1. Two blocks are connected by a massless rope as shown below. The mass of the block on the table is m, and the hanging mass is m₂. The table and the pulley are frictionless. a₁ m₁ y L X m₂ Subpart 1: Draw FBDs In your notebook, draw free body diagrams for m, and m₂ using the template as shown below. The forces acting on the system are weights of the blocks, m₁g, and m₂g, the tension in the string T and the normal reaction N₁ of the table on m₁. 111 a₂ m2
1. Two blocks are connected by a massless rope as shown below. The mass of the block on the table is m, and the hanging mass is m₂. The table and the pulley are frictionless. a₁ m₁ y L X m₂ Subpart 1: Draw FBDs In your notebook, draw free body diagrams for m, and m₂ using the template as shown below. The forces acting on the system are weights of the blocks, m₁g, and m₂g, the tension in the string T and the normal reaction N₁ of the table on m₁. 111 a₂ m2
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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
Transcribed Image Text:**Problem Statement**
1. Two blocks are connected by a massless rope as shown below. The mass of the block on the table is \( m_1 \) and the hanging mass is \( m_2 \). The table and the pulley are frictionless.
*Diagram Explanation:*
- The diagram shows two blocks connected by a rope that runs over a pulley.
- Block \( m_1 \) is on a horizontal surface, and block \( m_2 \) is hanging off the edge.
- The block \( m_1 \) experiences acceleration \( \vec{a_1} \) horizontally.
- The block \( m_2 \) experiences acceleration \( \vec{a_2} \) vertically downward.
**Subpart 1: Draw FBDs**
In your notebook, draw free body diagrams for \( m_1 \) and \( m_2 \) using the template as shown below. The forces acting on the system are weights of the blocks, \( m_1g \) and \( m_2g \), the tension in the string \( T \) and the normal reaction \( N_1 \) of the table on \( m_1 \).
*Free Body Diagram Template:*
- A coordinate system with axes labeled \( x \) (horizontal) and \( y \) (vertical).
- Represent \( m_1 \) and \( m_2 \) using circles and show vectors for forces such as weight, tension, and normal force.
**Subpart 2: Set up Newton's Second Law Equations**
*Instructions:*
- Apply Newton's Second Law to each block separately.
- For \( m_1 \), consider horizontal forces (tension and acceleration).
- For \( m_2 \), consider vertical forces (tension, weight, and acceleration).
![## Newton's Second Law Analysis
### (i) Newton’s Second Law for \( m_1 \)
In terms of weights of the blocks \( m_1g \) and \( m_2g \), the tension in the string \( T \) and the normal reaction \( N_1 \) of the table on \( m_1 \) can be written as (using the coordinate axes for signs of different forces):
\[
\sum F_x = \underline{\hspace{3cm}} = m_1 a_{1,x}
\]
\[
\sum F_y = \underline{\hspace{3cm}} = m_1 a_{1,y}
\]
### (ii) Newton’s Second Law for \( m_2 \)
In terms of weights of the blocks \( m_1g \) and \( m_2g \), the tension in the string \( T \) and the normal reaction \( N_1 \) of the table on \( m_1 \) can be written as:
*Note: The motion of \( m_2 \) is along the y-direction only.*
\[
\sum F_y = \underline{\hspace{3cm}} = m_2 a_{2,y}
\]
### (iii) Relation Between \( \vec{a_1} \) and \( \vec{a_2} \)
How are \( \vec{a_1} \) and \( \vec{a_2} \) related? What are the directions of \( \vec{a_1} \) and \( \vec{a_2} \)?
**Magnitudes of \( \vec{a_1} \) and \( \vec{a_2} \):**
A. \( a_1 \) is greater than \( a_2 \)
B. \( a_1 \) is less than \( a_2 \)
C. \( a_1 \) is equal to \( a_2 \)
**Directions of \( \vec{a_1} \) and \( \vec{a_2} \):**
A. \( \vec{a_1} \) is to the right and \( \vec{a_2} \) is up
B. \( \vec{a_1} \) is to the right and \( \vec{a_2} \) is](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F464fe16a-00d5-4182-8379-61bd4b8bbe02%2Fd83f0de7-930d-4687-9daa-1c3d5b1e890a%2Fno6tu9g_processed.png&w=3840&q=75)
Transcribed Image Text:## Newton's Second Law Analysis
### (i) Newton’s Second Law for \( m_1 \)
In terms of weights of the blocks \( m_1g \) and \( m_2g \), the tension in the string \( T \) and the normal reaction \( N_1 \) of the table on \( m_1 \) can be written as (using the coordinate axes for signs of different forces):
\[
\sum F_x = \underline{\hspace{3cm}} = m_1 a_{1,x}
\]
\[
\sum F_y = \underline{\hspace{3cm}} = m_1 a_{1,y}
\]
### (ii) Newton’s Second Law for \( m_2 \)
In terms of weights of the blocks \( m_1g \) and \( m_2g \), the tension in the string \( T \) and the normal reaction \( N_1 \) of the table on \( m_1 \) can be written as:
*Note: The motion of \( m_2 \) is along the y-direction only.*
\[
\sum F_y = \underline{\hspace{3cm}} = m_2 a_{2,y}
\]
### (iii) Relation Between \( \vec{a_1} \) and \( \vec{a_2} \)
How are \( \vec{a_1} \) and \( \vec{a_2} \) related? What are the directions of \( \vec{a_1} \) and \( \vec{a_2} \)?
**Magnitudes of \( \vec{a_1} \) and \( \vec{a_2} \):**
A. \( a_1 \) is greater than \( a_2 \)
B. \( a_1 \) is less than \( a_2 \)
C. \( a_1 \) is equal to \( a_2 \)
**Directions of \( \vec{a_1} \) and \( \vec{a_2} \):**
A. \( \vec{a_1} \) is to the right and \( \vec{a_2} \) is up
B. \( \vec{a_1} \) is to the right and \( \vec{a_2} \) is
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