---## Equation of Motion for a System of Particles### Learning Goal:Consider the mass and pulley system shown. Mass \(m_1 = 32 \, \text{kg}\) and mass \(m_2 = 10 \, \text{kg}\). The angle of the inclined plane is given, and the coefficient of kinetic friction between mass \(m_2\) and the inclined plane is \(\mu_k = 0.12\). Assume the pulleys are massless and frictionless.#### (Figure 1)---### FigureThe diagram depicts a mass and pulley system. There is an inclined plane at an angle to the horizontal. Mass \( m_2 \) sits on this inclined plane. The angle of inclination and the relative dimensions are shown as a right triangle with sides labeled 5, 12, and hypotenuse 13. Mass \( m_2 \) is connected via a rope over a pulley at the top of the incline. This rope then goes around another pulley and hangs down vertically, connecting to the second mass \( m_1 \) which hangs freely. Both pulleys in the system are considered to be massless and have no friction. ---Weather Icon: - It shows that the current weather is sunny and the temperature is 98°F.---This diagram and description are generally used to analyze the forces acting on the masses and pulleys, as well as to determine the motion of the system considering the given parameters. **Part A - Finding the acceleration of the mass on the inclined plane**What is the acceleration of mass \( m_2 \) on the inclined plane? Take positive acceleration to be up the ramp.Express your answer to three significant figures and include the appropriate units.\[ a_2 = \_\_\_\_ \, \text{Value} \, \_\_\_\_ \, \text{Units} \][Submit Button]**Part B - Finding the speed of the mass moving up the ramp after a given time**If the system is released from rest, what is the speed of mass \( m_2 \) after 4 s?Express your answer to three significant figures and include the appropriate units.[Submit Button]---### Explanation:**Graph/Diagram Overview:**There is no graph or diagram visible in the provided image. Only text input fields and some icons for accessing hints, submitting responses, and other functionalities are present.**Icons Explanation:**1. **[Icon of Two Vertical Bars]**: This typically represents a "Pause" or "Play" function.2. **[Icon of a Scale with Ball]**: This might be related to viewing hints or references specific to the question context.3. **[Left Arrow and Right Arrow Icons]**: These are usually for navigating back or forward, likely to cycle through different questions or hints.4. **[Question Mark Icon]**: Commonly represents additional help or hints available for the question.Instructions are provided for students to input their answers with the correct number of significant figures and proper units of measurement.

Equation of Motion for a System of Learning Goal: Consider the mass and pulley system shown. Mass m₁= 32 kg and mass m₂ = 10 kg. The angle of the inclined plane is given, and the coefficient of kinetic friction between mass me and the inclined plane is μ = 0.12. Assume the pulleys are massless and frictionless. (Figure 1) Figure 1 of 1

Equation of Motion for a System of Learning Goal: Consider the mass and pulley system shown. Mass m₁= 32 kg and mass m₂ = 10 kg. The angle of the inclined plane is given, and the coefficient of kinetic friction between mass me and the inclined plane is μ = 0.12. Assume the pulleys are massless and frictionless. (Figure 1) Figure 1 of 1

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Section: Chapter Questions

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Question

---
## Equation of Motion for a System of Particles

### Learning Goal:
Consider the mass and pulley system shown. Mass \(m_1 = 32 \, \text{kg}\) and mass \(m_2 = 10 \, \text{kg}\). The angle of the inclined plane is given, and the coefficient of kinetic friction between mass \(m_2\) and the inclined plane is \(\mu_k = 0.12\). Assume the pulleys are massless and frictionless.

#### (Figure 1)

---

### Figure

The diagram depicts a mass and pulley system. There is an inclined plane at an angle to the horizontal. Mass \( m_2 \) sits on this inclined plane. The angle of inclination and the relative dimensions are shown as a right triangle with sides labeled 5, 12, and hypotenuse 13. Mass \( m_2 \) is connected via a rope over a pulley at the top of the incline.

This rope then goes around another pulley and hangs down vertically, connecting to the second mass \( m_1 \) which hangs freely. Both pulleys in the system are considered to be massless and have no friction.

---

Weather Icon:
- It shows that the current weather is sunny and the temperature is 98°F.
---

This diagram and description are generally used to analyze the forces acting on the masses and pulleys, as well as to determine the motion of the system considering the given parameters.

**Part A - Finding the acceleration of the mass on the inclined plane**

What is the acceleration of mass \( m_2 \) on the inclined plane? Take positive acceleration to be up the ramp.

Express your answer to three significant figures and include the appropriate units.

\[ a_2 = \_\_\_\_ \, \text{Value} \, \_\_\_\_ \, \text{Units} \]

[Submit Button]

**Part B - Finding the speed of the mass moving up the ramp after a given time**

If the system is released from rest, what is the speed of mass \( m_2 \) after 4 s?

Express your answer to three significant figures and include the appropriate units.

[Submit Button]

---

### Explanation:

**Graph/Diagram Overview:**

There is no graph or diagram visible in the provided image. Only text input fields and some icons for accessing hints, submitting responses, and other functionalities are present.

**Icons Explanation:**

1. **[Icon of Two Vertical Bars]**: This typically represents a "Pause" or "Play" function.
2. **[Icon of a Scale with Ball]**: This might be related to viewing hints or references specific to the question context.
3. **[Left Arrow and Right Arrow Icons]**: These are usually for navigating back or forward, likely to cycle through different questions or hints.
4. **[Question Mark Icon]**: Commonly represents additional help or hints available for the question.

Instructions are provided for students to input their answers with the correct number of significant figures and proper units of measurement.

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