### Physics Problem: Equilibrium on an Inclined Plane#### Scenario 1: Determining the Mass \( m_1 \)The two masses shown in the figure are in equilibrium, and the inclined plane is frictionless.- **Given:** - Angle \( (\theta) = 32.0^\circ \) - Mass \( m_2 = 3.61 \text{ kg} \)- **Question:** Determine the mass \( m_1 \). - **Solution:** - **Calculated Mass \( m_1 \):** \( 18.75 \text{ kg} \) - **Diagram Explanation:** - The diagram depicts a right triangle inclined plane with an angle \( \theta \) at the base. - Mass \( m_2 \) is placed on the inclined plane. - Mass \( m_1 \) is hanging vertically, connected over a pulley to mass \( m_2 \).#### Scenario 2: Determining the Mass \( m_1 \) and Tension \( T \)The three masses shown in the figure are in equilibrium, and the inclined plane is frictionless.- **Given:** - Angle \( (\theta) = 38.4^\circ \) - Mass \( m_2 = 2.00 \text{ kg} \) - Mass \( m_3 = 4.86 \text{ kg} \) - **Question:** Determine the mass \( m_1 \) and the magnitude of the tension \( T \) in the string connecting \( m_2 \) and \( m_3 \).- **Solution:** - **Calculated Mass \( m_1 \):** \( 5.02 \text{ kg} \) - **Diagram Explanation:** - The diagram shows a right triangle inclined plane with an angle \( \theta \). - Mass \( m_2 \) is on the inclined plane connected via a pulley system. - Mass \( m_3 \) is also on the inclined plane but positioned lower than \( m_2 \). - Mass \( m_1 \) is hanging vertically, connected over a pulley to mass \( m_2 \).Understanding the balance of forces in such systems involves using the principles of Newton's laws of motion, specifically analyzing the components of gravitational forces acting along and perpendicular to the inclined plane. The

Given:Angle, θ=32°mass, m1 = m kgmass, m2 = 3.61 kg

Answered: The two masses shown in the figure are…

The two masses shown in the figure are in equilibrium and the inclined plane is frictionless. m₂ m₁ If e 32.0° and m₂ = 3.61 kg, determine the mass of m₁. 18.75 x kg

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

### Physics Problem: Equilibrium on an Inclined Plane

#### Scenario 1: Determining the Mass \( m_1 \)
The two masses shown in the figure are in equilibrium, and the inclined plane is frictionless.

- **Given:**
- Angle \( (\theta) = 32.0^\circ \)
- Mass \( m_2 = 3.61 \text{ kg} \)

- **Question:** Determine the mass \( m_1 \).

- **Solution:**
- **Calculated Mass \( m_1 \):** \( 18.75 \text{ kg} \)

- **Diagram Explanation:**
- The diagram depicts a right triangle inclined plane with an angle \( \theta \) at the base.
- Mass \( m_2 \) is placed on the inclined plane.
- Mass \( m_1 \) is hanging vertically, connected over a pulley to mass \( m_2 \).

#### Scenario 2: Determining the Mass \( m_1 \) and Tension \( T \)
The three masses shown in the figure are in equilibrium, and the inclined plane is frictionless.

- **Given:**
- Angle \( (\theta) = 38.4^\circ \)
- Mass \( m_2 = 2.00 \text{ kg} \)
- Mass \( m_3 = 4.86 \text{ kg} \)

- **Question:** Determine the mass \( m_1 \) and the magnitude of the tension \( T \) in the string connecting \( m_2 \) and \( m_3 \).

- **Solution:**
- **Calculated Mass \( m_1 \):** \( 5.02 \text{ kg} \)

- **Diagram Explanation:**
- The diagram shows a right triangle inclined plane with an angle \( \theta \).
- Mass \( m_2 \) is on the inclined plane connected via a pulley system.
- Mass \( m_3 \) is also on the inclined plane but positioned lower than \( m_2 \).
- Mass \( m_1 \) is hanging vertically, connected over a pulley to mass \( m_2 \).

Understanding the balance of forces in such systems involves using the principles of Newton's laws of motion, specifically analyzing the components of gravitational forces acting along and perpendicular to the inclined plane. The

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