A uniform board of length L and mass M lies near a boundary that separates two regions. In region 1, the coefficient of kinetic friction between the board and the surface is , and in region 2, the coefficient is 2. The positive direction is shown in the figure. (Figure 1) Figuro h ▼ Part A Find the net work W done by friction in pulling the board directly from region 1 to region 2. Assume that the board m constant velocity. Express the net work in terms of M, g, L, ₁, and 2- ► View Available Hint(s) W = Submit 15| ΑΣΦ ?

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**Educational Content Transcription**

**Problem Statement:**

A uniform board of length \( L \) and mass \( M \) lies near a boundary that separates two regions. In region 1, the coefficient of kinetic friction between the board and the surface is \( \mu_1 \), and in region 2, the coefficient is \( \mu_2 \). The positive direction is shown in the figure.

**Task:**

**Part A:**

Find the net work \( W \) done by friction in pulling the board directly from region 1 to region 2. Assume that the board moves with constant velocity.

**Express the net work in terms of \( M \), \( g \), \( L \), \( \mu_1 \), and \( \mu_2 \).**

\[ W = \, \]

**Figure Explanation:**

The figure consists of two diagrams labeled "Before" and "After." 

- **Before:** 
  - The board spans both regions, with part of its length \( L \) over region 1 (blue) where the coefficient of friction is \( \mu_1 \), and part over region 2 (orange) where the coefficient of friction is \( \mu_2 \).

- **After:** 
  - The board is shown entirely in region 2, having been moved in the positive direction indicated in the diagram.

**Part B:**

Complete previous part(s)

**Additional Instructions:**

Provide Feedback

---

**Note:** The task involves calculating the work done against friction as the board transitions from one region to another, requiring knowledge of frictional forces and work-energy principles.

**Copyright Information:**

Copyright © 2022 Pearson Education Inc. All rights reserved.

---
Transcribed Image Text:**Educational Content Transcription** **Problem Statement:** A uniform board of length \( L \) and mass \( M \) lies near a boundary that separates two regions. In region 1, the coefficient of kinetic friction between the board and the surface is \( \mu_1 \), and in region 2, the coefficient is \( \mu_2 \). The positive direction is shown in the figure. **Task:** **Part A:** Find the net work \( W \) done by friction in pulling the board directly from region 1 to region 2. Assume that the board moves with constant velocity. **Express the net work in terms of \( M \), \( g \), \( L \), \( \mu_1 \), and \( \mu_2 \).** \[ W = \, \] **Figure Explanation:** The figure consists of two diagrams labeled "Before" and "After." - **Before:** - The board spans both regions, with part of its length \( L \) over region 1 (blue) where the coefficient of friction is \( \mu_1 \), and part over region 2 (orange) where the coefficient of friction is \( \mu_2 \). - **After:** - The board is shown entirely in region 2, having been moved in the positive direction indicated in the diagram. **Part B:** Complete previous part(s) **Additional Instructions:** Provide Feedback --- **Note:** The task involves calculating the work done against friction as the board transitions from one region to another, requiring knowledge of frictional forces and work-energy principles. **Copyright Information:** Copyright © 2022 Pearson Education Inc. All rights reserved. ---
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