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m1=50kg dan m2=100 kg,tentukan 1.arah gerak sistem? 2.berapa percepatan balok? 3. berapakah tegangan tegangan tali?

The problem shown in the image involves two masses \( m_1 \) and \( m_2 \) connected by a pulley over an inclined plane. We are asked to determine:

1. The direction of motion of the system.
2. The acceleration of the blocks.
3. The tension in the rope.

### Known Information:
- \( m_1 = 50 \, \text{kg} \)
- \( m_2 = 100 \, \text{kg} \)
- The angle for \( m_1 \) is \( 30^\circ \)
- The angle for \( m_2 \) is \( 53^\circ \)

### Step 1: Forces Acting on Each Mass
For both masses, the force of gravity acting on the block has two components: one parallel and one perpendicular to the incline.

#### For \( m_1 \) (incline of 30°):
- Gravitational force: \( F_g = m_1 \cdot g \)
- The parallel component (which pulls the block down the incline): 
  \[
  F_{\parallel_1} = m_1 \cdot g \cdot \sin(30^\circ)
  \]
- The perpendicular component (normal force): 
  \[
  F_{\perp_1} = m_1 \cdot g \cdot \cos(30^\circ)
  \]

#### For \( m_2 \) (incline of 53°):
- Gravitational force: \( F_g = m_2 \cdot g \)
- The parallel component (which pulls the block down the incline): 
  \[
  F_{\parallel_2} = m_2 \cdot g \cdot \sin(53^\circ)
  \]
- The perpendicular component (normal force): 
  \[
  F_{\perp_2} = m_2 \cdot g \cdot \cos(53^\circ)
  \]

### Step 2: Equations of Motion
Using Newton’s Second Law for each block, we can set up the following equations. Assume that the tension in the string is \( T \) and the acceleration of the system is \( a \).

- For \( m_1 \):
  \[
  T - m_1 \cdot g \cdot \sin(30^\circ) = m_1 \cdot a
  \]
- For \( m_2 \):
  \[
  m_2 \cdot g \cdot \sin(53^\circ) - T = m_2 \cdot a
  \]

### Step 3: Solve for the Acceleration and Tension
Now, we can solve these two equations simultaneously to find the acceleration \( a \) and the tension \( T \) in the rope.

Let me calculate the results for you.The results for the system are:

1. **Direction of Motion**: Since \( F_{\parallel_2} > F_{\parallel_1} \), the system will move in the direction where \( m_2 \) is sliding down the incline, and \( m_1 \) is moving up the incline.
  
2. **Acceleration of the Blocks**: The acceleration of the system is approximately \( 3.58 \, \text{m/s}^2 \).
  
3. **Tension in the Rope**: The tension in the rope is approximately \( 424.22 \, \text{N} \).

Let me know if you'd like further clarification or details on any step!

### Relative Questions:
1. What would happen to the acceleration if \( m_1 \) and \( m_2 \) were equal?
2. How does the angle of inclination affect the motion of the blocks?
3. What would the tension in the rope be if the blocks were on a horizontal surface?
4. How does the mass ratio between \( m_1 \) and \( m_2 \) affect the acceleration?
5. Can the system be in equilibrium if the angles are altered?

### Tip:
When solving pulley problems, always resolve forces along the incline for each mass, and check if their net forces result in motion in the same or opposite directions.

m1=50kg dan m2=100 kg,tentukan 1.arah gerak sistem? 2.berapa percepatan balok? 3. berapakah tegangan tali?

Solve a pulley system problem where m1=50kg and m2=100kg are on inclined planes with angles of 30° and 53°, respectively. Learn how to calculate the system's direction of motion, the acceleration of the blocks, and the tension in the rope. Suitable for high school students in Grades 10-12.

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