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

Name: Please help me answer this problem and thoroughly explain the formulas
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: 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