这题怎么解---**Question 11**
**Question Stem:**
如图所示, 轻质弹簧的两端分别与小物块 A, B 相连, 并放在倾角为θ的固定斜面上, A 靠在固定的挡板 P 上, 弹簧与斜面平行, A、B 均静止。将物块 C 在物块 B 上方与 B 相距 x 处由静止释放, C 和 B 碰撞的时间极短, 碰撞后粘在一起不再分离, 已知 A, B, C 的质量均为 m, 弹簧劲度系数为 k, 且始终在弹性限度内, 不计一切摩擦, 则为保证 A 不离开挡板, x 的最大值为 (
**Translation of Question Stem (for context, not part of the required output):**
As shown in the figure, a light spring is connected to small blocks A and B at both ends respectively, and placed on a fixed inclined plane with an angle of inclination θ. A is leaning against the fixed plate P, the spring is parallel to the inclined plane, and both A and B are initially at rest. Block C is released from rest at a distance x above block B on the inclined plane. The collision between C and B is extremely short, and after the collision, they stick together and do not separate. It is known that the masses of A, B, and C are all m, the spring constant is k, and the spring is always within the elastic limit. Ignoring all friction, what is the maximum value of x to ensure that A does not leave the plate P?
**Options:**
(A) $\frac{4mg \sin \theta}{k}$
(B) $\frac{8mg \sin \theta}{k}$
(C) $\frac{4mg}{k}$
(D) $\frac{8mg}{k}$
**Chart/Diagram Description:**
* Type: Physics schematic diagram showing objects on an inclined plane.
* Main Elements:
* Inclined Plane: A slanted surface forming an angle $\theta$ with an implied horizontal.
* Fixed Plate P: A vertical barrier located at the top of the inclined plane.
* Block A: A rectangular block labeled 'A', placed on the inclined plane and leaning against the fixed plate P.
* Spring: A helical spring connecting Block A and Block B, oriented parallel to the inclined plane.
* Block B: A rectangular block labeled 'B', placed on the inclined plane below Block A and connected to Block A by the spring.
* Block C: A rectangular block labeled 'C', shown on the inclined plane above Block B, with an arrow pointing downwards along the incline, indicating its initial motion towards B.
* Angle $\theta$: The angle of inclination of the plane is labeled $\theta$.
* Distance x: The initial distance between the bottom of Block C and the top of Block B along the inclined plane is labeled as x.
* Context: The diagram depicts an initial state where A and B are connected by a spring on an incline, with A against a stop. Block C is about to move down the incline to collide with B.