### Educational Scenario: A Box on Frictional Floors**Concept:** This example involves a box moving across a series of frictional floors, illustrating principles of kinetic friction and energy dissipation.#### Scenario ExplanationA box with mass \( m = 2 \) kg enters a region where the floor is divided into frictional patches, each with a different coefficient of kinetic friction. The initial speed of the box \( v_0 \) is 10 m/s. Each frictional patch has a length \( d = \frac{10}{19.62} \) meters. The coefficient of kinetic friction for the \( n \)-th patch is denoted as \( \mu_n \).#### Diagram DescriptionThe diagram shows a horizontal surface with the box moving to the right, starting at position \( x = 0 \) with an initial speed \( v_0 \). The floor is divided into segments labeled \( \mu_1, \mu_2, \mu_3, \mu_4, \mu_5, \mu_6, \) and so on, indicating different frictional coefficients. Each segment has a uniform length \( d \), depicted by a double-headed arrow beneath the segments.**Detailed Information:**- The mass of the box: \( m = 2 \) kg- Initial speed of the box: \( v_0 = 10 \) m/s- Length of each frictional patch: \( d = \frac{10}{19.62} \) meters#### Learning Objectives:- **Understand Kinetic Energy:** Determine the initial kinetic energy of the box using the formula: \[ KE = \frac{1}{2} m v^2 \] - **Analyze Energy Dissipation:** Evaluate how the kinetic energy diminishes as the box traverses each patch, knowing that the work done by friction is responsible for energy loss.- **Evaluate Frictional Forces:** Understand how different coefficients of kinetic friction (\( \mu_n \)) affect the motion of the box and the distance traveled before stop.### Non-Included QuestionsNote that questions (a), (b), (c), and (d) in the original image have been omitted for simplicity.This example is designed to assist in understanding basic concepts in physics, particularly kinetic energy and the effect of frictional forces on moving objects.

Answered: Image /qna-images/answer/ca78b3ef-b2ac-4d69-af14-4d99d0d17e4b.jpg

3. Suppose a box enters a region of frictional floors, as seen in Fig. 3. x = 0 μ1 μ₂ M3 M4 με μ6 ← d = 10 The box with mass m = 2 kg enters the region with initial speed vo m/s. Each of the frictional patches has a length of d (10/19.62) m. The n-th frictional patch has a coefficient of kinetic friction given by n. = (a) What is the initial kinotic energy of the box? (b) 0.3 for all, how faroes the black travel before stopping? Find the thermal energy of the system at the end of each patch traversed Do the same if un (d) Do the same if µn = (10/11)". (Does this one ever stop?) m Vo

3. Suppose a box enters a region of frictional floors, as seen in Fig. 3. x = 0 μ1 μ₂ M3 M4 με μ6 ← d = 10 The box with mass m = 2 kg enters the region with initial speed vo m/s. Each of the frictional patches has a length of d (10/19.62) m. The n-th frictional patch has a coefficient of kinetic friction given by n. = (a) What is the initial kinotic energy of the box? (b) 0.3 for all, how faroes the black travel before stopping? Find the thermal energy of the system at the end of each patch traversed Do the same if un (d) Do the same if µn = (10/11)". (Does this one ever stop?) m Vo

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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Concept explainers

Static and Kinetic Friction

Kinetic friction comes into existence when there are moving surfaces means in other words we can say that the force which comes into existing between moving surfaces is known as kinetic friction.

Question

### Educational Scenario: A Box on Frictional Floors

**Concept:** This example involves a box moving across a series of frictional floors, illustrating principles of kinetic friction and energy dissipation.

#### Scenario Explanation

A box with mass \( m = 2 \) kg enters a region where the floor is divided into frictional patches, each with a different coefficient of kinetic friction. The initial speed of the box \( v_0 \) is 10 m/s. Each frictional patch has a length \( d = \frac{10}{19.62} \) meters. The coefficient of kinetic friction for the \( n \)-th patch is denoted as \( \mu_n \).

#### Diagram Description

The diagram shows a horizontal surface with the box moving to the right, starting at position \( x = 0 \) with an initial speed \( v_0 \). The floor is divided into segments labeled \( \mu_1, \mu_2, \mu_3, \mu_4, \mu_5, \mu_6, \) and so on, indicating different frictional coefficients. Each segment has a uniform length \( d \), depicted by a double-headed arrow beneath the segments.

**Detailed Information:**
- The mass of the box: \( m = 2 \) kg
- Initial speed of the box: \( v_0 = 10 \) m/s
- Length of each frictional patch: \( d = \frac{10}{19.62} \) meters

#### Learning Objectives:

- **Understand Kinetic Energy:**
Determine the initial kinetic energy of the box using the formula:
\[ KE = \frac{1}{2} m v^2 \]

- **Analyze Energy Dissipation:**
Evaluate how the kinetic energy diminishes as the box traverses each patch, knowing that the work done by friction is responsible for energy loss.

- **Evaluate Frictional Forces:**
Understand how different coefficients of kinetic friction (\( \mu_n \)) affect the motion of the box and the distance traveled before stop.

### Non-Included Questions

Note that questions (a), (b), (c), and (d) in the original image have been omitted for simplicity.

This example is designed to assist in understanding basic concepts in physics, particularly kinetic energy and the effect of frictional forces on moving objects.

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