Three objects are connected by light strings as shown in the figure below. The string connecting the m, = 5.60-kg object and the m, = 3.90-kg object passes over a light trictionle. pulley. m. m. 8.00 kg (a) Determine the acceleration of each object. object m, magnitudel m/s object m, direction |---Selectv object ma magnitude object ma object m, magnitude object ma m/s direction Selectv m/s direction Select-v (b) Determine the tension in the two strings.

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### Physics Problem: Pulley System with Connected Objects

Three objects are connected by light strings as depicted in the diagram. The string connects the \( m_1 = 5.60 \, \text{kg} \) object and the \( m_2 = 3.90 \, \text{kg} \) object, passing over a light frictionless pulley.

### Diagram Description
The diagram shows:
- Two masses (\( m_1 \) and \( m_2 \)) are hanging vertically, connected by strings over a pulley.
- A third object (mass = 3.00 kg) is attached to \( m_2 \) but positioned horizontally relative to it.

### Tasks

**(a) Determine the acceleration of each object:**

1. **Object \( m_1 \):**  
   - Magnitude: [Blank for user input] \( \text{m/s}^2 \)  
   - Direction: [Dropdown for user to select direction]

2. **Object \( m_2 \):**  
   - Magnitude: [Blank for user input] \( \text{m/s}^2 \)  
   - Direction: [Dropdown for user to select direction]

3. **Object \( m_3 \):**  
   - Magnitude: [Blank for user input] \( \text{m/s}^2 \)  
   - Direction: [Dropdown for user to select direction]

**(b) Determine the tension in the two strings:**

1. **String between \( m_1 \) and \( m_2 \):**  
   - Tension: [Blank for user input] N

2. **String between \( m_3 \) and the 3.00-kg object:**  
   - Tension: [Blank for user input] N
   
### Analysis
To solve this problem:
- Apply Newton's laws of motion to each object.
- Assume ideal conditions: no friction, massless strings, and a frictionless pulley. 
- Calculate accelerations and tensions using relevant equations from mechanics.

This exercise illustrates dynamics in a classic pulley system frequently discussed in physics education.
Transcribed Image Text:### Physics Problem: Pulley System with Connected Objects Three objects are connected by light strings as depicted in the diagram. The string connects the \( m_1 = 5.60 \, \text{kg} \) object and the \( m_2 = 3.90 \, \text{kg} \) object, passing over a light frictionless pulley. ### Diagram Description The diagram shows: - Two masses (\( m_1 \) and \( m_2 \)) are hanging vertically, connected by strings over a pulley. - A third object (mass = 3.00 kg) is attached to \( m_2 \) but positioned horizontally relative to it. ### Tasks **(a) Determine the acceleration of each object:** 1. **Object \( m_1 \):** - Magnitude: [Blank for user input] \( \text{m/s}^2 \) - Direction: [Dropdown for user to select direction] 2. **Object \( m_2 \):** - Magnitude: [Blank for user input] \( \text{m/s}^2 \) - Direction: [Dropdown for user to select direction] 3. **Object \( m_3 \):** - Magnitude: [Blank for user input] \( \text{m/s}^2 \) - Direction: [Dropdown for user to select direction] **(b) Determine the tension in the two strings:** 1. **String between \( m_1 \) and \( m_2 \):** - Tension: [Blank for user input] N 2. **String between \( m_3 \) and the 3.00-kg object:** - Tension: [Blank for user input] N ### Analysis To solve this problem: - Apply Newton's laws of motion to each object. - Assume ideal conditions: no friction, massless strings, and a frictionless pulley. - Calculate accelerations and tensions using relevant equations from mechanics. This exercise illustrates dynamics in a classic pulley system frequently discussed in physics education.
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