Shown in the figure below is a block and track system. All locations indicated by solid black lines are frictionless. The region indicated by the tan hash is a patch of friction with coefficient ?k = 0.350 whose length is d = 1.75 meters. A small block of mass m = 0.71 kg is initially at moving toward the right with a velocity of v1 = 6.149 meters/second. The mass rises up the hill of height y2 = 0.49 meters, passes across the frictional region and then compresses the spring which has a spring constant of k = 88.8 N/m.Calculate all the following:The velocity of the mass after the frictional area, v3 = m/sThe maximum compression of the spring, x4 = meters The diagram illustrates a physics problem involving a block of mass \( m \) moving along a track that includes an inclined surface, a section with friction, and a spring.1. **Initial Position and Velocity (Position 1):** - The block of mass \( m \) starts with an initial velocity \( v_1 \) on a horizontal section of the track.2. **Inclined Plane (Position 2):** - The block moves up an inclined plane and reaches position 2, where its velocity is \( v_2 \) (to be determined). The height of the incline is \( y_2 \).3. **Friction Zone (Position 3):** - After descending, the block travels through a horizontal section of the track with friction, covering a distance \( d \). At the end of this section, the block's velocity is \( v_3 \) (to be determined).4. **Spring Compression (Position 4):** - The block finally compresses a spring, coming to rest at position 4. The compression of the spring is \( x_4 \) (to be determined).**Key Elements:**- **Friction:** The frictional force acts over a distance \( d \) and influences the block’s velocity and kinetic energy.- **Spring:** The spring exerts a force opposite to the block’s motion and stores potential energy proportional to the compression distance \( x_4 \).This setup is typically used to explore concepts of energy conservation, frictional force, and spring mechanics in physics.

Answered: Image /qna-images/answer/16993b32-2526-4c00-9739-ca1f192b5b38.jpgThe velocity at 2 is, v2=5.311 m.sThe velocity at 3 is, v3=4.025 m/sThe compression, x4=0.359 m

Answered: Shown in the figure below is a block…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Shown in the figure below is a block and track system. All locations indicated by solid black lines are frictionless. The region indicated by the tan hash is a patch of friction with coefficient ?_k = 0.350 whose length is d = 1.75 meters. A small block of mass m = 0.71 kg is initially at moving toward the right with a velocity of v₁ = 6.149 meters/second. The mass rises up the hill of height y₂ = 0.49 meters, passes across the frictional region and then compresses the spring which has a spring constant of k = 88.8 N/m.

Calculate all the following:

The velocity of the mass after the frictional area, v₃ = m/s
The maximum compression of the spring, x₄ = meters

The diagram illustrates a physics problem involving a block of mass \( m \) moving along a track that includes an inclined surface, a section with friction, and a spring.

1. **Initial Position and Velocity (Position 1):**
- The block of mass \( m \) starts with an initial velocity \( v_1 \) on a horizontal section of the track.

2. **Inclined Plane (Position 2):**
- The block moves up an inclined plane and reaches position 2, where its velocity is \( v_2 \) (to be determined). The height of the incline is \( y_2 \).

3. **Friction Zone (Position 3):**
- After descending, the block travels through a horizontal section of the track with friction, covering a distance \( d \). At the end of this section, the block's velocity is \( v_3 \) (to be determined).

4. **Spring Compression (Position 4):**
- The block finally compresses a spring, coming to rest at position 4. The compression of the spring is \( x_4 \) (to be determined).

**Key Elements:**
- **Friction:** The frictional force acts over a distance \( d \) and influences the block’s velocity and kinetic energy.
- **Spring:** The spring exerts a force opposite to the block’s motion and stores potential energy proportional to the compression distance \( x_4 \).

This setup is typically used to explore concepts of energy conservation, frictional force, and spring mechanics in physics.

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