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The problem involves a system of three masses connected by ropes over pulleys, with given masses and distances, and includes friction on an inclined plane.

Given details:

1. \( M_1 = 10 \, \text{kg} \)
2. \( M_2 = P \, \text{kg} \) (Replacing \( P \) with 10 kg as per your instruction)
3. \( M_3 = 15 \, \text{kg} \)
4. Gravity \( g = 10 \, \text{m/s}^2 \)
5. Inclined plane angle: To find it, we'll use the triangle dimensions: 3 m (height) and 5 m (hypotenuse).
6. Friction coefficient \( \mu = 0. P \), where \( P = 10 \Rightarrow \mu = 0.10 \).

### Step-by-Step Solution

1. **Calculate the Angle of Incline (θ):**
   - Using \( \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{3}{5} \)
   - Thus, \( \theta = \arcsin\left(\frac{3}{5}\right) \approx 36.87^\circ \).

2. **Determine Forces on Each Mass:**
   - **Mass \( M_1 \)**: This mass is hanging vertically, so the only force acting on it is gravity.
     - Force due to gravity: \( F_{M_1} = M_1 \cdot g = 10 \cdot 10 = 100 \, \text{N} \).

   - **Mass \( M_2 \)** (on the incline):
     - Gravitational force down the incline: \( F_{g\parallel} = M_2 \cdot g \cdot \sin \theta \)
       \[
       F_{g\parallel} = 10 \cdot 10 \cdot \frac{3}{5} = 60 \, \text{N}
       \]
     - Frictional force up the incline: \( F_{\text{friction}} = \mu \cdot M_2 \cdot g \cdot \cos \theta \)
       \[
       F_{\text{friction}} = 0.10 \cdot 10 \cdot 10 \cdot \frac{4}{5} = 8 \, \text{N}
       \]
     - Net force on \( M_2 \) along the incline: \( F_{M_2} = F_{g\parallel} - F_{\text{friction}} = 60 - 8 = 52 \, \text{N} \).

   - **Mass \( M_3 \)**: This mass is also hanging, so the force acting on it is gravity.
     - Force due to gravity: \( F_{M_3} = M_3 \cdot g = 15 \cdot 10 = 150 \, \text{N} \).

3. **Net Force and Acceleration of the System:**
   - Net force: \( F_{\text{net}} = F_{M_3} - F_{M_2} - F_{M_1} = 150 - 52 - 100 = -2 \, \text{N} \).
   - Combined mass: \( M_{\text{total}} = M_1 + M_2 + M_3 = 10 + 10 + 15 = 35 \, \text{kg} \).
   - Acceleration: \( a = \frac{F_{\text{net}}}{M_{\text{total}}} = \frac{-2}{35} \approx -0.057 \, \text{m/s}^2 \).

The system has a negative acceleration, meaning the forces are balanced with a small discrepancy possibly due to rounding or minor friction, indicating near equilibrium or a very slow acceleration.

4. **Calculating Distance, Velocity, and Tension after 2 Seconds:**
   - **Distance (s)**: \( s = \frac{1}{2} a t^2 = \frac{1}{2} \times (-0.057) \times (2)^2 \approx -0.114 \, \text{m} \).
   - **Velocity (v)**: \( v = u + a \cdot t = 0 + (-0.057) \times 2 \approx -0.114 \, \text{m/s} \).
   - **Tensions (T):**
     - For \( M_1 \), the tension \( T_1 \) would balance the weight and acceleration, as would \( T_2 \) for \( M_3 \).

Would you like me to proceed with the specific tension calculations for each rope or have any questions on the steps? 

### Related Questions
1. How would the acceleration change if \( M_2 \) was increased?
2. What impact would doubling the coefficient of friction have on \( M_2 \)?
3. How would the results differ if the incline angle was reduced?
4. What if \( M_3 \) was lighter than \( M_1 \)? How would that affect the system's movement?
5. Can the acceleration be zero? Under what conditions?

#### Tip
When dealing with forces on an inclined plane, always break down gravity into parallel and perpendicular components to the incline.

Perhatikan gambar di bawah, diketahui 3 buah balok terhubung dengan tali melalui katrol. M1=10kg tertantung pada sisi sebelah kiri, M2=P kg berada pada bidang miring dan M3=15kg tergantung pada sisi kanan keduanya sistem dilepas dari keadaan diam. Jika percepatan gravitasi bumi g=10m/s2, dan koefisien gesek antara M2 dengan bidang miring μ=0,P. (Catatan P= digit ke 3 NIM + Digit Terakhir NIM). Hitunglah: 2 detik setelah dilepas berapa percepatan, kecepatan, jarak yang ditempuh dan tegangan tali saat itu?

Analyze a system of three blocks connected by a rope over pulleys with given masses (M1=10kg, M2=10kg, M3=15kg), gravity, and friction coefficient to determine the acceleration, speed, distance, and tension after 2 seconds. Suitable for high school students studying Newtonian mechanics.

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