You have an Attwood device where one block is on a smooth (frictionless), level table, attached to a block on a similarly smooth incline. Find the tension in the string and the acceleration of the blocks. m1=5 kg, m2=14 kg, and e=32°. Given ma= 5Ka O=3 29
You have an Attwood device where one block is on a smooth (frictionless), level table, attached to a block on a similarly smooth incline. Find the tension in the string and the acceleration of the blocks. m1=5 kg, m2=14 kg, and e=32°. Given ma= 5Ka O=3 29
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)...
Related questions
Question
I need help with this question how to set it up as well
![### Physics: Mechanics - Atwood's Machine with an Incline
**Problem Description:**
You have an Atwood device where one block is on a smooth (frictionless) level table attached to a block on a similarly smooth incline. Find the tension in the string and the acceleration of the blocks. The given values are:
- Mass of block \( m_1 \) = 5 kg
- Mass of block \( m_2 \) = 14 kg
- Angle of incline \( \theta \) = 32°
**Diagram Explanation:**
The provided diagram illustrates an Atwood machine setup:
- A pulley system with two blocks connected by a string.
- Block \( m_1 \) (5 kg) is situated on a frictionless horizontal table.
- Block \( m_2 \) (14 kg) is situated on a frictionless incline.
- The angle \( \theta \) of the incline is 32°.
**Steps to Solve the Problem:**
1. **Free Body Diagram Analysis:**
- Draw the forces acting on each block.
- For block \( m_1 \): Tension \( T \) in the string acts horizontally.
- For block \( m_2 \): Gravity decomposes into two components - one parallel to the incline (\( m_2 g \sin\theta \)) and one perpendicular to the incline (\( m_2 g \cos\theta \)). Tension \( T \) acts upward along the incline.
2. **Equations of Motion:**
- Block \( m_1 \) (horizontal):
\[
T = m_1 a
\]
- Block \( m_2 \) (inclined):
\[
m_2 g \sin\theta - T = m_2 a
\]
3. **Solve for Tension (T) and Acceleration (a):**
By combining the equations:
\[
T = m_1 a \quad \text{(1)}
\]
\[
m_2 g \sin(\theta) - T = m_2 a \quad \text{(2)}
\]
Substitute \( T \) from equation (1) into equation (2):
\[
m_2 g \sin(\theta) - m_1 a = m_2 a
\]
Combine to solve for \( a \):
\[
m_](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96058389-9737-4e92-9810-6187695664e8%2Fdebb71c2-d9b9-4a95-bcf2-96c4f2f70a98%2Fkebc63p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Physics: Mechanics - Atwood's Machine with an Incline
**Problem Description:**
You have an Atwood device where one block is on a smooth (frictionless) level table attached to a block on a similarly smooth incline. Find the tension in the string and the acceleration of the blocks. The given values are:
- Mass of block \( m_1 \) = 5 kg
- Mass of block \( m_2 \) = 14 kg
- Angle of incline \( \theta \) = 32°
**Diagram Explanation:**
The provided diagram illustrates an Atwood machine setup:
- A pulley system with two blocks connected by a string.
- Block \( m_1 \) (5 kg) is situated on a frictionless horizontal table.
- Block \( m_2 \) (14 kg) is situated on a frictionless incline.
- The angle \( \theta \) of the incline is 32°.
**Steps to Solve the Problem:**
1. **Free Body Diagram Analysis:**
- Draw the forces acting on each block.
- For block \( m_1 \): Tension \( T \) in the string acts horizontally.
- For block \( m_2 \): Gravity decomposes into two components - one parallel to the incline (\( m_2 g \sin\theta \)) and one perpendicular to the incline (\( m_2 g \cos\theta \)). Tension \( T \) acts upward along the incline.
2. **Equations of Motion:**
- Block \( m_1 \) (horizontal):
\[
T = m_1 a
\]
- Block \( m_2 \) (inclined):
\[
m_2 g \sin\theta - T = m_2 a
\]
3. **Solve for Tension (T) and Acceleration (a):**
By combining the equations:
\[
T = m_1 a \quad \text{(1)}
\]
\[
m_2 g \sin(\theta) - T = m_2 a \quad \text{(2)}
\]
Substitute \( T \) from equation (1) into equation (2):
\[
m_2 g \sin(\theta) - m_1 a = m_2 a
\]
Combine to solve for \( a \):
\[
m_
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 8 images
Knowledge Booster
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.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
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…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON