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dua balok dengan massa m1=50 kg dan m2=100kg dihubungkan dengan tali tanpa gesekan dan diletakkan diatas bidang miring licin seperti pada gambar 3.31. tentulan 1. kearah mana sistem akan bergerak ketika balok-balok dilepaskan dari keadaan diam? 2. berapa percepatan balok? 3. berapakah tegangan-tegangan tali?

To solve this problem, let's analyze the forces acting on the two blocks, \( m_1 \) and \( m_2 \), which are connected by a frictionless pulley on an inclined plane.

### Given dataTo solve this problem, let's analyze the forces acting on the two blocks, \( m_1 \) and \( m_2 \), which are connected by a frictionless pulley on an inclined plane.

### Given 
- \( m_1 = 50 \, \text{kg} \)
- \( m_2 = 100 \, \text{kg} \)
- The angles of the inclines are:
  - For \( m_1 \), the angle of incline is \( 30^\circ \)
  - For \( m_2 \), the angle of incline is \( 53^\circ \)
- The pulley and the surface are frictionless.

### Step 1: Identify the direction of motion
Since \( m_2 > m_1 \), the system will move such that \( m_2 \) slides down its incline, and \( m_1 \) will slide up its incline.

### Step 2: Forces acting on the blocks
For each block, we have the gravitational force components along the incline, tension in the rope, and normal force (which is balanced by the weight component perpendicular to the incline). The equations of motion for both masses are as follows:

For block \( m_1 \) (on the \( 30^\circ \) incline):
\[
m_1 a = T - m_1 g \sin(30^\circ)
\]

For block \( m_2 \) (on the \( 53^\circ \) incline):
\[
m_2 a = m_2 g \sin(53^\circ) - T
\]

Where:
- \( a \) is the acceleration of the system (same for both masses since they are connected).
- \( T \) is the tension in the rope.
- \( g = 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity.

### Step 3: Solving the system of equations
We can now solve these equations simultaneously. Let's first express \( T \) from one equation and substitute it into the other.

From the equation for \( m_1 \):
\[
T = m_1 a + m_1 g \sin(30^\circ)
\]

Substitute this into the equation for \( m_2 \):
\[
m_2 a = m_2 g \sin(53^\circ) - (m_1 a + m_1 g \sin(30^\circ))
\]

Now, we can solve for \( a \):

\[
m_2 a + m_1 a = m_2 g \sin(53^\circ) - m_1 g \sin(30^\circ)
\]

\[
a (m_1 + m_2) = m_2 g \sin(53^\circ) - m_1 g \sin(30^\circ)
\]

\[
a = \frac{m_2 g \sin(53^\circ) - m_1 g \sin(30^\circ)}{m_1 + m_2}
\]

### Step 4: Calculate the acceleration and tension
Let me compute the values of \( a \) and \( T \) for you.### Solution:
1. **Direction of motion**: The system will move in the direction where \( m_2 \) slides down the incline, meaning \( m_1 \) moves up.
   
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 \( 424.22 \, \text{N} \).

Would you like more details or have any further questions? Here are some related questions to consider:

1. How would the acceleration change if \( m_1 \) and \( m_2 \) were switched?
2. What happens if friction is introduced to one of the inclined planes?
3. How would the system behave if the pulley had a non-negligible mass?
4. Could you calculate the normal forces acting on each block?
5. How does increasing the angle of the incline for \( m_1 \) affect the system?

**Tip**: Always double-check units and signs when solving dynamics problems involving inclines.

Dua balok dengan massa m1=50 kg dan m2=100kg dihubungkan dengan tali tanpa gesekan dan diletakkan diatas bidang miring licin seperti pada gambar 3.31. Tentukan 1. Kearah mana sistem akan bergerak ketika balok-balok dilepaskan dari keadaan diam? 2. Berapa percepatan balok? 3. Berapakah tegangan-tegangan tali?

In this problem, two blocks with masses 50 kg and 100 kg are connected by a frictionless pulley and placed on inclined planes at angles of 30° and 53°. Learn how to calculate the system's direction of motion, acceleration, and the tension in the rope using Newton's Laws. Suitable for high school physics students.

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