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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In the figure, a tin of anti-oxidants (m1 = 4.7 kg) on a frictionless inclined surface is connected to a tin of corned beef (m2 = 2.4 kg). The pulley is massless and frictionless. An upward force of magnitude F = 6.4 N acts on the corned beef tin, which has a downward acceleration of 4.7 m/s2. What are (a) the tension in the connecting cord and (b) angle β?

### Mechanics: Inclined Plane and Pulley System

**Diagram Explanation:**

In this diagram, we have a classic physics problem involving an inclined plane and a pulley system. The setup is as follows:

- **Mass \( m_1 \):** Represented by a solid block positioned on an inclined plane. This inclined plane makes an angle \( \beta \) with the horizontal. 
- **Mass \( m_2 \):** Represented by another solid block hanging off the edge of the inclined plane. This block is connected to \( m_1 \) via a rope that runs over a frictionless pulley.
- **Pulley:** Positioned at the edge of the inclined plane where \( m_1 \) transitions to \( m_2 \). This pulley is assumed to be frictionless and massless for simplicity in calculations.
- **Force \( \vec{F} \):** An external force indicated by a blue arrow acting upward on \( m_2 \).

### Concepts Illustrated:

1. **Inclined Plane:** The inclined plane creates a component of gravitational force acting parallel to the surface of the plane, which impacts \( m_1 \).
  
2. **Pulley System:** The pulley changes the direction of the tension force in the rope connecting the two masses.
  
3. **Forces Acting on the System:**
   - For \( m_1 \):
     - Gravitational force (\( m_1 \cdot g \)), which can be resolved into two components: one perpendicular (\( m_1 \cdot g \cdot \cos(\beta) \)) and one parallel (\( m_1 \cdot g \cdot \sin(\beta) \)) to the plane.
     - Normal force exerted by the inclined plane.
     - Tension in the rope (\( T \)).
   - For \( m_2 \):
     - Gravitational force (\( m_2 \cdot g \)), acting downward.
     - Tension in the rope (\( T \)), acting upward.
     - Applied external force (\( \vec{F} \)), which also acts upward.

### Equations of Motion:

Using Newton's second law (\( F = ma \)), we can set up the equations for the system:

- For \( m_1 \):
\[ m_1 \cdot a = T - m_1 \cdot g \cdot \sin(\
Transcribed Image Text:### Mechanics: Inclined Plane and Pulley System **Diagram Explanation:** In this diagram, we have a classic physics problem involving an inclined plane and a pulley system. The setup is as follows: - **Mass \( m_1 \):** Represented by a solid block positioned on an inclined plane. This inclined plane makes an angle \( \beta \) with the horizontal. - **Mass \( m_2 \):** Represented by another solid block hanging off the edge of the inclined plane. This block is connected to \( m_1 \) via a rope that runs over a frictionless pulley. - **Pulley:** Positioned at the edge of the inclined plane where \( m_1 \) transitions to \( m_2 \). This pulley is assumed to be frictionless and massless for simplicity in calculations. - **Force \( \vec{F} \):** An external force indicated by a blue arrow acting upward on \( m_2 \). ### Concepts Illustrated: 1. **Inclined Plane:** The inclined plane creates a component of gravitational force acting parallel to the surface of the plane, which impacts \( m_1 \). 2. **Pulley System:** The pulley changes the direction of the tension force in the rope connecting the two masses. 3. **Forces Acting on the System:** - For \( m_1 \): - Gravitational force (\( m_1 \cdot g \)), which can be resolved into two components: one perpendicular (\( m_1 \cdot g \cdot \cos(\beta) \)) and one parallel (\( m_1 \cdot g \cdot \sin(\beta) \)) to the plane. - Normal force exerted by the inclined plane. - Tension in the rope (\( T \)). - For \( m_2 \): - Gravitational force (\( m_2 \cdot g \)), acting downward. - Tension in the rope (\( T \)), acting upward. - Applied external force (\( \vec{F} \)), which also acts upward. ### Equations of Motion: Using Newton's second law (\( F = ma \)), we can set up the equations for the system: - For \( m_1 \): \[ m_1 \cdot a = T - m_1 \cdot g \cdot \sin(\
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