https://file.aiquickdraw.com/mathbot/file/1727608664458hz1l3e25.jpg

m1= 50 kg dan m2=100 kg. Tentukan 1. arah gerak sistem? 2. percepatan sistem? 3. tegangan tali?

From the image, it looks like a physics problem involving two masses, \( m_1 \) and \( m_2 \), on inclined planes connected by a pulley.

### Given:
- \( m_1 = 50 \, \text{kg} \)
- \( m_2 = 100 \, \text{kg} \)
- Inclination angles: 
  - \( \theta_1 = 30^\circ \) (for \( m_1 \))
  - \( \theta_2 = 53^\circ \) (for \( m_2 \))

We'll assume that there's no friction unless stated otherwise. Let's solve the three parts:

---

### 1. **Direction of Motion**:

To determine the direction of motion, we compare the components of gravitational force along the planes for both masses.

For \( m_1 \) (moving down the incline of \( 30^\circ \)):
\[ F_{g1} = m_1 g \sin(30^\circ) = 50 \times 9.8 \times \sin(30^\circ) \]

For \( m_2 \) (moving down the incline of \( 53^\circ \)):
\[ F_{g2} = m_2 g \sin(53^\circ) = 100 \times 9.8 \times \sin(53^\circ) \]

Comparing \( F_{g1} \) and \( F_{g2} \), the larger force will dictate the direction of motion.

---

### 2. **Acceleration of the System**:

Using Newton's second law for the system, the net force is:
\[
F_{\text{net}} = F_{g2} - F_{g1}
\]
The total mass of the system is \( m_1 + m_2 \).

So, the acceleration is:
\[
a = \frac{F_{\text{net}}}{m_1 + m_2}
\]

---

### 3. **Tension in the Rope**:

Using the equation for one of the masses (e.g., \( m_1 \)):

\[
T = m_1 (g \sin(\theta_1) + a)
\]

We can also find the tension by solving for \( T \) using both masses in the system.

Let me calculate the numerical values for these parts.### Solution:

1. **Direction of Motion**:
   - \( F_{g1} = 245 \, \text{N} \)
   - \( F_{g2} = 782.66 \, \text{N} \)

Since \( F_{g2} > F_{g1} \), the system will move in the direction of \( m_2 \), meaning \( m_2 \) moves down the incline, and \( m_1 \) moves up the incline.

---

2. **Acceleration of the System**:
   - 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 \( 424.22 \, \text{N} \).

---

Do you have any questions or need further details? Here are 5 related questions you might consider:

1. How would the answers change if there were friction on the inclines?
2. What is the work done by the gravitational force on \( m_1 \) after moving a certain distance?
3. How would the system behave if \( m_1 = m_2 \)?
4. Can the system achieve a constant velocity, and under what conditions?
5. How does the angle of inclination affect the acceleration of the system?

**Tip**: Always check if external forces like friction are present when solving pulley problems, as they can significantly affect the results.

m1 = 50 kg dan m2 = 100 kg. Tentukan 1. arah gerak sistem? 2. percepatan sistem? 3. tegangan tali?

Solve a pulley system problem involving two masses on inclined planes (m1 = 50 kg, m2 = 100 kg) with angles 30° and 53°. Learn to calculate the direction of motion, system acceleration (3.58 m/s²), and tension in the rope (424.22 N).

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