5. In the diagram below m, is moving down the frictionless ramp. The pulley is massless and frictionless. Draw a Free Body Diagram. b. What is the Tension in the rope. a. C. What is the acceleration of m, ? m, =3 ug m, = 1 ng 2. m sin & Mz Cas & mg 38
5. In the diagram below m, is moving down the frictionless ramp. The pulley is massless and frictionless. Draw a Free Body Diagram. b. What is the Tension in the rope. a. C. What is the acceleration of m, ? m, =3 ug m, = 1 ng 2. m sin & Mz Cas & mg 38
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I have part a fine. Part b and c are giving me issues though.
![### Physics Problem: Frictionless Ramp and Pulley System
**Problem Statement:**
In the diagram below, \( m_1 \) is moving down the frictionless ramp. The pulley is massless and frictionless.
1. Draw a Free Body Diagram.
2. What is the tension in the rope?
3. What is the acceleration of \( m_1 \)?
**Diagram Explanation:**
- The system includes:
- A block \( m_1 = 3 \, \text{kg} \) on a frictionless ramp inclined at \( 30^\circ \).
- A block \( m_2 = 1 \, \text{kg} \) hanging vertically.
- A tension force \( T \) in the rope connecting the two masses over the pulley.
**Forces on \( m_1 \):**
- \( m_1g \sin \theta \): Component of gravitational force pulling \( m_1 \) down the ramp.
- \( m_1g \cos \theta \): Component of gravitational force perpendicular to the ramp.
- \( T \): Tension in the rope opposing the motion of \( m_1 \) down the ramp.
- \( n \): Normal force perpendicular to the ramp.
**Forces on \( m_2 \):**
- \( m_2g \): Gravitational force pulling \( m_2 \) downwards.
- \( T \): Tension in the rope opposing \( m_2 \)'s descent.
**Equations:**
- For \( m_1 \):
\[
m_1g \sin \theta - T = m_1a
\]
- For \( m_2 \):
\[
T - m_2g = -m_2a
\]
**Note:** \( g \) represents the acceleration due to gravity, typically \( 9.81 \, \text{m/s}^2 \).
The challenge is to solve for tension \( T \) and acceleration \( a \) of the masses in the system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2367310-44c7-43e5-b110-21237a7a5b46%2Fe1b84d9e-7be0-48bb-8b56-103c1f7e979a%2Fbl1t6b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Physics Problem: Frictionless Ramp and Pulley System
**Problem Statement:**
In the diagram below, \( m_1 \) is moving down the frictionless ramp. The pulley is massless and frictionless.
1. Draw a Free Body Diagram.
2. What is the tension in the rope?
3. What is the acceleration of \( m_1 \)?
**Diagram Explanation:**
- The system includes:
- A block \( m_1 = 3 \, \text{kg} \) on a frictionless ramp inclined at \( 30^\circ \).
- A block \( m_2 = 1 \, \text{kg} \) hanging vertically.
- A tension force \( T \) in the rope connecting the two masses over the pulley.
**Forces on \( m_1 \):**
- \( m_1g \sin \theta \): Component of gravitational force pulling \( m_1 \) down the ramp.
- \( m_1g \cos \theta \): Component of gravitational force perpendicular to the ramp.
- \( T \): Tension in the rope opposing the motion of \( m_1 \) down the ramp.
- \( n \): Normal force perpendicular to the ramp.
**Forces on \( m_2 \):**
- \( m_2g \): Gravitational force pulling \( m_2 \) downwards.
- \( T \): Tension in the rope opposing \( m_2 \)'s descent.
**Equations:**
- For \( m_1 \):
\[
m_1g \sin \theta - T = m_1a
\]
- For \( m_2 \):
\[
T - m_2g = -m_2a
\]
**Note:** \( g \) represents the acceleration due to gravity, typically \( 9.81 \, \text{m/s}^2 \).
The challenge is to solve for tension \( T \) and acceleration \( a \) of the masses in the system.
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