frictionless ramp from height h = 3.4 m and then collides with stationary block 2, which has mass m2 = 2m1. After the collision, block 2 slides into a region where the coefficient of kinetic friction μk is 0.15 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

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In the figure, block 1 of mass m1 slides from rest along a frictionless ramp from height h = 3.4 m and then collides with stationary block 2, which has mass m2 = 2m1. After the collision, block 2 slides into a region where the coefficient of kinetic friction μk is 0.15 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?

 

### Understanding Motion and Friction: Educational Diagram

This diagram illustrates a physical scenario involving motion and friction, which is ideal for demonstrating concepts in physics.

1. **Setup Description**:
   1.1. **Block 1 (Initial Position)**: A blue block, labeled as "1", rests at the top of a curved, frictionless ramp. The vertical height from the ground to this position is denoted as \( h \).
   1.2. **Frictionless Region**: The curved ramp and the area immediately following it are marked as "frictionless," meaning no frictional forces act on the block as it descends or moves forward initially.
   1.3. **Block 2 (Ground Position)**: A yellow block, labeled as "2", is placed on a flat surface that starts just after the frictionless region. This surface is characterized by a coefficient of kinetic friction, \( \mu_k \).

2. **Diagram Explanation**:
   2.1. **Curved Ramp**: The path followed by Block 1 is initially a curved incline. This section is marked "Frictionless", indicating no frictional forces act on the block while it is on this part of the path.
   2.2. **Flat Surface with Friction**: Beyond the frictionless region, the flat surface is rough, signified by the presence of the coefficient of kinetic friction (\( \mu_k \)). Block 2 rests on this surface, and any object moving over it will experience a frictional force that opposes its motion.

3. **Physical Concepts**:
   3.1. **Energy Conservation**: As Block 1 descends the ramp, its potential energy (\( mgh \), where \( m \) is mass, \( g \) is gravitational acceleration, and \( h \) is height) converts into kinetic energy.
   3.2. **Frictional Forces**: When Block 1 transitions from the frictionless ramp to the surface with kinetic friction (\( \mu_k \)), it encounters a resistive force proportional to \( \mu_k \), reducing its kinetic energy.

Understanding this diagram helps illustrate fundamental principles in mechanics, including energy conversion, the effect of frictional forces, and the dynamics of motion on curved and flat surfaces.
Transcribed Image Text:### Understanding Motion and Friction: Educational Diagram This diagram illustrates a physical scenario involving motion and friction, which is ideal for demonstrating concepts in physics. 1. **Setup Description**: 1.1. **Block 1 (Initial Position)**: A blue block, labeled as "1", rests at the top of a curved, frictionless ramp. The vertical height from the ground to this position is denoted as \( h \). 1.2. **Frictionless Region**: The curved ramp and the area immediately following it are marked as "frictionless," meaning no frictional forces act on the block as it descends or moves forward initially. 1.3. **Block 2 (Ground Position)**: A yellow block, labeled as "2", is placed on a flat surface that starts just after the frictionless region. This surface is characterized by a coefficient of kinetic friction, \( \mu_k \). 2. **Diagram Explanation**: 2.1. **Curved Ramp**: The path followed by Block 1 is initially a curved incline. This section is marked "Frictionless", indicating no frictional forces act on the block while it is on this part of the path. 2.2. **Flat Surface with Friction**: Beyond the frictionless region, the flat surface is rough, signified by the presence of the coefficient of kinetic friction (\( \mu_k \)). Block 2 rests on this surface, and any object moving over it will experience a frictional force that opposes its motion. 3. **Physical Concepts**: 3.1. **Energy Conservation**: As Block 1 descends the ramp, its potential energy (\( mgh \), where \( m \) is mass, \( g \) is gravitational acceleration, and \( h \) is height) converts into kinetic energy. 3.2. **Frictional Forces**: When Block 1 transitions from the frictionless ramp to the surface with kinetic friction (\( \mu_k \)), it encounters a resistive force proportional to \( \mu_k \), reducing its kinetic energy. Understanding this diagram helps illustrate fundamental principles in mechanics, including energy conversion, the effect of frictional forces, and the dynamics of motion on curved and flat surfaces.
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