fof maee meis supported against gravity by the bar at a A rigid, uniform, horizontal bar of mass m, and length L is supported by two identical massless strings (Figure 1)Both strings are vertical. String A is attached at a distance d
fof maee meis supported against gravity by the bar at a A rigid, uniform, horizontal bar of mass m, and length L is supported by two identical massless strings (Figure 1)Both strings are vertical. String A is attached at a distance d
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![### Problem Description
A rigid, uniform, horizontal bar of mass \( m_1 \) and length \( L \) is supported by two identical massless strings. Both strings are vertical. String A is attached at a distance \( d < \frac{L}{2} \) from the left end of the bar and is connected to the ceiling, while String B is attached to the left end of the bar and is connected to the floor. A small block of mass \( m_2 \) is supported against gravity by the bar at a distance \( x \) from the left end of the bar, as shown in the figure.
Throughout this problem, positive torque is that which spins an object counterclockwise. Use \( g \) for the magnitude of the free-fall acceleration due to gravity.
### Tasks
#### Part A
Find \( T_A \), the tension in string A.
- **Express the tension in string A in terms of** \( g, m_1, L, d, m_2, \) **and** \( x \).
\[ T_A = \]
#### Part B
Find \( T_B \), the magnitude of the tension in string B.
- **Express the magnitude of the tension in string B in terms of** \( T_A, m_1, m_2, \) **and** \( g \).
\[ T_B = \]
#### Part C
Complete previous part(s).
#### Part D
If the mass of the block is too large and the block is too close to the left end of the bar (near string B), then the horizontal bar may become unstable (i.e., the bar may no longer remain horizontal).
- **What is the smallest possible value of \( x \) such that the bar remains stable (call it** \( x_{\text{critical}} \))?**
- **Express your answer for** \( x_{\text{critical}} \) **in terms of** \( m_2, m_1, d, \) **and** \( L \).
\[ x_{\text{critical}} = \]
### Diagram Explanation
The diagram illustrates a horizontal bar supported by two vertical strings. String A is positioned at a distance \( d \) from the left end, while String B is attached at the very end. A block is placed on the bar at a distance \( x \) from the left, contributing to tension and torque forces in the system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e343f85-ac09-4dac-ae1f-fa90b444949b%2F74a3eea3-7684-4dee-a936-556efb0d8500%2Fwii4nl_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Description
A rigid, uniform, horizontal bar of mass \( m_1 \) and length \( L \) is supported by two identical massless strings. Both strings are vertical. String A is attached at a distance \( d < \frac{L}{2} \) from the left end of the bar and is connected to the ceiling, while String B is attached to the left end of the bar and is connected to the floor. A small block of mass \( m_2 \) is supported against gravity by the bar at a distance \( x \) from the left end of the bar, as shown in the figure.
Throughout this problem, positive torque is that which spins an object counterclockwise. Use \( g \) for the magnitude of the free-fall acceleration due to gravity.
### Tasks
#### Part A
Find \( T_A \), the tension in string A.
- **Express the tension in string A in terms of** \( g, m_1, L, d, m_2, \) **and** \( x \).
\[ T_A = \]
#### Part B
Find \( T_B \), the magnitude of the tension in string B.
- **Express the magnitude of the tension in string B in terms of** \( T_A, m_1, m_2, \) **and** \( g \).
\[ T_B = \]
#### Part C
Complete previous part(s).
#### Part D
If the mass of the block is too large and the block is too close to the left end of the bar (near string B), then the horizontal bar may become unstable (i.e., the bar may no longer remain horizontal).
- **What is the smallest possible value of \( x \) such that the bar remains stable (call it** \( x_{\text{critical}} \))?**
- **Express your answer for** \( x_{\text{critical}} \) **in terms of** \( m_2, m_1, d, \) **and** \( L \).
\[ x_{\text{critical}} = \]
### Diagram Explanation
The diagram illustrates a horizontal bar supported by two vertical strings. String A is positioned at a distance \( d \) from the left end, while String B is attached at the very end. A block is placed on the bar at a distance \( x \) from the left, contributing to tension and torque forces in the system.
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