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The problem involves three masses connected by a pulley system and interacting on a frictional inclined plane. Based on your instructions, \( P \) in the problem should be replaced with 5 kg for the mass \( M_2 \). Here’s the setup and the solution approach for each question:

### Known Data:
1. \( M_1 = 10 \, \text{kg} \)
2. \( M_2 = 5 \, \text{kg} \) (since \( P = 5 \))
3. \( M_3 = 15 \, \text{kg} \)
4. Incline angle for \( M_2 \): \( 37^\circ \)
5. Gravitational acceleration: \( g = 10 \, \text{m/s}^2 \)
6. Coefficient of friction \( \mu = 0.3 \) (for \( M_2 \) on the incline)

The questions to be solved are as follows:

### Question (a):
Calculate the system's acceleration, the speed, the distance covered after 2 seconds, and the tension in the cable at that moment.

### Question (b):
After 2 seconds, if the right side of the cable breaks, find the distance covered by each mass in the next 2 seconds and the new cable tension.

### Question (c):
Calculate the time and distance for \( M_1 = 10 \, \text{kg} \) and \( M_2 = 5 \, \text{kg} \) to stop right after the cable breaks.

### Question (d):
Calculate the distance traveled by \( M_2 = 5 \, \text{kg} \) 4 seconds after it temporarily stops.

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### Solution Outline:
1. **Calculate the Forces Acting on Each Mass**:
   - For \( M_1 \): \( F_{M1} = M_1 \cdot g \)
   - For \( M_2 \): Split forces along and perpendicular to the incline, factoring in friction.
   - For \( M_3 \): \( F_{M3} = M_3 \cdot g \)

2. **Set Up the Net Force Equation**:
   - Calculate the net force and use \( F = ma \) to find the acceleration of the system.

3. **Solve Each Question in Sequence**:
   - Apply kinematic equations to find distances, speed, and times as requested.
   - Re-calculate forces and tensions based on changing conditions, especially when the cable breaks.

Would you like me to proceed with the detailed step-by-step calculations for each part? 

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### Follow-Up Questions
1. How does the angle of the incline affect the tension and acceleration in the system?
2. What is the role of friction in determining the net force on \( M_2 \)?
3. How would the results change if \( M_2 \) were larger or smaller than 5 kg?
4. Why is it necessary to recalculate tension when the cable breaks?
5. What other methods could be used to verify the acceleration and tension in this system?

### Tip:
When working with pulleys and inclines, always resolve forces along the direction of motion and perpendicular to it, especially when friction is involved.

Calculate the acceleration, speed, distance covered, and tension in a pulley system involving three masses connected on an inclined plane with friction. After 2 seconds, if the cable on the right side breaks, find the distance traveled by each mass in the next 2 seconds and the new cable tension. Additionally, calculate the time and distance required for the 10 kg and 5 kg masses to stop, and the distance traveled by the 5 kg mass 4 seconds after it temporarily stops.

Analyze a pulley system with three masses, including a 10 kg, 5 kg, and 15 kg block, connected on an inclined plane with friction. Calculate acceleration, speed, and distance covered, and determine the tension in the cable. Explore kinematic equations in the context of a cable break scenario and solve for stopping distances.

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