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The problem in the image involves two masses, \( m_A = 4 \, \text{kg} \) and \( m_B = 6 \, \text{kg} \), connected by a rope. Mass \( m_B \) is being pulled by a force \( F = 40 \, \text{N} \) at an angle of \( 37^\circ \) to the horizontal. The kinetic friction coefficient \( \mu_k \) for both masses on the surface is given as \( 0.1 \).

We are asked to find:
a) The acceleration of both masses.
b) The tension in the rope between the two masses.

### Step 1: Resolve Forces
For \( m_B \), the force applied has a horizontal and vertical component. The horizontal component of the force is:
\[
F_x = F \cos \theta = 40 \times \cos 37^\circ
\]
And the vertical component is:
\[
F_y = F \sin \theta = 40 \times \sin 37^\circ
\]
We will need to adjust the normal force on \( m_B \) due to \( F_y \), which will affect the frictional force.

### Step 2: Calculate Frictional Forces
The frictional force on each mass is:
\[
f_A = \mu_k m_A g
\]
\[
f_B = \mu_k (m_B g - F_y)
\]
Where \( g = 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity.

### Step 3: Apply Newton's Second Law
For each mass, apply Newton’s second law \( F = ma \) to set up the equations of motion.

- For \( m_A \) (mass without applied force):
\[
T - f_A = m_A a
\]
- For \( m_B \) (mass with applied force):
\[
F_x - T - f_B = m_B a
\]

### Step 4: Solve the System of Equations
Solve these two equations simultaneously to find \( a \) (acceleration) and \( T \) (tension in the rope).

I will now calculate the values step by step.Here are the results based on the calculations:

1. The horizontal component of the applied force is \( F_x = 31.95 \, \text{N} \).
2. The vertical component of the applied force is \( F_y = 24.07 \, \text{N} \).
3. The frictional force on mass \( m_A \) is \( f_A = 3.92 \, \text{N} \).
4. The frictional force on mass \( m_B \) is \( f_B = 3.47 \, \text{N} \).
5. The acceleration of both masses is \( a = 2.46 \, \text{m/s}^2 \).
6. The tension in the rope between the two masses is \( T = 13.74 \, \text{N} \).

Would you like more details or have any questions?

Here are some related questions for deeper exploration:
1. How does changing the angle of the applied force affect the acceleration?
2. What happens if the coefficient of friction is increased?
3. How would the situation change if the surface was frictionless?
4. What if the force was applied vertically? How would the tension change?
5. How would increasing the mass of one block change the system?

**Tip:** Always resolve forces into components when dealing with forces applied at an angle.

Massa A = 4 kg, massa B = 6 kg dihubungkan dengan tali dan ditarik gaya F = 40 N ke kanan dengan sudut 37° terhadap arah horizontal. Jika koefisien gesekan kinetis kedua massa dengan lantai adalah 0,1, tentukan: a) Percepatan gerak kedua massa b) Tegangan tali penghubung antara kedua massa.

Solve a physics problem involving two masses connected by a rope. Mass A (4 kg) and Mass B (6 kg) are pulled by a 40 N force at a 37° angle. Learn how to find the acceleration of the system and the tension in the rope, applying Newton's laws of motion and considering friction with a coefficient of 0.1.

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