3. A boy pulls a 27.0-kg box with a 170-N force at 33° above a horizontal surface. If the coefficient of kinetic friction between the box and the horizontal surface is 0.28 and the box is pulled a distance of 40.0 m, what is the net work do on the box? J 60 ssiu ssf60 f60 ssi f60

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)...
icon
Related questions
Topic Video
Question
### Physics Problem: Net Work Done on a Box on a Horizontal Surface

**Problem Statement:**

A boy pulls a 27.0-kg box with a 170-N force at 33° above a horizontal surface. If the coefficient of kinetic friction between the box and the horizontal surface is 0.28 and the box is pulled a distance of 40.0 m, what is the net work done on the box?

**Given:**
- Mass of the box (m): 27.0 kg
- Applied force (F): 170 N
- Angle of the applied force above the horizontal (θ): 33°
- Coefficient of kinetic friction (μ_k): 0.28
- Distance moved (d): 40.0 m

**Solution:**

Let's break the problem into steps to find the net work done on the box.

1. **Horizontal Component of the Applied Force:**

\[ F_{\text{horizontal}} = F \cos(θ) \]

\[ F_{\text{horizontal}} = 170 \, \text{N} \cos(33°) \]

2. **Vertical Component of the Applied Force:**

\[ F_{\text{vertical}} = F \sin(θ) \]

\[ F_{\text{vertical}} = 170 \, \text{N} \sin(33°) \]

3. **Normal Force:**

The normal force (\( F_N \)) can be found by considering the vertical forces acting on the box. It is reduced by the vertical component of the applied force.

\[ F_N = mg - F_{\text{vertical}} \]

4. **Force of Kinetic Friction:**

\[ F_{\text{kinetic friction}} = μ_k F_N \]

5. **Work Done by the Applied Force:**

\[ W_{\text{applied}} = F_{\text{horizontal}} \times d \]

6. **Work Done Against Friction:**

\[ W_{\text{friction}} = F_{\text{kinetic friction}} \times d \]

7. **Net Work Done on the Box:**

\[ W_{\text{net}} = W_{\text{applied}} - W_{\text{friction}} \]

Plugging in the values correctly, compute each step, and finally, you will obtain the net work done. Don't forget to check units at each step to ensure consistency.

**Calculated Answer
Transcribed Image Text:### Physics Problem: Net Work Done on a Box on a Horizontal Surface **Problem Statement:** A boy pulls a 27.0-kg box with a 170-N force at 33° above a horizontal surface. If the coefficient of kinetic friction between the box and the horizontal surface is 0.28 and the box is pulled a distance of 40.0 m, what is the net work done on the box? **Given:** - Mass of the box (m): 27.0 kg - Applied force (F): 170 N - Angle of the applied force above the horizontal (θ): 33° - Coefficient of kinetic friction (μ_k): 0.28 - Distance moved (d): 40.0 m **Solution:** Let's break the problem into steps to find the net work done on the box. 1. **Horizontal Component of the Applied Force:** \[ F_{\text{horizontal}} = F \cos(θ) \] \[ F_{\text{horizontal}} = 170 \, \text{N} \cos(33°) \] 2. **Vertical Component of the Applied Force:** \[ F_{\text{vertical}} = F \sin(θ) \] \[ F_{\text{vertical}} = 170 \, \text{N} \sin(33°) \] 3. **Normal Force:** The normal force (\( F_N \)) can be found by considering the vertical forces acting on the box. It is reduced by the vertical component of the applied force. \[ F_N = mg - F_{\text{vertical}} \] 4. **Force of Kinetic Friction:** \[ F_{\text{kinetic friction}} = μ_k F_N \] 5. **Work Done by the Applied Force:** \[ W_{\text{applied}} = F_{\text{horizontal}} \times d \] 6. **Work Done Against Friction:** \[ W_{\text{friction}} = F_{\text{kinetic friction}} \times d \] 7. **Net Work Done on the Box:** \[ W_{\text{net}} = W_{\text{applied}} - W_{\text{friction}} \] Plugging in the values correctly, compute each step, and finally, you will obtain the net work done. Don't forget to check units at each step to ensure consistency. **Calculated Answer
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Mechanical Work done
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON