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This problem involves a mass \( m \) on an inclined plane with an angle \( \alpha \), attached to a string, with the entire setup moving horizontally with constant acceleration \( a \). The task is to determine the acceleration of the mass \( B \) along the inclined plane as the plane moves.

### Variables and assumptions:
- \( m \): Mass of object \( B \).
- \( \alpha \): Angle of the inclined plane.
- \( a \): Horizontal acceleration of the inclined plane to the right.
- The string is inextensible and massless, so no energy is lost to stretching.

### Steps to solve:

1. **Break down forces acting on the object \( B \):**
   - The force due to gravity acts vertically down with magnitude \( mg \).
   - The tension in the string keeps the object on the plane.
   - The incline moves horizontally with acceleration \( a \), which affects the motion of \( B \).

2. **Consider the horizontal motion:**
   - The horizontal motion of the system affects the forces on object \( B \). In the non-inertial reference frame of the moving inclined plane, there is an additional pseudo-force acting on \( B \) due to the acceleration \( a \). This pseudo-force has a magnitude of \( ma \) and acts opposite to the direction of the plane's motion.

3. **Resolve forces parallel and perpendicular to the incline:**
   - Resolve the gravitational force into components: \( mg \sin \alpha \) (parallel to the incline) and \( mg \cos \alpha \) (perpendicular to the incline).
   - The pseudo-force also needs to be resolved into components. The component along the incline due to the pseudo-force will be \( ma \sin \alpha \), and it adds to the gravitational force trying to pull the mass down the incline.

4. **Apply Newton's second law:**
   For the motion along the inclined plane:
   \[
   m a_{\text{B}} = m g \sin \alpha + m a \sin \alpha
   \]
   Where \( a_{\text{B}} \) is the acceleration of the object \( B \) along the incline.

5. **Final acceleration of object \( B \):**
   \[
   a_{\text{B}} = (g + a) \sin \alpha
   \]

Given that the desired form in the book shows the result \( 2a \sin \frac{\alpha}{2} \), this suggests that we need to consider how the horizontal motion combines with the vertical forces in this setup. 

Would you like to go deeper into any specific part of this problem or see detailed calculations?

### Related Questions:
1. How does the tension in the string affect the motion of object \( B \)?
2. What happens if the plane is stationary (i.e., \( a = 0 \))? 
3. How does changing the angle \( \alpha \) affect the acceleration of object \( B \)?
4. What role does the pseudo-force play in non-inertial reference frames?
5. Can we solve this problem using energy conservation instead of force analysis?

### Tip:
Always break forces into components when dealing with inclined planes and accelerated systems for a clearer understanding of the net motion.

Trên mặt phẳng nghiêng góc α có một dây không đàn hồi. Một đầu dây gắn vào tường ở A, đầu kia buộc vào một vật B có khối lượng m. Mặt phẳng nghiêng chuyển động sang phải với gia tốc a nằm ngang không đổi. Hãy xác định gia tốc của vật B khi nó còn ở trên mặt phẳng nghiêng.

This physics problem involves a mass on an inclined plane with an angle α, connected to a string and the whole setup moving with horizontal acceleration a. Learn how to calculate the acceleration of the mass B along the incline. Suitable for high school students.

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