
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Please help me answer this problem and thoroughly explain the formulas behind each step, especially those relating to the spring and equilibrium. Thank you!
![### Problem Statement:
1. For the diagram shown, \( k = 250 \text{N/m} \) for the spring, \( m_1 = 8.0 \text{kg} \), \( \theta = 30^\circ \) and \( m_2 = 8.0 \text{kg} \). Draw free body diagrams for each mass, label each force, determine their values and determine how much the spring is stretched when the system is in equilibrium.
### Diagram Analysis:
The diagram depicts a system consisting of:
- A block \( m_1 \) on an inclined plane at an angle \( \theta \).
- A spring with spring constant \( k \) attached to block \( m_1 \).
- A pulley system with a hanging block \( m_2 \).
### Instructions for Solving the Problem:
1. **Draw Free Body Diagrams (FBD):**
- **For \( m_1 \)**:
- Weight (\( W_1 \)): \( W_1 = m_1 g \)
- Normal force (\( N \)) perpendicular to the inclined plane.
- Spring force (\( F_s \)) acting along the plane.
- Friction force (if applicable).
- Gravitational component parallel (\( W_{1x} = m_1 g \sin \theta \)) and perpendicular to the plane (\( W_{1y} = m_1 g \cos \theta \)).
- **For \( m_2 \)**:
- Weight (\( W_2 \)): \( W_2 = m_2 g \)
- Tension (\( T \)) in the string connected to \( m_2 \).
2. **Force Equations:**
- For \( m_1 \) on the inclined plane:
- Along the plane: \( F_s = m_1 g \sin \theta \)
- Perpendicular to the plane: \( N = m_1 g \cos \theta \)
- For \( m_2 \) (since the system is in equilibrium):
- \( T = m_2 g \)
3. **Spring Force Calculation:**
Since the system is in equilibrium:
\[
m_1 g \sin \theta = k \Delta x
\]
Where:
- \( \Delta x \) is](https://content.bartleby.com/qna-images/question/b9c0e305-fa66-4c78-b971-b9623ece9418/bd1c978a-f64e-4c2e-8da0-95ed48a1c619/bu0ocz_thumbnail.jpeg)
Transcribed Image Text:### Problem Statement:
1. For the diagram shown, \( k = 250 \text{N/m} \) for the spring, \( m_1 = 8.0 \text{kg} \), \( \theta = 30^\circ \) and \( m_2 = 8.0 \text{kg} \). Draw free body diagrams for each mass, label each force, determine their values and determine how much the spring is stretched when the system is in equilibrium.
### Diagram Analysis:
The diagram depicts a system consisting of:
- A block \( m_1 \) on an inclined plane at an angle \( \theta \).
- A spring with spring constant \( k \) attached to block \( m_1 \).
- A pulley system with a hanging block \( m_2 \).
### Instructions for Solving the Problem:
1. **Draw Free Body Diagrams (FBD):**
- **For \( m_1 \)**:
- Weight (\( W_1 \)): \( W_1 = m_1 g \)
- Normal force (\( N \)) perpendicular to the inclined plane.
- Spring force (\( F_s \)) acting along the plane.
- Friction force (if applicable).
- Gravitational component parallel (\( W_{1x} = m_1 g \sin \theta \)) and perpendicular to the plane (\( W_{1y} = m_1 g \cos \theta \)).
- **For \( m_2 \)**:
- Weight (\( W_2 \)): \( W_2 = m_2 g \)
- Tension (\( T \)) in the string connected to \( m_2 \).
2. **Force Equations:**
- For \( m_1 \) on the inclined plane:
- Along the plane: \( F_s = m_1 g \sin \theta \)
- Perpendicular to the plane: \( N = m_1 g \cos \theta \)
- For \( m_2 \) (since the system is in equilibrium):
- \( T = m_2 g \)
3. **Spring Force Calculation:**
Since the system is in equilibrium:
\[
m_1 g \sin \theta = k \Delta x
\]
Where:
- \( \Delta x \) is
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- Hello, Can someone please show how to solve this problem? Thanksarrow_forwardI am very lost concerning this. Please work it out for me so I may see! You are very appreciated!! problem: A mass is attached to a spring and the spring is stretched to an initial position 50cm from its rest position. The mass returns to its initial position in 0.75 seconds. (a)write an equation that gives the displacement of the mass from its rest position at "t" seconds. (b) Find the distance traveled by the mass in 12 seconds. Assume that the damping is negligible.arrow_forwardThe mass is pulled to the right a distance of 0.2 m and released. Rank the following spring–mass combinations according to their oscillation periods from longest to shortest. If any combinations have the same period, give them the same rank. You should assume that there is no friction between the mass and the horizontal surface. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.) k = 0.3 N/m; m = 0.50 kg k = 0.3 N/m; m = 1.00 kg k = 0.3 N/m; m = 2.00 kg k = 0.6 N/m; m = 0.50 kg k = 0.6 N/m; m = 1.00 kgarrow_forward
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