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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Question
Express equation 7 in terms of distances and forces in figure 9.4
![**Equation 7**
\[
\sum \tau_{\text{clockwise}} = \sum \tau_{\text{counterclockwise}}
\]
This equation represents the condition for rotational equilibrium in physics. It states that for an object to be in rotational equilibrium, the sum of all clockwise torques must equal the sum of all counterclockwise torques acting on the object.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b0e7686-0c0d-4eba-ac81-54e736b47f2f%2Fb63ee881-7b69-4125-933f-a79d35a727ef%2F2glzfd4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Equation 7**
\[
\sum \tau_{\text{clockwise}} = \sum \tau_{\text{counterclockwise}}
\]
This equation represents the condition for rotational equilibrium in physics. It states that for an object to be in rotational equilibrium, the sum of all clockwise torques must equal the sum of all counterclockwise torques acting on the object.
![The image shows a diagram of a balanced meter stick used to demonstrate the principles of torque and equilibrium. Here's a description suitable for an educational website:
---
### Understanding Torque and Equilibrium
The diagram illustrates a meter stick in rotational equilibrium, balanced on a fulcrum. Key elements of the diagram include:
- **Fulcrum:** The pivot point of the meter stick, marked at the center.
- **Center of Gravity:** Indicated near the middle of the meter stick but not necessarily at the geometric center, labeled as "center of gravity."
- **Forces:**
- \( m_1g \): The downward gravitational force exerted by mass \( m_1 \) placed at position \( x_1 \) from the fulcrum.
- \( m_2g \): The downward gravitational force exerted by mass \( m_2 \) placed at position \( x_2 \) from the fulcrum.
- \( w_{\text{meter stick}} \): The weight of the meter stick itself acting downward through its center of gravity.
- \( F_{\text{by fulcrum}} \): The upward force exerted by the fulcrum.
- **Positions:**
- \( x_1 \): Distance from the 0 cm mark to the position of \( m_1 \).
- \( x_2 \): Distance from the 100 cm mark to the position of \( m_2 \).
- \( x_{\text{fulcrum}} \): Position of the fulcrum along the meter stick.
- \( x_{\text{c-of-g}} \): The center of gravity's position on the meter stick.
The overall setup demonstrates the principle of rotational equilibrium, where the sum of the clockwise torques equals the sum of the counterclockwise torques around the fulcrum:
\[ \sum \tau_{\text{clockwise}} = \sum \tau_{\text{counterclockwise}} \]
This principle can be used to solve for unknown values such as mass positions or the weight of the meter stick.
**Figure 9.4** shows the described setup.
---
This text can help students understand how forces and torques interact to maintain equilibrium on a balanced beam.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b0e7686-0c0d-4eba-ac81-54e736b47f2f%2Fb63ee881-7b69-4125-933f-a79d35a727ef%2Fnd19hs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image shows a diagram of a balanced meter stick used to demonstrate the principles of torque and equilibrium. Here's a description suitable for an educational website:
---
### Understanding Torque and Equilibrium
The diagram illustrates a meter stick in rotational equilibrium, balanced on a fulcrum. Key elements of the diagram include:
- **Fulcrum:** The pivot point of the meter stick, marked at the center.
- **Center of Gravity:** Indicated near the middle of the meter stick but not necessarily at the geometric center, labeled as "center of gravity."
- **Forces:**
- \( m_1g \): The downward gravitational force exerted by mass \( m_1 \) placed at position \( x_1 \) from the fulcrum.
- \( m_2g \): The downward gravitational force exerted by mass \( m_2 \) placed at position \( x_2 \) from the fulcrum.
- \( w_{\text{meter stick}} \): The weight of the meter stick itself acting downward through its center of gravity.
- \( F_{\text{by fulcrum}} \): The upward force exerted by the fulcrum.
- **Positions:**
- \( x_1 \): Distance from the 0 cm mark to the position of \( m_1 \).
- \( x_2 \): Distance from the 100 cm mark to the position of \( m_2 \).
- \( x_{\text{fulcrum}} \): Position of the fulcrum along the meter stick.
- \( x_{\text{c-of-g}} \): The center of gravity's position on the meter stick.
The overall setup demonstrates the principle of rotational equilibrium, where the sum of the clockwise torques equals the sum of the counterclockwise torques around the fulcrum:
\[ \sum \tau_{\text{clockwise}} = \sum \tau_{\text{counterclockwise}} \]
This principle can be used to solve for unknown values such as mass positions or the weight of the meter stick.
**Figure 9.4** shows the described setup.
---
This text can help students understand how forces and torques interact to maintain equilibrium on a balanced beam.
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